@Preamble{"\input bibnames.sty"
# "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} "
# "\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi"
# "\ifx \undefined \cyr \let \cyr = \relax \fi"
# "\ifx \undefined \cdprime \def \cdprime {''} \fi"
# "\ifx \undefined \k \let \k = \c \fi"
# "\ifx \undefined \erfc \def \erfc #1{{\rm #1}} \fi"
# "\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}} \fi"
# "\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}} \fi"
# "\ifx \undefined \pkg \def \pkg #1{{{\tt #1}}} \fi"
# "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi"
# "\hyphenation{ Rich-ard }"
}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
@String{ack-mv = "Matti Vuorinen,
Department of Mathematics and Statistics,
University of Turku,
Vesilinnantie 5,
20014 Turku, Finland,
e-mail: \path|vuorinen@utu.fi|,
URL: \path|http://users.utu.fi/vuorinen/|"}
@String{ack-nj = "Norbert Juffa,
2445 Mission College Blvd.,
Santa Clara, CA 95054,
USA,
e-mail: \path|norbert@@iit.com|"}
@String{ack-rfb = "Ronald F. Boisvert,
Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA,
Tel: +1 301 975 3812,
e-mail: \path=boisvert@cam.nist.gov="}
@String{inst-ANL = "Argonne National Laboratory"}
@String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL
60439-4801, USA"}
@String{inst-ATT-BELL = "AT\&T Bell Laboratories"}
@String{inst-ATT-BELL:adr = "Murray Hill, NJ, USA"}
@String{inst-BERKELEY-CS = "Department of Computer Science, University
of California"}
@String{inst-BERKELEY-CS:adr = "Berkeley, CA, USA"}
@String{inst-CECM = "Centre for Experimental and Constructive
Mathematics (CECM) at Simon Fraser
University (SFU)"}
@String{inst-CECM:adr = "Burnaby, BC V5A 1S6, Canada"}
@String{inst-CPAM-UCB = "Center for Pure and Applied Mathematics,
University of California, Berkeley"}
@String{inst-CPAM-UCB:adr = "Berkeley, CA, USA"}
@String{inst-CSC = "Center for Scientific Computing,
Department of Mathematics, University of
Utah"}
@String{inst-CSC:adr = "Salt Lake City, UT 84112, USA"}
@String{inst-INST-ADV-STUDY = "Institute for Advanced Study"}
@String{inst-INST-ADV-STUDY:adr = "Princeton, NJ, USA"}
@String{inst-IPTC = "{Institut f{\"u}r Physikalische und
Theoretische Chemie}"}
@String{inst-IPTC:adr = "{Universit{\"a}t Regensburg, D-93040
Regensburg}"}
@String{inst-LASL = "Los Alamos Scientific Laboratory"}
@String{inst-LASL:adr = "Los Alamos, NM, USA"}
@String{inst-LORIA-INRIA-LORRAINE = "LORIA/INRIA Lorraine"}
@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
Nancy-Brabois, 615 rue du jardin
botanique, F-54602
Villers-l{\`e}s-Nancy Cedex, France"}
@String{inst-MATH-NPS = "Department of Mathematics, Naval Postgraduate
School"}
@String{inst-MATH-NPS:adr = "Monterey CA 93943, USA"}
@String{inst-PRINCETON = "Princeton University"}
@String{inst-PRINCETON:adr = "Princeton, NJ, USA"}
@String{inst-STAN-CS = "Stanford University, Department of
Computer Science"}
@String{inst-STAN-CS:adr = "Stanford, CA, USA"}
@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}
@String{j-ACTA-INFO = "Acta Informatica"}
@String{j-ACTA-MATH = "Acta Mathematica"}
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-ADV-APPL-MATH = "Advances in Applied Mathematics"}
@String{j-ADV-COMPUT-MATH = "Advances in Computational Mathematics"}
@String{j-ADV-QUANTUM-CHEM = "Advances in Quantum Chemistry"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANAL-APPL = "Analysis and Applications (Singapore)"}
@String{j-ANN-APPL-STAT = "Annals of Applied Statistics"}
@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of
Statistical Mathematics"}
@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
Intelligence"}
@String{j-ANN-STAT = "Annals of Statistics"}
@String{j-ANZIAM-J = "The ANZIAM Journal"}
@String{j-APPL-COMPUT-HARMON-ANAL = "Applied and Computational Harmonic
Analysis. Time-Frequency and
Time-Scale Analysis, Wavelets,
Numerical Algorithms, and
Applications"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPL-MATH-SCI-RUSE = "Applied Mathematical Sciences (Ruse)"}
@String{j-APPL-NUM-MATH = "Applied Numerical Mathematics: Transactions
of IMACS"}
@String{j-APPL-OPTICS = "Applied Optics"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"}
@String{j-ARCH-RAT-MECH-ANAL = "Archive for Rational Mechanics and Analysis"}
@String{j-ASTROPHYS-SPACE-SCI = "Astrophysics and Space Science"}
@String{j-ATMOS-SCI-LETT = "Atmospheric Science Letters"}
@String{j-AUST-J-STAT = "Australian Journal of Statistics"}
@String{j-AUSTRALIAN-J-PHYS = "Australian Journal of Physics"}
@String{j-AUTOMATICA = "Automatica: the journal of IFAC, the
International Federation of Automatic
Control"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-BIOMETRIKA = "Biometrika"}
@String{j-BIT = "BIT (Nordisk tidskrift for
informationsbehandling)"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BRITISH-J-HIST-MATH = "British Journal for the History of
Mathematics"}
@String{j-BRITISH-J-PHILOS-SCI = "British Journal for the Philosophy of
Science"}
@String{j-BULL-AMS = "Bulletin of the American Mathematical
Society"}
@String{j-C-R-ACAD-BULGARE-SCI = "Comptes rendus de l'Acad{\'e}mie bulgare
des sciences"}
@String{j-CACM = "Communications of the ACM"}
@String{j-CALCOLO = "Calcolo"}
@String{j-CAN-J-MATH = "Canadian Journal of Mathematics =
Journal canadien de
math{\'e}matiques"}
@String{j-CAN-MATH-BULL = "Bulletin canadien de
math\-{\'e}\-mat\-iques = Canadian
Mathematical Bulletin"}
@String{j-CCCUJ = "C/C++ Users Journal"}
@String{j-CELEST-MECH-DYN-ASTR = "Celestial Mechanics and Dynamical Astronomy"}
@String{j-CENTAURUS = "Centaurus: An International Journal of the
History of Science and its Cultural Aspects"}
@String{j-COLLEGE-MATH-J = "College Mathematics Journal"}
@String{j-COMM-PURE-APPL-MATH = "Communications on Pure and Applied
Mathematics (New York)"}
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
and Computation"}
@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
Methods"}
@String{j-COMP-ARCH-NEWS = "ACM SIGARCH Computer Architecture News"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-COMPUT-MATH-APPL = "Computers and Mathematics with Applications"}
@String{j-COMPUT-MATH-MATH-PHYS = "Computational Mathematics and Mathematical
Physics"}
@String{j-COMPUT-PHYS = "Computers in Physics"}
@String{j-COMPUT-PHYS-REP = "Computer Physics Reports"}
@String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"}
@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}
@String{j-COMPUTER = "Computer"}
@String{j-COMPUTING = "Computing: Archiv fur informatik und
numerik"}
@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}
@String{j-CONST-APPROX = "Constructive Approximation"}
@String{j-CYBER = "Cybernetics"}
@String{j-DDJ = "Dr. Dobb's Journal of Software Tools"}
@String{j-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"}
@String{j-DOKL-AKAD-NAUK = "Doklady Akademii nauk SSSR"}
@String{j-EDN = "EDN"}
@String{j-ELECT-LETTERS = "Electronics Letters"}
@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
Computer Science"}
@String{j-ELECTRON-COMMUN-JPN = "Electronics and communications in Japan"}
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
Analysis (ETNA)"}
@String{j-ELECTRONIC-DESIGN = "Electronic Design"}
@String{j-ELECTRONICS = "Electronics"}
@String{j-ELECTRONIK = "Elektronik"}
@String{j-ELEKTRONIKER = "Elektroniker (Switzerland)"}
@String{j-ELEK-RECHENANLAGEN = "Elektronische Rechenanlagen"}
@String{j-EMBED-SYS-PROG = "Embedded Systems Programming"}
@String{j-ENTROPY = "Entropy"}
@String{j-EXP-MATH = "Experimental mathematics"}
@String{j-FIB-QUART = "Fibonacci Quarterly"}
@String{j-FORM-METHODS-SYST-DES = "Formal Methods in System Design"}
@String{j-HEWLETT-PACKARD-J = "Hew\-lett-Pack\-ard Journal: technical
information from the laboratories of
Hew\-lett-Pack\-ard Company"}
@String{j-HIST-MATH = "Historia Mathematica"}
@String{j-HIST-SCI-2 = "Historia Scientiarum. Second Series.
International Journal of the History
of Science Society of Japan"}
@String{j-IBM-JRD = "IBM Journal of Research and Development"}
@String{j-IBM-SYS-J = "IBM Systems Journal"}
@String{j-IBM-TDB = "IBM Technical Disclosure Bulletin"}
@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital Techniques"}
@String{j-IEEE-CGA = "IEEE Computer Graphics and Applications"}
@String{j-IEEE-COMMUN-LET = "IEEE Communications Letters"}
@String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"}
@String{j-IEEE-MICRO = "IEEE Micro"}
@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"}
@String{j-IEEE-SPECTRUM = "IEEE Spectrum"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE Transactions on Circuits and
Systems. 2, Analog and Digital Signal
Processing"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS = "IEEE Transactions on
Circuits and Systems II: Express Briefs"}
@String{j-IEEE-TRANS-COMM = "IEEE Transactions on Communications"}
@String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"}
@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}
@String{j-IEEE-TRANS-EMERG-TOP-COMPUT = "IEEE Transactions on Emerging Topics in
Computing"}
@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}
@String{j-IEEE-TRANS-MICROWAVE-THEORY-TECH = "IEEE Transactions on Microwave
Theory and Techniques"}
@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
Distributed Systems"}
@String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"}
@String{j-IEEE-TRANS-VLSI-SYST = "IEEE Transactions on Very Large Scale
Integration (VLSI) Systems"}
@String{j-IEEE-TRANS-VEH-TECHNOL = "IEEE Transactions on Vehicular Technology"}
@String{j-IEEE-TRANS-WIREL-COMMUN = "IEEE Transactions on Wireless
Communications"}
@String{j-IJQC = "International Journal of Quantum Chemistry"}
@String{j-IJSAHPC = "The International Journal of Supercomputer
Applications and High Performance Computing"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-INFO-PROC-LETT = "Information Processing Letters"}
@String{j-INT-J-COMPUT-INF-SCI = "International Journal of Computer and
Information Sciences"}
@String{j-INT-J-COMPUT-MATH = "International Journal of Computer
Mathematics"}
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
Computing"}
@String{j-INT-J-MATH-EDU-SCI-TECH = "International journal of mathematical
education in science and technology"}
@String{j-INT-J-MATH-MATH-SCI = "International Journal of Mathematics and
Mathematical Sciences"}
@String{j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER = "International Journal on
Software Tools for Technology Transfer (STTT)"}
@String{j-INTEGRATION-VLSI-J = "Integration, the VLSI journal"}
@String{j-INTEL-TECH-J = "Intel Technology Journal"}
@String{j-INTERNET-J-CHEM = "Internet Journal of Chemistry"}
@String{j-INTERVAL-COMP = "Interval Computations = Interval'nye
vychisleniia"}
@String{j-IRE-TRANS-ELEC-COMPUT = "IRE Transactions on Electronic Computers"}
@String{j-ISIS = "Isis"}
@String{j-J-ACM = "Journal of the Association for Computing
Machinery"}
@String{j-J-ACOUST-SOC-AM = "Journal of the Acoustical Society of America"}
@String{j-J-ALG = "Journal of Algorithms"}
@String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical
Association"}
@String{j-J-APPL-STAT = "Journal of Applied Statistics"}
@String{j-J-APPROX-THEORY = "Journal of Approximation Theory"}
@String{j-J-AUSTRAL-MATH-SOC-SER-B = "Journal of the Australian Mathematical
Society: Series B, Applied Mathematics"}
@String{j-J-AUTOM-REASON = "Journal of Automated Reasoning"}
@String{j-J-COMB-THEORY-A = "Journal of Combinatorial Theory (Series A)"}
@String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-J-COMPUT-CHEM = "Journal of Computational Chemistry"}
@String{j-J-COMPUT-GRAPH-STAT = "Journal of Computational and Graphical
Statistics"}
@String{j-J-COMPLEXITY = "Journal of complexity"}
@String{j-J-COMPUT-PHYS = "Journal of Computational Physics"}
@String{j-J-FRANKLIN-INST = "Journal of {The Franklin Institute}"}
@String{j-J-GRAPHICS-GPU-GAME-TOOLS = "Journal of Graphics, GPU, and Game Tools"}
@String{j-J-GRID-COMP = "Journal of Grid Computing"}
@String{j-J-HIGH-ENERGY-PHYS = "Journal of High Energy Physics"}
@String{j-J-INST-MATH-APPL = "Journal of the Institute of Mathematics and
its Applications"}
@String{j-J-KOREA-INFO-SCI-SOCIETY = "Journal of the Korea Information Science
Society = Chongbo Kwahakhoe nonmunji"}
@String{j-J-MATH-ANAL-APPL = "Journal of Mathematical Analysis and
Applications"}
@String{j-J-MATH-CHEM = "Journal of Mathematical Chemistry"}
@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-MATH-PHYS-MIT = "Journal of Mathematics and Physics (MIT)"}
@String{j-J-MOL-STRUCT-THEOCHEM = "Journal of Molecular Structure. Theochem"}
@String{j-J-MULTIVAR-ANAL = "Journal of Multivariate Analysis"}
@String{j-J-NUMBER-THEORY = "Journal of Number Theory"}
@String{j-J-NUMER-METHODS-COMPUT-APPL = "Journal on Numerical Methods and
Computer Applications"}
@String{j-J-OPT-THEORY-APPL = "Journal of Optimization Theory and
Applications"}
@String{j-J-PAR-DIST-COMP = "Journal of Parallel and Distributed
Computing"}
@String{j-J-PHYS-A = "Journal of Physics A (Mathematical and General)"}
@String{j-J-R-STAT-SOC-SER-B-METHODOL = "Journal of the Royal Statistical
Society. Series B (Methodological)"}
@String{j-J-R-STAT-SOC-SER-D-STATISTICIAN = "Journal of the Royal Statistical
Society. Series D (The Statistician)"}
@String{j-J-RES-NATL-BUR-STAND-1934 = "Journal of Research of the National
Bureau of Standards (1934)"}
@String{j-J-RES-NATL-BUR-STAND-B = "Journal of Research of the National Bureau
of Standards. Section B, Mathematics
and Mathematical Physics"}
@String{j-J-SCI-COMPUT = "Journal of Scientific Computing"}
@String{j-J-SOV-MATH = "Journal of Soviet Mathematics"}
@String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and
Simulation"}
@String{j-J-STAT-SOFT = "Journal of Statistical Software"}
@String{j-J-SUPERCOMPUTING = "The Journal of Supercomputing"}
@String{j-J-SYMBOLIC-COMP = "Journal of Symbolic Computation"}
@String{j-J-SYMBOLIC-LOGIC = "Journal of Symbolic Logic"}
@String{j-J-UCS = "J.UCS: The Journal of Universal Computer Science"}
@String{j-J-VLSI-SIGNAL-PROC = "Journal of VLSI Signal Processing"}
@String{j-JETC = "ACM Journal on Emerging Technologies
in Computing Systems (JETC)"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-LECT-NOTES-MATH = "Lecture Notes in Mathematics"}
@String{j-LIN-AND-MULT-ALGEBRA = "Linear and Multilinear Algebra"}
@String{j-LMS-J-COMPUT-MATH = "LMS Journal of Computation and Mathematics"}
@String{j-LOGIN = ";login: the USENIX Association newsletter"}
@String{j-MATH-COMP-SIM = "Mathematics and Computers in Simulation"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-COMPUT-APPL = "Mathematical and Computational Applications"}
@String{j-MATH-COMPUT-SCI = "Mathematics in Computer Science"}
@String{j-MATH-GAZ = "The Mathematical Gazette"}
@String{j-MATH-MAG = "Mathematics Magazine"}
@String{j-MATH-MODEL-NUM-ANA = "Mathematical modelling and numerical
analysis = Modelisation math{\'e}matique et
analyse num{\'e}rique: $M^2AN$"}
@String{j-MATH-OP-RES = "Mathematics of Operations Research"}
@String{j-MATH-PROG = "Mathematical Programming"}
@String{j-MATH-SCI = "The Mathematical Scientist"}
@String{j-MATH-STUDENT = "The Mathematics Student"}
@String{j-MATH-TABLES-AIDS-COMPUT = "Mathematical Tables and Aids to
Computation"}
@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
to Computation"}
@String{j-MATH-Z = "{Mathematische Zeitschrift}"}
@String{j-MATHEMATICA-J = "Mathematica Journal"}
@String{j-METHODS-APPL-ANAL = "Methods and Applications of Analysis"}
@String{j-MICROPROC-MICROPROG = "Microprocessing and Microprogramming"}
@String{j-MICROPROC-MICROSYS = "Microprocessors and Microsystems"}
@String{j-MONAT-MATH = "Monatshefte f{\"u}r Mathematik"}
@String{j-NACH-ELEK = "Nachrichtentechnik Elektronik"}
@String{j-NAMS = "Notices of the American Mathematical
Society"}
@String{j-NEURAL-COMP = "Neural Computation"}
@String{j-NEURAL-NETWORKS = "Neural Networks"}
@String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for
informationsbehandling"}
@String{j-NOTRE-DAME-J-FORM-LOG = "Notre Dame Journal of Formal Logic"}
@String{j-NUCL-INSTR-METH = "Nuclear Instruments and Methods"}
@String{j-NUCL-PHYS-B-PROC-SUPPL = "Nuclear Physics B, Proceedings Supplements"}
@String{j-NUM-MATH = "Numerische Mathematik"}
@String{j-NUMER-ALGORITHMS = "Numerical Algorithms"}
@String{j-OPER-RES = "Operations Research"}
@String{j-PAC-J-MATH = "Pacific Journal of Mathematics"}
@String{j-PACMPL = "Proceedings of the ACM on Programming
Languages (PACMPL)"}
@String{j-PARALLEL-COMPUTING = "Parallel Computing"}
@String{j-PHILOS-MAG = "Philosophical Magazine"}
@String{j-PHILOS-TRANS-R-SOC-LOND = "Philosophical Transactions of the Royal
Society of London"}
@String{j-PHYS-REV-A = "Physical Review A"}
@String{j-PHYS-REV-A-3 = "Physical Review A (3)"}
@String{j-PHYS-REV-E = "Physical Review E (Statistical physics,
plasmas, fluids, and related
interdisciplinary topics)"}
@String{j-PHYS-TODAY = "Physics Today"}
@String{j-PHYSICA-D = "Physica D"}
@String{j-PROBAB-ENGRG-INFORM-SCI = "Probability in the Engineering and
Informational Sciences"}
@String{j-PROC-AM-MATH-SOC = "Proceedings of the American Mathematical
Society"}
@String{j-PROC-CAMBRIDGE-PHIL-SOC = "Proceedings of the Cambridge Philosophical
Society. Mathematical and physical sciences"}
@String{j-PROC-IEEE = "Proceedings of the IEEE"}
@String{j-PROC-LONDON-MATH-SOC-1 = "Proceedings of the London Mathematical
Society. First Series"}
@String{j-PROC-LONDON-MATH-SOC-2 = "Proceedings of the London Mathematical
Society. Second Series"}
@String{j-PROC-LONDON-MATH-SOC-3 = "Proceedings of the London Mathematical
Society. Third Series"}
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS = "Proceedings of the Royal Society of
London. Series A, Containing Papers of a
Mathematical and Physical Character"}
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI = "Proceedings of the Royal
Society of London. Series A, Mathematical
and physical sciences"}
@String{j-PROG-COMP-SOFT = "Programming and Computer Software;
translation of Programmirovaniye (Moscow,
USSR) Plenum"}
@String{j-PROGRAMMIROVANIE = "Programmirovanie"}
@String{j-QUART-APPL-MATH = "Quarterly of Applied Mathematics"}
@String{j-REND-CIRC-MAT = "Rendiconti del Circolo matematico di
Palermo"}
@String{j-REV-MOD-PHYS = "Reviews of Modern Physics"}
@String{j-RUSS-J-MATH-PHYS = "Russian Journal of Mathematical Physics"}
@String{j-SCI-COMPUT-PROGRAM = "Science of Computer Programming"}
@String{j-SCRIPTA-MATH = "Scripta Mathematica"}
@String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"}
@String{j-SIAM-J-COMPUT = "SIAM Journal on Computing"}
@String{j-SIAM-J-CONTROL-OPTIM = "SIAM Journal on Control and Optimization"}
@String{j-SIAM-J-MAT-ANA-APPL = "SIAM Journal on Matrix Analysis and
Applications"}
@String{j-SIAM-J-MATH-ANA = "SIAM journal on mathematical analysis"}
@String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and
Applied Mathematics: Series B, Numerical
Analysis"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"}
@String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and Statistical
Computing"}
@String{j-SIAM-NEWS = "SIAM News"}
@String{j-SIAM-REVIEW = "SIAM Review"}
@String{j-SIGADA-LETTERS = "ACM SIGADA Ada Letters"}
@String{j-SIGCSE = "SIGCSE Bulletin (ACM Special Interest Group
on Computer Science Education)"}
@String{j-SIGNUM = "ACM SIGNUM Newsletter"}
@String{j-SIGPLAN = "ACM SIGPLAN Notices"}
@String{j-SIGSAM = "SIGSAM Bulletin (ACM Special Interest Group
on Symbolic and Algebraic Manipulation)"}
@String{j-SOFTWAREX = "SoftwareX"}
@String{j-SPE = "Soft\-ware\emdash Prac\-tice and Experience"}
@String{j-STAT-PROB-LETT = "Statistics \& Probability Letters"}
@String{j-TECHNIQUE-SCI-INFORMATIQUES = "Technique et Science Informatiques"}
@String{j-TECHNOMETRICS = "Technometrics"}
@String{j-TECS = "ACM Transactions on Embedded Computing
Systems"}
@String{j-TELO = "ACM Transactions on Evolutionary
Learning and Optimization (TELO)"}
@String{j-THEOR-COMP-SCI = "Theoretical Computer Science"}
@String{j-TOKYO-J-MATH = "Tokyo journal of mathematics"}
@String{j-TOMS = "ACM Transactions on Mathematical Software"}
@String{j-TRANS-AM-MATH-SOC = "Transactions of the American Mathematical
Society"}
@String{j-TRANS-INFO-PROCESSING-SOC-JAPAN = "Transactions of the Information
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Singapore 9128"}
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@Article{Horner:1819:XNM,
author = "William George Horner",
title = "{XXI}. {A} new method of solving numerical equations
of all orders, by continuous approximation",
journal = j-PHILOS-TRANS-R-SOC-LOND,
volume = "109",
pages = "308--335",
year = "1819",
CODEN = "PTRSAV",
DOI = "https://doi.org/10.1098/rstl.1819.0023",
ISSN = "0370-2316 (print), 2053-9207 (electronic)",
bibdate = "Sat Oct 21 12:27:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1819.0023",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Transactions of the Royal Society of
London",
journal-URL = "http://rsta.royalsocietypublishing.org/",
keywords = "Horner's nested form; number of multiplications to
evaluate a polynomial",
read = "1 July 1819",
remark-1 = "Communicated by Davies Gilbert, Esq. F.R.S.",
remark-2 = "On page 310 of this paper, Horner gives the steps of
the nested form as a chain of fused multiply-add
operations, and credits this idea to Joseph-Louis
Lagrange (1736--1813) in his 1813 book
\booktitle{Th{\'e}orie des fonctions analytiques}.",
remark-3 = "Knuth \cite[p. 486]{Knuth:1998:SA} gives this paper as
the reference for Horner's nested form, but also
reports that Isaac Newton used it in unpublished notes
150 years earlier, and that it was employed by the
Chinese in the 13th century CE.",
}
@Article{Lovelace:1843:SAE,
author = "Ada Augusta Lovelace",
title = "Sketch of the {Analytical Engine}",
journal = "Scientific Memoirs",
volume = "3",
number = "??",
pages = "666--731",
month = "????",
year = "1843",
bibdate = "Sun Aug 18 09:31:28 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Reprinted in \cite{Lovelace:1989:SAE}.",
acknowledgement = ack-nhfb,
keywords = "Bernoulli numbers",
remark = "This paper contains what some view as possibly the
world's first computer program, a recipe for computing
Bernoulli numbers on Charles Babbage's Analytical
Engine, which was not successfully constructed until
more than a century after their deaths, in 1852 and
1871, respectively. It is not, however, the world's
first computational algorithm: that credit is given to
Euclid's procedure for fast computation of the greatest
common denominator, about 300 BCE, but possibly known a
few hundred years earlier.",
}
@Book{Greenhill:1892:AEF,
author = "Alfred George Greenhill",
title = "The Applications of Elliptic Functions",
publisher = pub-MACMILLAN,
address = pub-MACMILLAN:adr,
pages = "xi + 357",
year = "1892",
bibdate = "Wed Mar 15 08:21:33 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "1847--1927",
remark = "Reprinted in \cite{Greenhill:1959:AEF}.",
}
@Article{Dawson:1897:NV,
author = "H. G. Dawson",
title = "On the Numerical Value of $ \int_0^h e^{x^2} \, d x
$",
journal = j-PROC-LONDON-MATH-SOC-1,
volume = "s1-29",
number = "1",
pages = "519--522",
month = nov,
year = "1897",
CODEN = "PLMTAL",
DOI = "https://doi.org/10.1112/plms/s1-29.1.519",
ISSN = "0024-6115 (print), 1460-244X (electronic)",
ISSN-L = "0024-6115",
bibdate = "Sat Jun 12:08:16 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
fjournal = "Proceedings of the London Mathematical Society. First
Series",
journal-URL = "http://plms.oxfordjournals.org/content/by/year",
remark = "This paper is the origin of Dawson's integral and the
function dawson(x).",
}
@Book{Kennelly:1914:TCH,
author = "Arthur E. (Arthur Edwin) Kennelly",
title = "Tables of Complex Hyperbolic and Circular Functions",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "iii + 212",
year = "1914",
LCCN = "QA342 .K45",
bibdate = "Sat Apr 1 14:49:41 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1861--1939",
subject = "Exponential functions",
}
@Book{Pairman:1919:TDT,
author = "Eleanor Pairman",
title = "Tables of the Digamma and Trigamma Functions",
volume = "I",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "9 + 11",
year = "1919",
LCCN = "QA47 .T7 no.1",
bibdate = "Sat Mar 25 16:17:54 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
series = "Tracts for computers",
acknowledgement = ack-nhfb,
remark = "Edited by Karl Pearson. According to
\cite{Davis:1935:EPF}, the author coined the phrase
`polygamma function' in this booklet. English
dictionaries usually do not include the word
`polygamma'.",
subject = "Gamma functions",
}
@Book{Kennelly:1921:TCH,
author = "Arthur Edwin Kennelly",
title = "Tables of Complex Hyperbolic and Circular Functions",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "iii + 240",
year = "1921",
LCCN = "QA342 .K45 1921",
bibdate = "Sat Apr 1 14:49:41 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1861--",
subject = "Functions, Exponential",
}
@Article{King:1921:SNF,
author = "Louis Vessot King",
title = "On Some New Formulae for the Numerical Calculation of
the Mutual Induction of Coaxial Circles",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS,
volume = "100",
number = "702",
pages = "60--66",
day = "4",
month = oct,
year = "1921",
DOI = "https://doi.org/10.1098/rspa.1921.0070",
ISSN = "0950-1207 (print), 2053-9150 (electronic)",
bibdate = "Wed Feb 03 09:07:10 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
note = "This is the first known publication of the AGM method,
discovered by the author in 1913, for computing
Jacobian elliptic functions. See also
\cite{King:1924:DNC,King:2007:DNC}.",
URL = "http://www.jstor.org/stable/93861",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series A,
Containing Papers of a Mathematical and Physical
Character",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@Book{King:1924:DNC,
author = "Louis Vessot King",
title = "On the Direct Numerical Calculation of Elliptic
Functions and Integrals",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "viii + 42",
year = "1924",
LCCN = "QA343",
bibdate = "Wed Feb 03 08:53:04 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
remark = "The AGM method for Jacobian elliptic functions was
discovered by this book's author at McGill University
in 1913, first published in \cite{King:1921:SNF}, and
then in this monograph (reprinted in
\cite{King:2007:DNC}).",
}
@Article{Ritt:1925:EFT,
author = "J. F. Ritt",
title = "Elementary functions and their inverses",
journal = j-TRANS-AM-MATH-SOC,
volume = "27",
number = "1",
pages = "68--90",
year = "1925",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-1925-1501299-9",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "30A05 (33B10)",
MRnumber = "MR1501299",
bibdate = "Wed Apr 13 06:46:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/journals/tran/1925-027-01/S0002-9947-1925-1501299-9/",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
}
@Article{Dederick:1926:QDDc,
author = "L. S. Dederick",
title = "Questions and Discussions: Discussions: a Modified
Method for Cube Roots and Fifth Roots",
journal = j-AMER-MATH-MONTHLY,
volume = "33",
number = "9",
pages = "469--472",
month = nov,
year = "1926",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:12 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2299613",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Mahler:1930:NUG,
author = "K. Mahler",
title = "{{\"U}ber die Nullstellen der unvollstaendigen
Gammafunktionen}. ({German}) [{On} the zeros of the
incomplete gamma-functions]",
journal = j-REND-CIRC-MAT,
volume = "54",
number = "??",
pages = "1--41",
month = "????",
year = "1930",
CODEN = "RCMMAR",
ISSN = "0009-725X (print), 1973-4409 (electronic)",
ISSN-L = "0009-725X",
bibdate = "Sat Feb 18 14:57:12 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://carma.newcastle.edu.au/mahler/collected.html;
https://carma.newcastle.edu.au/mahler/docs/002.pdf",
acknowledgement = ack-nhfb,
fjournal = "Rendiconti del Circolo matematico di Palermo",
language = "German",
remark = "Based on doctoral dissertation, Frankfurt, Germany
(1927).",
}
@Book{Hobson:1931:TSE,
author = "Ernest William Hobson",
title = "The Theory of Spherical and Ellipsoidal Harmonics",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xi + 500",
year = "1931",
LCCN = "QA406 .H7",
bibdate = "Sat Apr 1 14:40:56 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1856--1933",
subject = "Spherical harmonics; Lam\'e's functions",
}
@Article{Kalbfell:1934:QDN,
author = "D. C. Kalbfell",
title = "Questions, Discussions and Notes: On a Method for
Calculating Square Roots",
journal = j-AMER-MATH-MONTHLY,
volume = "41",
number = "8",
pages = "504--506",
month = oct,
year = "1934",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:31 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2300417",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{McLachlan:1934:BFE,
author = "N. W. (Norman William) McLachlan",
title = "{Bessel} Functions for Engineers",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xi + 1 + 192",
year = "1934",
LCCN = "QA408 .M3",
bibdate = "Sat Apr 1 14:44:36 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "The Oxford engineering science series",
acknowledgement = ack-nhfb,
author-dates = "1888--",
subject = "Bessel functions",
}
@Article{Davis:1935:EPF,
author = "H. T. Davis",
title = "An extension to polygamma functions of a theorem of
{Gauss}",
journal = j-BULL-AMS,
volume = "41",
number = "4",
pages = "243--248",
month = apr,
year = "1935",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/s0002-9904-1935-06055-0",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Sat Mar 25 16:16:08 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
remark = "A footnote on the first page says ``The name polygamma
is suggested by the paper, \booktitle{Tables of the
Digamma and Trigamma Functions}, by Eleanor Pairman,
Tracts for Computers, No. 1, 1919''
\cite{Pairman:1919:TDT}.",
}
@Article{Airey:1937:CFA,
author = "J. R. Airey",
title = "The ``converging factor'' in asymptotic series and the
calculation of {Bessel}, {Laguerre} and other
functions",
journal = j-PHILOS-MAG,
volume = "24",
number = "162",
pages = "521--552",
month = "????",
year = "1937",
CODEN = "PHMAA4",
DOI = "https://doi.org/10.1080/14786443708565133",
ISSN = "0031-8086",
ISSN-L = "0031-8086",
bibdate = "Thu Dec 01 14:26:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Magazine",
journal-URL = "http://www.tandfonline.com/loi/tphm19",
}
@Article{Escott:1937:QDN,
author = "E. B. Escott",
title = "Questions, Discussions, and Notes: Rapid Method for
Extracting a Square Root",
journal = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2301484",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Ostrowski:1937:KAN,
author = "A. M. Ostrowski",
title = "{{\"U}ber die Konvergenz und die
Abr{\"u}ndungsfestigkeit des Newtonschen Verfahren}.
({German}) [{On} the convergence and rounding strength
of {Newton}'s method]",
journal = "Rec. Math.",
volume = "2",
number = "??",
pages = "1073--1098",
month = "????",
year = "1937",
bibdate = "Mon Oct 23 14:58:35 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Ostrowski:1938:NMA,
author = "A. M. Ostrowski",
title = "On {Newton}'s method of approximation",
journal = "British Association for the Advancement of Science",
volume = "??",
number = "??",
pages = "392--??",
month = "????",
year = "1938",
bibdate = "Mon Oct 23 14:57:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Emde:1940:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "B. T. Teubner",
address = "Leipzig, Germany and Berlin, Germany",
pages = "xii + 181",
year = "1940",
LCCN = "QA47 .E5",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://lccn.loc.gov/45006177",
acknowledgement = ack-nhfb,
author-dates = "1873--1951",
language = "German",
}
@Article{Stoner:1941:FEF,
author = "Paul Matthew Stoner",
title = "Fitting the Exponential Function and the {Gompertz}
Function by the Method of Least Squares",
journal = j-J-AM-STAT-ASSOC,
volume = "36",
number = "216",
pages = "515--518",
month = dec,
year = "1941",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314095;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2278959",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Book{Stratton:1941:ECS,
author = "Julius Adams Stratton and Philip M. (Philip McCord)
Morse and Lan Jen Chu and Reina Albagli Hutner",
title = "Elliptic cylinder and spheroidal wave functions,
including tables of separation constants and
coefficients",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 127",
year = "1941",
LCCN = "QC174.2 .S78",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1901--1994",
remark = "A publication of the Technology Press, Massachusetts
Institute of Technology.",
subject = "Wave mechanics; Mathematics; Tables",
}
@PhdThesis{Dopper:1942:AOV,
author = "Herman Pieter Dopper",
title = "Asymptotische Ontwikkelingen van de Onvolledige
Gammafuncties. ({Dutch}) [{Asymptotic} developments of
the Incomplete Gamma Functions]",
type = "{Ph.D.} thesis",
school = "Rijksuniversiteit Groningen",
address = "Groningen, The Netherlands",
pages = "????",
year = "1942",
bibdate = "Sat Feb 18 14:32:59 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Dutch",
remark = "Cited in \cite{Paris:2016:UAE}.",
}
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Archibald:1943:TTF,
author = "Raymond Clare Archibald",
title = "Tables of Trigonometric Functions in Non-Sexagesimal
Arguments",
journal = j-MATH-TABLES-AIDS-COMPUT,
volume = "1",
number = "2",
pages = "33--44",
month = apr,
year = "1943",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-43-99136-7",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
journal-URL = "http://www.ams.org/mcom/",
remark = "Original journal has only `R. C. A.' as author:
possibly R. C. Archibald. AMS metadata now shows the
full name.",
}
@Book{Tolke:1943:PFE,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 1. Elementare und
elementare transzendente Funktionen, Unterstufe}.
({German}) [{Practical} functional theory. 1.
{Elementary} and elementary transcendental functions,
lower stage]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 261",
year = "1943",
bibdate = "Mon Feb 13 19:15:35 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Turing:1943:MCZ,
author = "A. M. Turing",
title = "A method for the calculation of the zeta-function",
journal = j-PROC-LONDON-MATH-SOC-2,
volume = "48",
pages = "180--197",
year = "1943",
ISSN = "0024-6115 (print), 1460-244X (electronic)",
ISSN-L = "0024-6115",
MRclass = "10.0X",
MRnumber = "MR0009612 (5,173a)",
MRreviewer = "C. L. Siegel",
bibdate = "Sat Nov 19 13:23:32 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/17",
ZMnumber = "0061.08304",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the London Mathematical Society. Second
Series",
received = "7 March 1939",
remark = "According to \cite[page 260]{Newman:1955:AMT},
publication was delayed four years by war-time
difficulties.",
}
@Article{Bateman:1944:GTB,
author = "Harry Bateman and Raymond Clare Archibald",
title = "A Guide to Tables of {Bessel} Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "7",
pages = "205--308",
month = jul,
year = "1944",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1944-0011175-4",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRnumber = "6,132b",
MRreviewer = "G. Szeg{\H{o}}",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lehmer:1944:NCB,
author = "Derrick Henry Lehmer",
title = "Note on the Computation of the {Bessel} Function {$
I_n(X) $}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "5",
pages = "133--135",
month = apr,
year = "1944",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-44-99053-8",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Original journal has only `D. H. L.' as author:
probably D. H. Lehmer. AMS metadata now shows the full
name.",
}
@Book{Lewis:1944:SCH,
author = "Charles J. Lewis",
title = "A survey of the confluent hypergeometric function",
publisher = "????",
address = "Washington, DC, USA",
pages = "155",
year = "1944",
LCCN = "QA351 .L53",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Abramowitz:1945:ZCB,
author = "Milton Abramowitz",
title = "Zeros of certain {Bessel} functions of fractional
order",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "1",
number = "9",
pages = "353--354",
month = jan,
year = "1945",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1945-0011176-7",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "6,132c",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Briggs:1945:TAL,
author = "Lyman J. Briggs and Arnold N. Lowan",
title = "Tables of Associated {Legendre} Functions",
publisher = pub-U-COLUMBIA,
address = pub-U-COLUMBIA:adr,
pages = "xlvi + 303 + 3",
year = "1945",
LCCN = "QA406 .U5 1945",
bibdate = "Sat Apr 1 14:47:02 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Prepared by the Mathematical Tables Project and
conducted under the sponsorship of the National bureau
of Standards. Present volume begun under the auspices
of the Work Projects Administration for the City of New
York and completed with the support of the Office of
Scientific Research and Development. Lyman J. Briggs,
Director, National Bureau of Standards and official
sponsor. Arnold N. Lowan, Project Director,
Mathematical Tables Project. Reproduced by a photo
offset process.",
subject = "Legendre's functions",
}
@Book{Emde:1945:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "Edwards Bros.",
address = "Ann Arbor, MI, USA",
pages = "xii + 181",
year = "1945",
LCCN = "????",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Original edition published in 1940.",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Anonymous:1946:MZC,
author = "Anonymous",
title = "More Zeros of Certain {Bessel} Functions of Fractional
Order",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "2",
number = "15",
pages = "118--119",
month = jul,
year = "1946",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1946-0016689-0",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Anonymous:1948:TBF,
author = "Anonymous",
title = "Tables of the {Bessel} Functions {$ Y_0 (x) $}, {$ Y_1
(x) $}, {$ K_0 (x) $}, {$ K_1 (x) $}, $ 0 \leq x \leq 1
$",
volume = "1",
publisher = pub-US-GPO,
address = pub-US-GPO:adr,
pages = "ix + 60",
year = "1948",
LCCN = "QA3 .U5 no. 1",
bibdate = "Sat Nov 04 16:47:30 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = ser-APPL-MATH-SER-NBS,
acknowledgement = ack-nhfb,
}
@Book{Emde:1948:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
edition = "Second",
pages = "xii + 181",
year = "1948",
LCCN = "QA55 .E5 1948",
MRclass = "65.0X",
MRnumber = "11,263k",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the square-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Wise:1948:IBF,
author = "M. E. Wise",
title = "The Incomplete Beta Function and the Incomplete Gamma
Function: An Acknowledgment",
journal = j-J-R-STAT-SOC-SER-B-METHODOL,
volume = "10",
number = "2",
pages = "264--264",
month = "????",
year = "1948",
CODEN = "JSTBAJ",
DOI = "https://doi.org/10.2307/2983781",
ISSN = "0035-9246",
ISSN-L = "0035-9246",
bibdate = "Fri Jan 23 11:53:21 MST 2015",
bibsource = "http://www.jstor.org/stable/i349688;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-b.bib",
URL = "http://www.jstor.org/stable/2983781",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series B
(Methodological)",
journal-URL = "http://www.jstor.org/journals/00359246.html",
}
@Article{Hartree:1949:NIP,
author = "D. R. Hartree",
title = "Notes on iterative processes",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "45",
number = "2",
pages = "230--236",
month = apr,
year = "1949",
CODEN = "PCPSA4",
DOI = "https://doi.org/10.1017/s0305004100024762",
ISSN = "0008-1981",
ISSN-L = "0008-1981",
MRclass = "65.0X",
MRnumber = "29268",
MRreviewer = "E. Bodewig",
bibdate = "Thu Aug 3 09:15:52 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Correction: in equation (29) at the bottom of page
233, replace the denominator term $ 2 y_0 $ by $ 2 y_1
$, matching the denominator in equation (32) on page
234.",
URL = "https://ui.adsabs.harvard.edu/abs/1949PCPS...45..230H",
ZMnumber = "0033.19003",
acknowledgement = ack-nhfb,
author-dates = "Douglas Rayner Hartree (27 March 1897--12 February
1958)",
fjournal = "Proceedings of the Cambridge Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
keywords = "$1/p$-th root; iterative process; reciprocal square
root; square root",
ZBmath = "3051117",
}
@Article{Lowan:1949:CLN,
author = "Arnold N. Lowan",
title = "The {Computation Laboratory of the National Bureau of
Standards}",
journal = j-SCRIPTA-MATH,
volume = "15",
number = "??",
pages = "33--63",
month = "????",
year = "1949",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0034.07002",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
ZBmath = "3052129",
}
@Book{Magnus:1949:FTS,
author = "Wilhelm Magnus and Fritz Oberhettinger",
title = "Formulas and theorems for the special functions of
mathematical physics",
publisher = "Chelsea Pub. Co.",
address = "New York, NY, USA",
pages = "172",
year = "1949",
LCCN = "QA41 M19e",
bibdate = "Sat Oct 30 18:44:51 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translated from the German by John Wermer.",
acknowledgement = ack-nhfb,
}
@Article{Mitchell:1949:TFA,
author = "K. Mitchell",
title = "Tables of the function $ \int_0^z - \log |1 - y| / y
\, d y $ with an account of some properties of this and
related functions",
journal = j-PHILOS-MAG,
volume = "40",
number = "302",
pages = "351--368",
year = "1949",
CODEN = "PHMAA4",
DOI = "https://doi.org/10.1080/14786444908561256",
ISSN = "0031-8086",
bibdate = "Sat Jun 17 17:47:16 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.tandfonline.com/doi/abs/10.1080/14786444908561256",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Magazine",
journal-URL = "http://www.tandfonline.com/loi/tphm19",
received = "9 April 1948",
}
@InProceedings{Polya:1949:RCP,
author = "G. P{\'o}lya",
editor = "J. Neyman",
booktitle = "Proceedings of the First Berkeley Symposium on
Mathematical Statistics and Probability",
title = "Remarks on computing the probability integral in one
and two dimensions",
publisher = pub-U-CALIFORNIA-PRESS,
address = pub-U-CALIFORNIA-PRESS:adr,
pages = "63--78",
year = "1949",
bibdate = "Sat Dec 16 17:23:49 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{USNBSCL:1949:TCH,
author = "{United States National Bureau of Standards
Computation Laboratory }",
title = "Tables of the confluent hypergeometric function {$ F(n
/ 2, 1 / 2, x) $ and related functions}",
volume = "3",
publisher = pub-US-GPO,
address = pub-US-GPO:adr,
pages = "xxii + 73",
year = "1949",
LCCN = "QA3 .U5 no. 3",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Applied mathematics series",
URL = "http://openlibrary.org/works/OL1218358W/Tables_of_the_confluent_hypergeometric_function_F%28n_2_1_2_x%29_and_related_functions",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions; Mathematics; Tables",
}
@Article{Norlund:1950:HF,
author = "Niels Erik N{\o}rlund",
title = "Hypergeometric functions",
journal = "Mat. Tidsskr. B.",
volume = "1950",
number = "??",
pages = "18--21",
year = "1950",
MRclass = "33.0X",
MRnumber = "MR0045259 (13,554e)",
MRreviewer = "S. C. van Veen",
bibdate = "Thu Dec 01 12:41:44 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0067.29402",
acknowledgement = ack-nhfb,
language = "Danish",
}
@TechReport{Stanley:1950:TRG,
author = "John Pearson Stanley and Maurice V. Wilkes",
title = "Table of the reciprocal of the gamma function for
complex argument",
type = "Report",
institution = "Computation Centre, University of Toronto",
address = "Toronto, ON, Canada",
pages = "????",
year = "1950",
MRclass = "65.0X",
MRnumber = "48144",
MRreviewer = "S. C. van Veen",
bibdate = "Sat Sep 07 16:52:05 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0040.06903",
abstract = "Toronto, ON, Canada",
acknowledgement = ack-nhfb,
author-dates = "Sir Maurice Vincent Wilkes (26 June 1913--29 November
2010)",
RSBM-number = "22",
ZBmath = "3060432",
}
@Book{Tolke:1950:PFE,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 1. Elementare und
elementare transzendente Funktionen}. ({German})
[{Practical} functional theory. 1. {Elementary} and
elementary transcendental functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 440",
year = "1950",
bibdate = "Mon Feb 13 19:12:35 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Tricomi:1950:AEU,
author = "F. G. Tricomi",
title = "{Asymptotische Eigenschaften der unvollst{\"a}ndigen
Gammafunktion}. ({German}) [{Asymptotic} properties of
the incomplete gamma function]",
journal = j-MATH-Z,
volume = "53",
number = "2",
pages = "136--148",
month = apr,
year = "1950",
CODEN = "MAZEAX",
DOI = "https://doi.org/10.1007/BF01162409",
ISSN = "0025-5874 (print), 1432-1823 (electronic)",
ISSN-L = "0025-5874",
bibdate = "Sat Feb 18 14:47:24 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/BF01162409",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Zeitschrift",
journal-URL = "http://link.springer.com/journal/209",
language = "German",
}
@Article{Cadwell:1951:BNI,
author = "J. H. Cadwell",
title = "The Bivariate Normal Integral",
journal = j-BIOMETRIKA,
volume = "38",
number = "3/4",
pages = "475--479",
month = dec,
year = "1951",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2332596",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
MRclass = "60.0X",
MRnumber = "0045960 (13,662h)",
MRreviewer = "G. E. Noether",
bibdate = "Sat Jun 21 14:32:38 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315418;
https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2332596",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://biomet.oxfordjournals.org/content/by/year;
http://www.jstor.org/journals/00063444.html",
}
@Article{Fogel:1951:FTE,
author = "{\`E}. K. Fogel'",
title = "A finite theory of elementary functions. {I}.
{Logarithmic} and exponential functions. ({Russian})",
journal = "Latvijas PSR Zin\=at{\c{n}}u Akad. V\=estis",
volume = "5",
number = "46",
pages = "801--813",
year = "1951",
MRclass = "33.0X",
MRnumber = "15,218b",
MRreviewer = "H. N. Shapiro",
bibdate = "Sat Apr 25 13:05:19 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@InProceedings{Gellman:1951:CCH,
author = "Harvey Gellman",
booktitle = "Proceedings of a Computation Seminar [{IBM Department
of Education, Endicot, NY, from December 5 to 9,
1949}]",
title = "The Calculation of Complex Hypergeometric Functions
with the {IBM Type 602-A} Calculating Punch",
publisher = "IBM",
address = "New York, NY, USA",
pages = "161--168",
year = "1951",
bibdate = "Mon Jun 18 06:09:24 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "A Computation Seminar, sponsored by the International
Business Machines Corporation, was held in the IBM
Department of Education, Endicot, NY, from December 5
to 9, 1949. Attending the Seminar were one hundred and
seven research engineers and scientists who are
experienced both in applying mathematical methods to
the solution of physical problems and in the associated
punched card methods of computation.",
}
@Article{Rutishauser:1951:BAK,
author = "Heinz Rutishauser",
title = "{Bemerkungen zur Arbeit von K. Emden ``Eine L{\"o}sung
f{\"u}r $ \int e^{b(x + a \cos x)} \, d x $}''.
({German}) [{Remarks} on the work by {K. Emden, ``A
solution for $ \int e^{b (x + a \ cos x)} \, d x
$''}]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "2",
number = "4",
pages = "292--293",
month = jul,
year = "1951",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/bf02579691",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRclass = "26.1X",
MRnumber = "44598",
MRreviewer = "F. J. Murray",
bibdate = "Mon Aug 24 21:56:15 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Heinz Rutishauser (30 January 1918--10 November
1970)",
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
ZAMP. Journal of Applied Mathematics and Physics.
Journal de Math\'{e}matiques et de Physique
Appliqu\'{e}es",
journal-URL = "http://link.springer.com/journal/33",
language = "German",
}
@Article{Salzer:1951:FCE,
author = "H. E. Salzer",
title = "Formulas for Calculating the Error Function of a
Complex Variable",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "34",
pages = "67--70",
month = apr,
year = "1951",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1951-0048150-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Salzer:1951:RTT,
author = "H. E. Salzer",
title = "Radix Table for Trigonometric Functions and their
Inverses to High Accuracy",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "33",
pages = "9--11",
month = jan,
year = "1951",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-51-99447-1",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Wilkes:1951:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
pages = "167",
year = "1951",
LCCN = "QA76.5 .W55 1951",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also second edition \cite{Wilkes:1957:PPE}, and
reprint \cite{Wilkes:1982:PPE}.",
acknowledgement = ack-nhfb,
tableofcontents = "Part I \\
Chapter 1. The Design of Programs for Electronic
Computing Machines / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machines / 2 \\
1-3 Description of the EDSAC / 3 \\
1-4 The EDSAC order code / 5 \\
1-5 Notes on the order code / 6 \\
1-6 The use of conditional orders / 7 \\
1-7 Modification of orders by the program / 8 \\
1-8 Multiaddress codes / 11 \\
1-9 Binary--decimal conversion / 12 \\
1-10 Checking facilities / 14 \\
Chapter 2. Input of Orders / 15 \\
2-1 Initial orders / 15 \\
2-2 Pseudo-orders / 17 \\
2-3 Examples / 17 \\
2-4 Control combinations / 17 \\
2-5 Starting the program / 18 \\
2-6 Use of code letters / 19 \\
2-7 Constants / 20 \\
2-8 Notation / 20 \\
Chapter 3. Subroutines and Parameters / 22 \\
3-1 Open subroutines / 22 \\
3-2 closed subroutines / 22 \\
3-3 preset parameters / 23 \\
3-4 program parameters / 23 \\
Chapter 4. Library Subroutines and their Use in
Constructing Programs / 25 \\
4-1 Library catalog / 25 \\
4-2 Input and output subroutines / 25 \\
4-3 Division subroutines / 27 \\
4-4 Trigonometrical and other functions / 27 \\
4-5 Quadrature / 27 \\
4-6 Assembly subroutines / 27 \\
4-7 Integration of differential equations / 32 \\
4-8 Processes, Interpretive subroutines / 34 \\
Chapter 5. Pitfalls / 38 \\
5-1 Proofreading of programs, points to be checked / 38
\\
5-2 Location of mistakes in a program / 39 \\
5-3 Counting operations / 41 \\
Chapter 6. Use of the EDSAC \& Its Associated Equipment
/ 42 \\
6-1 Tape Punching \& editing facilities / 42 \\
6-2 Storage of library subroutines / 43 \\
6-3 EDSAC organization / 43 \\
6-4 EDSAC controls / 43 \\
Chapter 7. Examples / 45 \\
7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
7-2 Example 2. Calculation of $\pi$ by evaluation of
definite integral / 48 \\
7-3 Alternative method for Example 2 / 52 \\
7-4 Example 2, with extra print orders for checking /
53 \\
7-5 Application of checking subroutine C11 to Example 2
/ 54 \\
7-6 Example of integration of an ordinary differential
equation / 46 \\
7-7 Evaluation of a definite integral / 61 \\
7-8 Program to facilitate the solution of algebraic
equation / 66 \\
Part II. Specifications of Library Subroutines / 72 \\
A. Subroutines to carry out floating point arithmetic /
73 \\
B. Subroutines to carry out arithmetical operations on
complex numbers / 78 \\
C. Checking subroutines / 79 \\
D. Division subroutines / 82 \\
E. Exponential subroutines / 83 \\
F. General routines relating to functions / 84 \\
G. Subroutines for integration of ordinary differential
equations / 86 \\
J. Subroutines for calculating special functions
[Legendre polynomials] / 88 \\
K. Subroutines for the summation of power series / 88
\\
L. Subroutines for evaluating logarithms / 91 \\
M. Miscellaneous subroutines / 91 \\
P. Print subroutines / 92 \\
Q. Quadrature subroutines / 95 \\
R. Input subroutines / 96 \\
S. Subroutines for evaluation of fractional powers / 98
\\
T. Subroutines for calculating trigonometrical
functions / 99 \\
U. Subroutines for counting operations / 101 \\
V1. Multiplication of vector by symmetric matrix / 102
\\
V2. Addition and subtraction of $n$ dimensional vectors
/ 103 \\
Part III. Programs of Selected Library Subroutines /
104 \\
Appendix A. Keyboard perforator code, etc. / 158 \\
Appendix B. The initial orders / 159 \\
Appendix C. Control combinations / 161 \\
Appendix D. Interpretive subroutines: example of
packing of orders / 162 \\
Appendix E. Methods of counting in a simple cycle / 164
\\
Index",
}
@Book{Anonymous:1952:BFP,
author = "Anonymous",
title = "{Bessel} Functions, {Part II}",
volume = "10",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "????",
year = "1952",
bibdate = "Tue Nov 14 14:59:31 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "British Association Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: was Leslie Fox a co-author?? Who were the
authors?? Page count??",
}
@InBook{Goncarov:1952:EFC,
author = "V. L. Gon{\v{c}}arov",
booktitle = "Encyclopaedia of elementary mathematics. {Book III}.
{Functions} and limits (the foundations of analysis)",
title = "Elementary functions of a complex variable",
publisher = "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
address = "Moscow-Leningrad, USSR",
pages = "491--552",
year = "1952",
MRclass = "30.0X",
MRnumber = "14,1073c",
MRreviewer = "R. P. Boas, Jr.",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Goncarov:1952:EFR,
author = "V. L. Gon{\v{c}}arov",
booktitle = "Encyclopaedia of elementary mathematics. {Book III}.
{Functions} and limits (the foundations of analysis)",
title = "Elementary functions of a real variable. Limits of
sequences and functions. {The} general concept of a
function",
publisher = "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
address = "Moscow-Leningrad, USSR",
pages = "9--296",
year = "1952",
MRclass = "27.2X",
MRnumber = "14,1070d",
MRreviewer = "R. P. Boas, Jr.",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Kuipers:1952:PSE,
author = "L. Kuipers",
title = "Properties of some elementary functions",
journal = "Nederl. Akad. Wetensch. Proc. Ser. A. = Indagationes
Math.",
volume = "55",
number = "14",
pages = "388--393",
year = "1952",
MRclass = "27.0X",
MRnumber = "14,360e",
MRreviewer = "E. Frank",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Bowman:1953:IEF,
author = "Frank Bowman",
title = "Introduction to Elliptic Functions with Applications",
publisher = "English Universities Press",
address = "London, UK",
pages = "115",
year = "1953",
LCCN = "QA343 .B76 1953",
bibdate = "Wed Mar 15 06:50:49 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
subject = "Elliptic functions; Elliptische functies",
}
@InProceedings{Lovelace:1953:AET,
author = "Ada Augusta Lovelace",
title = "{Appendix 1}: {Extracts} From {{\booktitle{Taylor's
Scientific Memoirs}}, Vol. III}",
crossref = "Bowden:1953:FTT",
pages = "341--408",
year = "1953",
bibdate = "Fri Jun 08 08:33:30 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Reprint of \cite{Lovelace:1843:SAE}. Pages 400--408
describe the computation of the Bernoulli numbers.",
acknowledgement = ack-nhfb,
}
@Article{Salzer:1953:RTO,
author = "Herbert E. Salzer",
title = "Radix Table for Obtaining Hyperbolic and Inverse
Hyperbolic Functions to Many Places",
journal = j-J-MATH-PHYS-MIT,
volume = "32",
number = "1--4",
pages = "197--202",
month = apr,
year = "1953",
CODEN = "JMPHA9",
DOI = "https://doi.org/10.1002/sapm1953321197",
ISSN = "0097-1421",
ISSN-L = "0097-1421",
bibdate = "Sat Aug 19 13:35:59 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib",
URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1953321197",
acknowledgement = ack-nhfb,
ajournal = "J. Math. Phys. (MIT)",
fjournal = "Journal of Mathematics and Physics (MIT)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590",
onlinedate = "April 1953",
}
@Article{Scherberg:1953:ACP,
author = "Max G. Scherberg and John F. Riordan",
title = "Analogue Calculation of Polynomial and Trigonometric
Expansions (in {Other Aids to Computation})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "7",
number = "41",
pages = "61--65",
month = jan,
year = "1953",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-53-99373-9",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Stiefel:1953:ITF,
author = "E. Stiefel",
title = "{Zur Interpolation von tabellierten Funktionen durch
Exponentialsummen und zur Berechnung von Eigenwerten
aus den Schwarzschen Konstanten}. ({German}) [{On}
interpolation of tabulated functions by exponential
sums and on the calculation of eigenvalues from the
{Schwarz}'s constants]",
journal = j-Z-ANGE-MATH-MECH,
volume = "33",
pages = "260--262",
year = "1953",
CODEN = "ZAMMAX",
DOI = "https://doi.org/10.1002/zamm.19530330806",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
MRclass = "65.0X",
MRnumber = "59061",
MRreviewer = "D. C. Gilles",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
fjournal = "Zeitschrift f{\"{u}}r Angewandte Mathematik und
Mechanik. Ingenieurwissenschaftliche
Forschungsarbeiten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
language = "German",
}
@Article{Turing:1953:SCR,
author = "A. M. Turing",
title = "Some calculations of the {Riemann} zeta-function",
journal = j-PROC-LONDON-MATH-SOC-3,
volume = "3",
number = "3",
pages = "99--117",
year = "1953",
CODEN = "PLMTAL",
ISSN = "0024-6115 (print), 1460-244X (electronic)",
ISSN-L = "0024-6115",
MRclass = "65.0X",
MRnumber = "MR0055785 (14,1126e)",
MRreviewer = "D. H. Lehmer",
bibdate = "Sat Nov 19 13:23:32 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See corrections and improvements
\cite{Lehman:1970:DZR}, and \cite{Trudgian:2011:ITM}.
The latter comments: ``Turing's Method has become the
standard technique used in modern verification of the
Riemann hypothesis.'' See also
\cite{Lehmer:1956:RRZ}.",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/21",
ZMnumber = "0050.08101",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the London Mathematical Society. Third
Series",
}
@Article{Aaboe:1954:AKI,
author = "Asger Aaboe",
title = "{Al-K{\=a}sh{\v{\i}}}'s iteration method for the
determination of $ \sin 1^\circ $",
journal = j-SCRIPTA-MATH,
volume = "20",
number = "??",
pages = "24--29",
month = "????",
year = "1954",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
MRclass = "01.0X",
MRnumber = "62046",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0055.00104",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
ZBmath = "3086736",
}
@Article{Atta:1954:CGH,
author = "Susie E. Atta and Ward C. Sangren",
title = "Calculation of Generalized Hypergeometric Series",
journal = j-J-ACM,
volume = "1",
number = "4",
pages = "170--172",
month = oct,
year = "1954",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320783.320785",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 08 21:50:00 1994",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Cahill:1954:PCH,
author = "W. F. Cahill",
title = "Programs for Computing the Hypergeometric Series (in
Automatic Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
number = "45",
pages = "36--37",
month = jan,
year = "1954",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-54-99344-8",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Clenshaw:1954:PAE,
author = "C. W. Clenshaw",
title = "Polynomial approximations to elementary functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
number = "47",
pages = "143--147",
month = jul,
year = "1954",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1954-0063487-2",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "41.1X",
MRnumber = "16,128f",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Fox:1954:STB,
author = "L. Fox",
title = "A Short Table for {Bessel} Functions of Integer Orders
and Large Arguments",
volume = "3",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "28",
year = "1954",
MRclass = "65.0X",
MRnumber = "65245",
MRreviewer = "R. C. Archibald",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Royal Society Shorter Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@TechReport{Franklin:1954:CARa,
author = "J. Franklin and B. Friedman",
title = "A convergent asymptotic representation for integrals",
institution = "Division of Electromagnetic Research, Institute of
Mathematical Sciences, New York University",
address = "New York, NY, USA",
pages = "i + 17",
year = "1954",
MRclass = "40.0X",
MRnumber = "0068019",
MRreviewer = "J. G. van der Corput",
bibdate = "Tue Feb 06 15:03:36 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Res. Rep. No. BR-9",
acknowledgement = ack-nhfb,
remark = "See applications in
\cite{Temme:2015:AMI,Navas-Palencia:2018:HPC}.",
}
@Article{LaFara:1954:MCI,
author = "Robert L. LaFara",
title = "A Method for Calculating Inverse Trigonometric
Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "8",
number = "47",
pages = "132--139",
month = jul,
year = "1954",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1954-0063150-8",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InCollection{Ostrowski:1954:TPA,
author = "A. M. Ostrowski",
title = "On two problems in abstract algebra connected with
{Horner}'s rule",
crossref = "Birkhoff:1954:SMM",
pages = "40--48",
year = "1954",
bibdate = "Fri Oct 20 10:13:10 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "number of multiplications to evaluate a polynomial",
remark = "TO DO: Find copy of this book section.",
}
@Article{Shenton:1954:INI,
author = "L. R. Shenton",
title = "Inequalities for the Normal Integral Including a New
Continued Fraction",
journal = j-BIOMETRIKA,
volume = "41",
number = "1/2",
pages = "177--189",
month = jun,
year = "1954",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2333015",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
MRclass = "62.0X",
MRnumber = "0061785 (15,884e)",
MRreviewer = "E. Lukacs",
bibdate = "Sat Jun 21 14:32:43 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315422;
https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2333015",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://biomet.oxfordjournals.org/content/by/year;
http://www.jstor.org/journals/00063444.html",
}
@InProceedings{Todd:1954:MWN,
author = "John Todd",
editor = "????",
booktitle = "Transactions of {2nd Symposium on Applied Mathematics,
29 April 1954, University of Chicago}",
title = "Motivation for working on numerical analysis",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "????",
year = "1954",
bibdate = "Fri Oct 20 13:28:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Sponsored by the American Mathematical Society and the
Office of Ordnance Research",
}
@Article{Booth:1955:NAP,
author = "A. D. Booth",
title = "A note on approximating polynomials for trigonometric
functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
number = "49",
pages = "21--23",
month = jan,
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1955-0069579-7",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "69579",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@TechReport{Carlson:1955:RAF,
author = "Bengt Carlson and Max Goldstein",
title = "Rational Approximations of Functions",
type = "Report",
number = "LA-1943",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "iv + 46",
month = aug,
year = "1955",
DOI = "https://doi.org/10.2172/4374577",
bibdate = "Sat Dec 27 09:41:36 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.osti.gov/scitech/biblio/4374577-0deJO9/;
http://www.osti.gov/scitech/servlets/purl/4374577",
acknowledgement = ack-nhfb,
keywords = "$-\ln(x)/(1 - x)$; $\art(x) / x$; $\cos(x)$;
$\exp(-x)$; $\sin(x) / x$; $\tan(x) / x$; $x \cot(x)$;
$x**(1/2)$; $x**(1/3)$; $x**(1/4)$; $x**(1/5)$;
$x**(1/6)$; $x**(1/7)$; continued fractions; rational
approximations",
remark = "Cited in \cite[page 71]{Abramowitz:1964:HMF}.",
}
@Article{Clenshaw:1955:NSC,
author = "C. W. Clenshaw",
title = "A Note on the Summation of {Chebyshev} Series",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
number = "51",
pages = "118--120",
month = jul,
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "0071856",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Chebyshev series; Clenshaw algorithm; Clenshaw
summation; Horner polynomial evaluation",
remark = "Hidden inside \cite{Brenner:1955:TNS}, but important
in its own right for commentary on the recursive
algorithm for summation of Chebyshev series, and a
brief analysis of its accuracy.",
}
@Article{Froberg:1955:NTC,
author = "Carl-Erik Fr{\"o}berg",
title = "Numerical Treatment of {Coulomb} Wave Functions",
journal = j-REV-MOD-PHYS,
volume = "27",
number = "4",
pages = "399--411",
month = oct,
year = "1955",
CODEN = "RMPHAT",
DOI = "https://doi.org/10.1103/RevModPhys.27.399",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
bibdate = "Tue May 22 16:36:44 MDT 2012",
bibsource = "http://rmp.aps.org/toc/RMP/v27/i4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/revmodphys1950.bib",
URL = "http://link.aps.org/doi/10.1103/RevModPhys.27.399;
http://rmp.aps.org/abstract/RMP/v27/i4/p399_1",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
}
@Book{Hastings:1955:ADC,
author = "Cecil {Hastings, Jr.}",
title = "Approximations for Digital Computers",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "viii + 201",
year = "1955",
ISBN = "0-691-07914-5",
ISBN-13 = "978-0-691-07914-1",
LCCN = "QA76 .H37",
bibdate = "Mon Oct 01 15:59:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
note = "Assisted by Jeanne T. Hayward and James P. Wong, Jr.",
series = "The Rand series",
acknowledgement = ack-nhfb,
remark-1 = "Reprinted 1957, 1959, 1962, 1966, and 1970. I have
fourth printing (1962).",
remark-2 = "Hastings gives a polynomial approximation for
computing random numbers from a normal distribution.",
subject = "Electronic digital computers; Numerical analysis",
tableofcontents = "Preface / v \\
Part I \\
1: Concerning Best Fit / 3 \\
2: Linear Weights / 19 \\
3: An Iterative Procedure / 27 \\
4: Solution of Equations / 35 \\
5: Chebyshev Polynomials / 47 \\
6: Concerning Weights / 65 \\
7: Function With a Peak / 75 \\
8: Rates of Convergence / 83 \\
9: Choice of Form / 95 \\
10: A Scoring-Camera Problem / 115 \\
Part II \\
1: $\log_{10} x$ / 125 \\
5: $\phi(x) = (1 - e^{-x}) / x$ / 129 \\
8: $\arctan x$ / 132 \\
14: $\sin (\pi/2) x$ / 138 \\
17: $10^x$ / 141 \\
21: $W(x) = e^{-x} / (1 + e^{-x})^2$ / 145 \\
24: $P_k(x) = 1.72 + 42 x^2$ or $0.136 / x^2$ / 148 \\
27: $E'(x) = (1 / \sqrt{2 \pi}) e^{-(1/2)x^2}$ / 151
\\
30: ``Total Klein-Nishina Cross Section'' Function /
154 \\
31: $\Gamma(1 + x)$ / 155 \\
35: $\arcsin x$ / 159 \\
40: $\log_2 x$ / 164 \\
43: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \,
dt$ / 167 \\
46: $K(k) = \int_0^{\pi/2} (1 / \sqrt{1 - k^2 \sin^2
\phi}) \, d\phi$ / 170 \\
49: $E(k) = \int_0^{\pi/2} (\sqrt{1 - k^2 \sin^2 \phi})
\, d\phi$ / 173 \\
52: $\ln(1 + x)$ / 176 \\
57: $e^{-x}$ / 181 \\
61: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \,
dt$ / 185 \\
64: $-{\rm Ei}(-x) = \int_x^\infty (e^{-t} / t) \, dt$
/ 188 \\
67: $q = (1 / \sqrt{2 \pi}) \int_{x(q)}^\infty
e^{-(1/2)t^2} \, dt$ / 191 \\
69: $W(z) = \int_0^\infty (e^(-u z) / (K_1^2(u) + \pi^2
I_1^2(u))) (1/u) \, du$ / 193 \\
71: $P(x) = \int_x^\infty (\sin(t - x) / t) \, dt$ /
195 \\
74: $Q(x) = \int_x^\infty (\cos(t - x) / t) \, dt$ /
195 \\
References for Part II / 201",
}
@Book{Hobson:1955:TSE,
author = "Ernest William Hobson",
title = "The Theory of Spherical and Ellipsoidal Harmonics",
publisher = "Chelsea Pub. Co.",
address = "New York, NY, USA",
pages = "500",
year = "1955",
LCCN = "QA406 .H7 1955",
bibdate = "Sat Apr 1 14:40:56 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1856--1933",
subject = "Spherical harmonics; Lam{\'e}'s functions",
}
@Book{McLachlan:1955:BFE,
author = "N. W. (Norman William) McLachlan",
title = "{Bessel} Functions for Engineers",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
edition = "Second",
pages = "xii + 239",
year = "1955",
LCCN = "QA408 .M3 1955",
bibdate = "Sat Apr 1 14:44:36 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "The Oxford engineering science series",
acknowledgement = ack-nhfb,
author-dates = "1888--",
subject = "Bessel functions",
}
@Article{Motzkin:1955:EP,
author = "T. S. Motzkin",
title = "Evaluation of polynomials",
journal = j-BULL-AMS,
volume = "61",
number = "2",
pages = "163--163",
month = mar,
year = "1955",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Fri Oct 20 09:06:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
issue = "635",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
keywords = "number of multiplications to evaluate a polynomial",
received = "12 November 1954",
remark = "One-paragraph abstract only, with reference-less
mention of Ostrowski.",
}
@Article{Motzkin:1955:ERF,
author = "T. S. Motzkin",
title = "Evaluation of rational functions",
journal = j-BULL-AMS,
volume = "61",
number = "2",
pages = "163--163",
month = mar,
year = "1955",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Fri Oct 20 09:06:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
issue = "635",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
keywords = "number of multiplications to evaluate a polynomial",
received = "12 November 1954",
remark = "One-paragraph abstract only, with reference to
Ostrowski.",
}
@Article{Norlund:1955:HF,
author = "Niels Erik N{\o}rlund",
title = "Hypergeometric functions",
journal = j-ACTA-MATH,
volume = "94",
number = "??",
pages = "289--349",
month = "????",
year = "1955",
CODEN = "ACMAA8",
DOI = "https://doi.org/10.1007/BF02392494",
ISSN = "0001-5962 (print), 1871-2509 (electronic)",
ISSN-L = "0001-5962",
MRclass = "33.0X",
MRnumber = "MR0074585 (17,610d)",
MRreviewer = "A. Erd{\'e}lyi",
bibdate = "Thu Dec 01 10:09:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Acta Mathematica",
journal-URL = "http://link.springer.com/journal/11511",
}
@Article{Preston:1955:ACS,
author = "F. S. Preston",
title = "An Analog Computer for the Solution of Tangents",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-4",
number = "3",
pages = "101--106",
month = "????",
year = "1955",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/IRETELC.1955.507908",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407908",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Robinson:1955:EAC,
author = "A. S. Robinson",
title = "An Electronic Analog Computing Technique for the
Solution of Trigonometric Problems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-4",
number = "3",
pages = "95--101",
month = "????",
year = "1955",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/IRETELC.1955.5407907",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407907",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Salzer:1955:CZE,
author = "Herbert E. Salzer",
title = "Complex zeros of the error function",
journal = j-J-FRANKLIN-INST,
volume = "260",
number = "3",
pages = "209--211",
month = sep,
year = "1955",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(55)90732-8",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "65.1X",
MRnumber = "71880",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Franklin Institute",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Todd:1955:MWN,
author = "John Todd",
title = "Motivation for working in numerical analysis",
journal = j-COMM-PURE-APPL-MATH,
volume = "8",
number = "1",
pages = "97--116",
month = feb,
year = "1955",
CODEN = "CPAMAT, CPMAMV",
DOI = "https://doi.org/10.1002/cpa.3160080107",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
MRclass = "65.0X",
MRnumber = "70251",
MRreviewer = "G. E. Forsythe",
bibdate = "Fri Oct 20 08:38:37 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0064.37402",
acknowledgement = ack-nhfb,
ajournal = "Comm. Pure Appl. Math.",
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
keywords = "characteristic roots (eigenvalues) of finite matrices;
game theory; integral equations; modified differences;
Monte Carlo; number of multiplications to evaluate a
polynomial; polynomial evaluation; quadrature; recent
activity in numerical analysis; sequence convergence
acceleration; theory of machines (automata)",
remark-1 = "This may be the earliest paper to note that a
polynomial of degree $n$ can be evaluated with fewer
than $n$ multiplications, but requiring more than $n$
additions. The normal Horner form requires $n$ multiply
and $n$ add operations: $ h = a_n $, $ h = x h + a_k $
(for $ k = n - 1 $ to $0$), and on modern hardware can
be conveniently evaluated in $n$ consecutive fused
multiply-add operations. However, the evaluation of the
altered forms often has terms of differing signs, and
may be subject to catastrophic leading digit loss, when
the original polynomial, if it had coefficients of the
same sign, might have been computed stably for $ x >
0$. In some cases, the new coefficients are complex,
even when those of the original polynomial are real
numbers. See also related publications
\cite{Ostrowski:1954:TPA, Todd:1954:MWN,
Motzkin:1955:EP, Motzkin:1955:ERF, Belaga:1958:SPI,
Pan:1959:CSC, Pan:1959:SCP, Floyd:1961:ACE,
Dorn:1962:GHR, Knuth:1962:EPC, Eisman:1963:PER,
Eve:1964:EP, Rice:1965:CPR, Winograd:1970:NMN,
Rabin:1972:FEP, Miller:1975:CCN, Knuth:1998:EP,
Kusterer:1979:SEP, Ceberio:2002:HRI, Cameron:2024:AHM}.
Rice reports extreme numerical instability of the
Belaga and Motzkin forms, and moderate instability of
the Pan forms, while the Chebyshev form is never
unstable. Todd cites Motzkin's work as ``to appear'',
and those two one-paragraph abstracts were received 12
November 1954 and published in March 1955, but Todd's
paper has no received date, so we cannot determine
their relative priority. Entry
\cite{Ostrowski:1954:TPA} may be prior art, but a copy
of that work has not yet been located. The quotation in
entry \cite{Eve:1964:E} summarizes the bounds on the
number of add and multiply operations.",
remark-2 = "Knuth's treatment (Knuth:1962:EPC) concentrates on
operation counts, because the polynomial variable need
not be a real scalar floating-point number: it could be
complex, multiple precision, matrix, series, ..., where
multiplication is relatively expensive. Knuth remarks
on page 485 that ``numerical analysis of the accuracy
achieved \ldots{} is beyond the scope of this book: the
reader should be careful to investigate the accuracy of
any calculations undertaken with floating-point
arithmetic.'' On page 486, Knuth notes that the nested
form is often attributed to Horner:1819:XNM, but that
Isaac Newton used it in unpublished notes 150 years
earlier, and it was employed by the Chinese in the 13th
century CE.",
remark-3 = "The year of this paper is erroneously cited in
reference lists of several sources as 1951, rather than
the correct 1955.",
ZBmath = "3109832",
}
@Book{Achieser:1956:TA,
author = "N. I. Achieser",
title = "Theory of Approximation",
publisher = "Frederick Ungar Publishing Company",
address = "New York, NY, USA",
pages = "x + 307",
year = "1956",
LCCN = "QA221 .A533 1956",
bibdate = "Fri Oct 20 08:06:59 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Translation of Russian original, Lek{\"e}t{\`\i}sii po
teorii approksima{\"e}t{\`\i}sii. Reprinted in
\cite{Achieser:1992:TA}.",
subject = "Mathematical analysis",
tableofcontents = "Approximation Problems in Linear Normalized Spaces
\\
Formulation of the Principal Problem in the Theory of
Approximation / 1 \\
The Concept of Metric Space / 1 \\
The Concept of Linear Normalized Space / 2 \\
Examples of Linear Normalized Spaces / 3 \\
The Inequalities of Holder and Minkowski / 4 \\
Additional Examples of Linear Normalized Spaces / 7 \\
Hilbert Space / 8 \\
The Fundamental Theorem of Approximation Theory in
Linear Normalized Spaces / 10 \\
Strictly Normalized Spaces / 11 \\
An Example of Approximation in the Space $L^p$ / 12 \\
Geometric Interpretation / 13 \\
Separable and Complete Spaces / 14 \\
Approximation Theorems in Hilbert Space / 15 \\
An Example of Approximation in Hilbert Space / 19 \\
More About the Approximation Problem in Hilbert Space /
21 \\
Orthonormalized Vector Systems in Hilbert Space / 22
\\
Orthogonalization of Vector Systems / 23 \\
Infinite Orthonormalized Systems / 25 \\
An Example of a Non-Separable System / 29 \\
Weierstrass' First Theorem / 29 \\
Weierstrass' Second Theorem / 32 \\
The Separability of the Space C / 33 \\
The Separability of the Space $L^p$ / 34 \\
Generalization of Weierstrass' Theorem to the Space
$L^p$ / 37 \\
The Completeness of the Space $L^p$ / 38 \\
Examples of Complete Orthonormalized Systems in
L[superscript 2] / 40 \\
Muntz's Theorem / 43 \\
The Concept of the Linear Functional / 46 \\
F. Riesz's Theorem / 47 \\
A Criterion for the Closure of a Set of Vectors in
Linear Normalized Spaces / 49 \\
P. L. Tchebysheff's Domain of Ideas \\
Statement of the Problem / 51 \\
A Generalization of the Theorem of de la Vallee-Poussin
/ 52 \\
The Existence Theorem / 53 \\
Tchebysheff's Theorem / 55 \\
A Special Case of Tchebysheff's Theorem / 57 \\
The Tchebysheff Polynomials of Least Deviation from
Zero / 57 \\
A Further Example of P. Tchebysheff's Theorem / 58 \\
An Example for the Application of the General Theorem
of de la Vallee-Poussin / 60 \\
An Example for the Application of P. L. Tchebysheff's
General Theorem / 62 \\
The Passage to Periodic Functions / 64 \\
An Example of Approximating with the Aid of Periodic
Functions / 66 \\
The Weierstrass Function / 66 \\
Haar's Problem / 67 \\
Proof of the Necessity of Haar's Condition / 68 \\
Proof of the Sufficiency of Haar's Condition / 69 \\
An Example Related to Haar's Problem / 72 \\
P. L. Tchebysheff's Systems of Functions / 73 \\
Generalization of P. L. Tchebysheff's Theorem / 74 \\
On a Question Pertaining to the Approximation of a
Continuous Function in the Space $L$ / 76 \\
A. A. Markoff's Theorem / 82 \\
Special Cases of the Theorem of A. A. Markoff / 85 \\
Elements of Harmonic Analysis \\
The Simplest Properties of Fourier Series / 89 \\
Fourier Series for Functions of Bounded Variation / 93
\\
The Parseval Equation for Fourier Series / 97 \\
Examples of Fourier Series / 98 \\
Trigonometric Integrals / 101 \\
The Riemann--Lebesgue Theorem / 103 \\
Plancherel's Theory / 104 \\
Watson's Theorem / 106 \\
Plancherel's Theorem / 108 \\
Fejer's Theorem / 110 \\
Integral-Operators of the Fejer Type / 113 \\
The Theorem of Young and Hardy / 116 \\
Examples of Kernels of the Fejer Type / 118 \\
The Fourier Transformation of Integrable Functions /
120 \\
The Faltung of two Functions / 122 \\
V. A. Stekloff's Functions / 123 \\
Multimonotonic Functions / 125 \\
Conjugate Functions / 126 \\
Certain Extremal Properties of Integral Transcendental
Functions of the Exponential Type \\
Integral Functions of the Exponential Type / 130 \\
The Borel Transformation / 132 \\
The Theorem of Wiener and Paley / 134 \\
Integral Functions of the Exponential Type which are
Bounded along the Real Axis / 137 \\
S. N. Bernstein's Inequality / 140 \\
B. M. Levitan's Polynomials / 146 \\
The Theorem of Fejer and Riesz. A Generalization of
This Theorem / 152 \\
A Criterion for the Representation of Continuous
Functions as Fourier--Stieltjes Integrals / 154 \\
Questions Regarding the Best Harmonic Approximation of
Functions Preliminary Remarks / 160 \\
The Modulus of Continuity / 161 \\
The Generalization to the Space $L^p$ ($p \geq 1$) /
162 \\
An Example of Harmonic Approximation / 165 \\
Some Estimates for Fourier Coefficients / 169 \\
More about V. A. Stekloff's Functions / 173 \\
Two Lemmas / 175 \\
The Direct Problem of Harmonic Approximation / 176 \\
A Criterion due to B. Sz.-Nagy / 183 \\
The Best Approximation of Differentiable Functions /
187 \\
Direct Observations Concerning Periodic Functions / 195
\\
Jackson's Second Theorem / 199 \\
The Generalized Fejer Method / 201 \\
Berstein's Theorem / 206 \\
Priwaloff's Theorem / 210 \\
Generalizations of Bernstein's Theorems to the Space
$L^p$ ($p \geq 1$) / 211 \\
The Best Harmonic Approximation of Analytic Functions /
214 \\
A Different Formulation of the Result of the Preceding
Section / 218 \\
The Converse of Bernstein's Theorem / 221 \\
Wiener's Theorem on Approximation \\
Wiener's Problem / 224 \\
The Necessity of Wiener's Condition / 224 \\
Some Definitions and Notation / 225 \\
Several Lemmas / 227 \\
The Wiener--Levy Theorem / 230 \\
Proof of the Sufficiency of Wiener's Condition / 233
\\
Wiener's General Tauber Theorem / 234 \\
Weakly Decreasing Functions / 235 \\
Remarks on the Terminology / 237 \\
Ikehara's Theorem / 238 \\
Carleman's Tauber Theorem / 241 \\
Various Addenda and Problems \\
Elementary Extremal Problems and Certain Closure
Criteria / 243 \\
Szego's Theorem and Some of Its Applications / 256 \\
Further Examples of Closed Sequences of Functions / 267
\\
The Caratheodory--Fejer Problem and Similar Problems /
270 \\
Solotareff's Problems and Related Problems / 280 \\
The Best Harmonic Approximation of the Simplest
Analytic Functions / 289 \\
Notes / 296 \\
Index / 306",
}
@InProceedings{Haynes:1956:EIE,
author = "John G. Haynes",
editor = "????",
booktitle = "{ACM'56: Proceedings of the 1956 11th ACM national
meeting}",
title = "Evaluation of incomplete elliptic integrals by
{Gaussian} integration",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "56--59",
year = "1956",
DOI = "https://doi.org/10.1145/800258.808948",
bibdate = "Fri Dec 21 08:53:15 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=808948",
acknowledgement = ack-nhfb,
}
@Book{Jeffreys:1956:MMP,
author = "Harold Jeffreys and Bertha {Swirles Jeffreys}",
title = "Methods of Mathematical Physics",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Third",
pages = "714",
year = "1956",
LCCN = "QA401 .J4 1956",
bibdate = "Thu Aug 17 10:48:45 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://en.wikipedia.org/wiki/Bertha_Swirles;
https://en.wikipedia.org/wiki/Harold_Jeffreys",
acknowledgement = ack-nhfb,
author-dates = "Sir Harold Jeffreys (22 April 1891--18 March 1989);
Lady Bertha Swirles Jeffreys (22 May 1903--18 December
1999)",
remark = "References to Douglas Hartree in",
remark-1 = "First edition 1946, second edition 1950, third edition
1956, first paperback edition 1972, reprinted 1978,
1980, 1988, 1992, 1999, 2001. Third edition preface is
dated April 1953. Second edition preface is dated 15
November 1948. First edition preface is dated 1946.
Reprinted in \cite{Jeffreys:1999:MMP}.",
subject-dates = "Douglas Rayner Hartree (27 March 1897--12 February
1958)",
tableofcontents = "Preface \\
Authors' Notes \\
1: The Real Variable \\
2: Scalars and Vectors \\
3: Tensors \\
4: Matrices \\
5: Multiple Integrals \\
6: Potential Theory \\
7: Operational Methods \\
8: Physical Applications of the Operational Method \\
9: Numerical Methods \\
10: Calculus of Variations \\
11: Functions of a Complex Variable \\
12: Contour Integration and Bromwich's Integral \\
13: Conformal Representation \\
14: Fourier's Theorem \\
15: The Factorial and Related Functions \\
16: Solution of Linear Differential Equation \\
17: Asymptotic Expansions \\
18: The Equations of Potential, Waves, and Heat
Conduction \\
19: Waves in One Dimension and Waves With Spherical
Symmetry \\
20: Conduction of Heat in One and Three Dimensions \\
21: Bessel Functions \\
22: Applications of Bessel Functions \\
23: The Confluent Hypergeometric Function \\
24: Legendre Functions and Associated Functions \\
25: Elliptic Functions \\
Notes \\
Appendix on Notation \\
Index",
}
@Article{Lehmer:1956:RRZ,
author = "D. H. Lehmer",
title = "On the roots of the {Riemann} zeta-function",
journal = j-ACTA-MATH,
volume = "95",
number = "1",
pages = "291--298",
month = dec,
year = "1956",
CODEN = "ACMAA8",
DOI = "https://doi.org/10.1007/BF02401102",
ISSN = "0001-5962 (print), 1871-2509 (electronic)",
ISSN-L = "0001-5962",
MRclass = "10.1X",
MRnumber = "0086082 (19,121a)",
MRreviewer = "L. Schoenfeld",
bibdate = "Mon Sep 28 16:18:23 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Acta Mathematica",
journal-URL = "http://link.springer.com/journal/11511",
remark-1 = "See \cite[references 38--39, page
54]{Bullynck:2015:CPT} for Turing's role in this work,
published two years after Turing's death in 1954.
Turing's incomplete work appears in
\cite{Turing:1953:SCR}.",
remark-2 = "From page 293: ``Plans to extend the work of
Titchmarsh [on the zeros of the Riemann zeta function]
by use of a differential analyzer were made in 1939 by
the late A. M. Turing. These were interrupted by the
war and later rendered obsolete by the advent of the
electronic digital computers.''",
remark-3 = "From page 293: ``In 1947 the writer programmed an
extension of the work of Titchmarsh [on the zeros of
the Riemann zeta function] for the ENIAC, the only
electronic computer then in operation. However, before
the program could be run, the ENIAC was drastically
modified thus rendering it useless for the problem.''",
remark-4 = "From page 293: ``In June 1950, Turing used the
Manchester University Mark 1 electronic digital
computer to examine the zeta-function for $24,937.96 <
t < 25,735.93$ (that is for $63 < \sqrt{\tau} < 6.4$)
and found in this region of the critical strip that
there are about 1070 simple zeros all with $a = 1/2$.
In another short run the validity of the Riemann
Hypothesis was verified between Titchmarsh's upper
limit of $t = 1468$ and $t = 1540$. Only some twenty
hours of machine time was used. Unfortunately no
further time was made available and these incomplete
results were published in 1953.''",
}
@InProceedings{Luke:1956:RFAa,
author = "Yudell L. Luke",
editor = "????",
booktitle = "{ACM'56: Proceedings of the 1956 11th ACM national
meeting}",
title = "On rational function approximations to the exponential
function with application to the practical solution of
linear differential difference equations with constant
coefficients",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "13--16",
year = "1956",
DOI = "https://doi.org/10.1145/800258.808937",
bibdate = "Fri Dec 21 08:53:15 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See errata and addenda \cite{Luke:1956:RFAb}.",
URL = "https://dl.acm.org/ft_gateway.cfm?id=808937",
acknowledgement = ack-nhfb,
}
@InProceedings{Luke:1956:RFAb,
author = "Yudell L. Luke",
editor = "????",
booktitle = "{ACM'56: Proceedings of the 1956 11th ACM national
meeting}",
title = "On rational function approximations to the exponential
function with application to the practical solution of
linear differential difference equations with constant
coefficients: Errata and addenda",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "177--178",
year = "1956",
DOI = "https://doi.org/10.1145/800258.808979",
bibdate = "Fri Dec 21 08:53:15 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Luke:1956:RFAa}.",
URL = "https://dl.acm.org/ft_gateway.cfm?id=808979",
acknowledgement = ack-nhfb,
}
@Book{Sneddon:1956:SFM,
author = "Ian Naismith Sneddon",
title = "Special Functions of Mathematical Physics and
Chemistry",
volume = "19",
publisher = "Oliver and Boyd",
address = "Edinburgh, UK",
edition = "Third",
pages = "viii + 164",
year = "1956",
LCCN = "QA1 U588 v. 19",
bibdate = "Sat Oct 30 18:41:48 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "University mathematical texts",
acknowledgement = ack-nhfb,
remark = "See second edition \cite{Sneddon:1961:SFM} and third
edition \cite{Sneddon:1980:SFM}.",
subject = "Functions, Special",
}
@Book{Stratton:1956:SWF,
author = "Julius Adams Stratton",
title = "Spheroidal Wave Functions, Including Tables of
Separation Constants and Coefficients",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 613",
year = "1956",
LCCN = "QA405 .S8",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1901--1994",
subject = "Wave mechanics; Spheroidal functions",
}
@Book{Flammer:1957:SWF,
author = "Carson Flammer",
title = "Spheroidal Wave Functions",
publisher = pub-STANFORD,
address = pub-STANFORD:adr,
pages = "ix + 220",
year = "1957",
LCCN = "QA405 .F55",
bibdate = "Sat Apr 1 14:32:29 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "A Stanford Research Institute monograph",
acknowledgement = ack-nhfb,
remark = "The basis for this monograph was work done at Stanford
Research Institute for the United States Air Force
Cambridge Research Center under Contract AF 19
(604)-1296.",
subject = "Spheroidal functions",
}
@Article{Franklin:1957:CARb,
author = "Joel Franklin and Bernard Friedman",
title = "A convergent asymptotic representation for integrals",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "53",
pages = "612--619",
year = "1957",
CODEN = "PCPSA4",
ISSN = "0008-1981",
MRclass = "42.1X",
MRnumber = "0090691",
MRreviewer = "P. Henrici",
bibdate = "Tue Feb 06 15:03:36 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2F167020D3A1F98182882E99549E7751/S0305004100032667a.pdf/a-convergent-asymptotic-representation-for-integrals.pdf",
abstract = "This paper represents a new method for obtaining an
asymptotic representation for integrals of the form $
\int_0^\infty e^{-p x} x^{c - 1} f(x) \, d x $ when $p$
is large. It is shown that if $ f(x)$ satisfies certain
conditions this representation is also convergent.
Numerical calculations seem to show that the first term
of the representation gives a close approximation to
the value of the integral for a wide range of values of
$p$.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
remark = "See applications in
\cite{Temme:2015:AMI,Navas-Palencia:2018:HPC}.",
}
@Article{Hitchcock:1957:PAB,
author = "A. J. M. Hitchcock",
title = "Polynomial Approximations to {Bessel} Functions of
Order Zero and One and to Related Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "86--88",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kogbetliantz:1957:CEN,
author = "E. G. Kogbetliantz",
title = "Computation of {$ e^N $} for $ - \infty < {N} < +
\infty $ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "110--115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.12.0110",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "68.0X",
MRnumber = "19,775d",
bibdate = "Tue Sep 06 20:55:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "W. F. Freiberger",
}
@Article{Linskii:1957:CEF,
author = "V. S. Linski{\u{\i}}",
title = "Calculation of elementary functions on automatic
digital machines. ({Russian})",
journal = "Vy{\v{c}}isl. Mat.",
volume = "2",
pages = "90--119",
year = "1957",
MRclass = "68.00",
MRnumber = "21 \#982",
MRreviewer = "J. W. Carr, III",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Luke:1957:C,
author = "Yudell L. Luke",
title = "On the Computation of $ \log {Z} $ and $ \operatorname
{arc} \tan {Z} $",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "57",
pages = "16--18",
month = jan,
year = "1957",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1957-0084855-1",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Miller:1957:NGS,
author = "J. C. P. Miller",
title = "Note on the General Solution of the Confluent
Hypergeometric Equation",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "97--99",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Southard:1957:ATW,
author = "Thomas H. Southard",
title = "Approximation and Table of the {Weierstrass} $ \wp $
Function in the Equianharmonic Case for Real Argument",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "99--100",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002156",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Stegun:1957:GBF,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Generation of {Bessel} Functions on High Speed
Computers",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "60",
pages = "255--257",
month = oct,
year = "1957",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1957-0093939-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{T:1957:CHS,
author = "C. B. T.",
title = "Comment: {T. H. Southard, \booktitle{Approximation and
table of the Weierstrass $ \wp $ function in the
equianharmonic case for real argument}. [MTAC, this
issue, p. 99--100]}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "110--110",
month = apr,
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Feb 27 08:05:17 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002157",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Wilkes:1957:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xiv + 238",
year = "1957",
LCCN = "QA76.5 .W52 1957",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also first edition \cite{Wilkes:1951:PPE}.",
URL = "https://b-ok.org/book/3668116/b363ff",
acknowledgement = ack-nhfb,
remark-1 = "According to \cite{Anderson:2019:SAM}, this book
discusses the computation of integer population counts
on the Electronic Delay Storage Automatic Calculator
(EDSAC) computer using a recursive divide-and-conquer
algorithm. See also somewhat negative 1958 review by
Fernando J. Corbat{\'o}
\cite{https://doi.org/10.1063/1.3062687}.
Floating-point arithmetic is discussed on pages 60,
90--91, and 135--137.",
remark-2 = "From page 5: ``Each storage location in the EDSAC
holds 17 binary digits. In words representing numbers,
the binary point is regarded as being to the right of
the extreme left-hand digit; this digit (the most
significant digit) is used as a sign indicator and is
referred to as the sign digit. \ldots{} the capacity of
the accumulator is 70 digits; there is, therefore,
plenty of room to hold the full 33-digit product of two
17-digit numbers. \ldots{} A negative number $-x$
(where $O < x \leq 1$) is represented by a $1$ in the
sign-digit position, followed by the digits of $(1 -
x)$; for example, $1.1100\ldots{}$ represents $-(1 -
3/4) = -1/4$. \ldots{}. Another way of explaining the
representation of negative numbers is to regard the
sign digit as an ordinary numerical digit, and to say
that $-x$ is stored as the number $(2 - x)$. Note in
particular that $1.0000\ldots{}$ represents $-1$.''
[Page 59 calls this a {\em True complements}
representation, distinguished from one's complement.]",
remark-3 = "From page 35: ``The EDSAC has a facility which enables
an even-numbered storage location and the following
odd-numbered storage to be used as a single storage
location holding 35 binary digits.'' [This suggests the
word size in 18, not 17 as page 5 suggests. The
Wikipedia article on the EDSAC reports: ``The EDSAC's
main memory consisted of 1024 locations, though only
512 locations were initially installed. Each contained
18 bits, but the topmost bit was always unavailable due
to timing problems, so only 17 bits were used.'']",
remark-4 = "From page 36: ``The multiplier register of the
arithmetical unit is of sufficient capacity to hold a
long number, and the accumulator is of sufficient
capacity to hold the complete (69) binary digit
[including the sign bit] product of two long
numbers.''",
remark-5 = "From page 36: ``In some calculations, long numbers may
not provide sufficient precision. In such cases, the
programmer may make use of what is known as
double-length or double-precision working, in which two
long storage locations are used to hold the digits of a
single number.'' [this would be a quad-word number
holding 69 bits, including the sign bit.].",
remark-6 = "From page 60: ``\ldots{} two double-length numbers,
each stored in two locations, can be added and the
result put in two locations in the store, by means of
six orders''.",
remark-7 = "From page 90: ``Each number is expressed in the form
$a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
p < 63$ and is represented in the store by $a \cdot
2^{-11} + p \cdot 2^{-6}$.''",
remark-8 = "From page 91: ``Numbers are expressed in the form $a
\cdot 10^p$, where $a$ and $p$ are packed into a single
storage location. The number of digits defining $p$ may
be varied from 4 to 15 by means of a preset parameter,
so that a suitable value for the permissible range of
variation of numbers may be selected for a given
calculation.''",
remark-9 = "From page 91: ``Although the use of floating-point
operation can simplify the programmer's task by
relieving him of undue preoccupation with scaling, it
must not be thought that it solves all his
difficulties. In particular, the loss of significant
digits resulting from the subtraction of a number from
a nearly equal number can have serious consequences
unless proper precautions are taken.''",
tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machine / 1 \\
1-3 The EDSAC / 3 \\
1-4 Store / 5 \\
1-5 Arithmetical unit / 5 \\
1-6 Form of numbers in the machine / 5 \\
1-7 Form of orders in the machine / 6 \\
1-8 Storage of orders / 6 \\
1-9 Written form of orders / 7 \\
1-10 Some simple examples / 7 \\
Exercises A / 9 \\
1-11 Jump orders / 9 \\
Exercises B / 11 \\
1-12 Repeated groups of orders / 11 \\
1-13 The use of the B-register / 15 \\
Exercises C / 18 \\
1-14 Equivalence between orders and numbers;
pseudo-orders / 18 \\
1-15 Use of the arithmetical unit for constructing or
modifying orders / 20 \\
1-16 The mix order / 23 \\
Exercises D / 24 \\
CHAPTER 2. SUBROUTINES / 25 \\
2-1 Introduction / 25 \\
2-2 Relative numbering of addresses / 25 \\
2-3 Internal and external forms of orders / 26 \\
2-4 Reading of orders from the input tape / 28 \\
2-5 Open and closed subroutines / 29 \\
2-6 Entering and leaving a closed subroutine / 29 \\
2-7 Closed B subroutines / 30 \\
2-8 Closed A subroutines / 31 \\
2-9 Use of library subroutines / 32 \\
Exercises E / 33 \\
2-10 Long numbers / 35 \\
2-11 Some further orders in the order code / 36 \\
2-12 Scale factors / 38 \\
2-13 Control combinations / 39 \\
Exercises F / 40 \\
2-14 Relative addresses in control combinations / 41
\\
2-15 Extension of the use of relative addresses / 41
\\
2-16 Setting of the constants to be added by terminal
code letters / 43 \\
2-17 Complete table of terminal code letters / 44 \\
2-18 Parameters / 45 \\
2-19 Preset parameters / 46 \\
2-20 Program parameters / 46 \\
2-21 Standard procedure for setting preset parameters /
46 \\
2-22 Interpretive subroutines / 47 \\
Exercises G / 49 \\
CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
3-1 Introduction / 51 \\
3-2 Single-address codes / 52 \\
3-3 Multi-address codes / 53 \\
3-4 Multiplication and division / 56 \\
3-5 Source-destination codes / 57 \\
3-6 Representation of negative numbers / 59 \\
3-7 Miscellaneous facilities / 60 \\
3-8 Minimum-access coding / 61 \\
3-9 The evaluation of an order code / 63 \\
3-10 Use of an auxiliary store / 64 \\
CHAPTER 4. INPUT AND OUTPUT / 66 \\
4-1 Introduction / 66 \\
4-2 Input of numbers / 66 \\
4-3 Output of numbers / 67 \\
4-4 Input of orders / 69 \\
4-5 Recognition of the code letter S / 72 \\
4-6 Economy of input and output time / 72 \\
4-7 Some features of input systems used with other
machines / 73 \\
4-8 Punched tape / 73 \\
4-9 Punched cards / 75 \\
CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
5-1 Introduction / 80 \\
5-2 Library catalog / 80 \\
5-3 Input subroutines / 81 \\
5-4 Output subroutines / 81 \\
5-5 Division subroutines / 82 \\
5-6 Trigonometric and other functions / 82 \\
5-7 The economization of a power series by the use of
Chebyshev polynomials / 83 \\
5-8 Quadrature / 86 \\
5-9 Integration of ordinary differential equations / 87
\\
5-10 Library subroutines Gl2 and G13: Runge--Kutta
processes / 88 \\
5-11 The independent variable / 88 \\
5-12 Definition of the Runge--Kutta--Gill process / 89
\\
5-13 Taylor-series method / 90 \\
5-14 Interpretive subroutines / 90 \\
5-15 Floating-point subroutines / 90 \\
CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
6-1 Introduction / 92 \\
6-2 Proofreading of programs / 93 \\
6-3 Punching / 93 \\
6-4 Locating mistakes in a program- / 94 \\
6-5 Subroutines for checking programs / 96 \\
6-6 The development of a program / 97 \\
CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
/ 99 \\
EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
EXAMPLE 2 The evaluation of a definite integral / 102
\\
EXAMPLE 3 Integration of an ordinary differential
equation / 108 \\
EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
EXAMPLE 5 Evaluation of a definite integral / 118 \\
CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
8-1 Introduction / 126 \\
8-2 Conversion versus interpretation / 127 \\
8-3 Assembly of a program / 127 \\
8-4 Floating addresses / 129 \\
8-5 Formula recognition / 136 \\
Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
139 \\
CATEGORY A. Subroutines to carry out floating-point
arithmetic / 140 \\
CATEGORY B. Subroutines to perform arithmetical
operations on complex numbers / 142 \\
CATEGORY C. Error-diagnosis subroutines / 144 \\
CATEGORY D. Division subroutines / 146 \\
CATEGORY E. Exponential subroutines / 148 \\
CATEGORY F. General subroutines relating to functions /
148 \\
CATEGORY G. Subroutines for the integration of
differential equations / 150 \\
CATEGORY L. Subroutines for evaluating logarithms / 153
\\
CATEGORY M. Miscellaneous subroutines / 154 \\
CATEGORY N. Operations on double-length numbers / 156
\\
CATEGORY P. Print subroutines / 158 \\
CATEGORY Q. Quadrature subroutines / 162 \\
CATEGORY R. Input subroutines / 164 \\
CATEGORY s. Subroutines for evaluating fractional
powers / 168 \\
CATEGORY T. Subroutines for calculating trigonometric
functions / 169 \\
CATEGORY Z. Post-mortem routines / 170 \\
PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
SUBROUTINES / 173 \\
APPENDIX 1. Input and output codes of the EDSAC / 212
\\
APPENDIX 2. Order code and controls of the EDSAC / 214
\\
APPENDIX 3. The initial input routine of the EDSAC /
218 \\
APPENDIX 4. Control combinations / 221 \\
APPENDIX 5. Specimen solutions to programming exercises
/ 223 \\
BIBLIOGRAPHY / 233 \\
INDEX / 237",
}
@Article{Beattie:1958:TFZ,
author = "Curtis L. Beattie",
title = "Table of First 700 Zeros of {Bessel} Functions --- {$
J_l(x) $} and {$ J^{\prime }_l(x) $}",
journal = j-BELL-SYST-TECH-J,
volume = "37",
number = "3",
pages = "689--697",
month = may,
year = "1958",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "65.00",
MRnumber = "0093928 (20 \#448)",
MRreviewer = "J. C. P. Miller",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1958/BSTJ.1958.3703.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol37/bstj37-3-689.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Belaga:1958:SPI,
author = "{\`E}. G. Belaga",
title = "Some problems involved in the calculation of
polynomials",
journal = j-DOKL-AKAD-NAUK,
volume = "123",
pages = "775--777",
year = "1958",
CODEN = "DANKAS",
ISSN = "0002-3264",
MRclass = "65.00",
MRnumber = "105192",
MRreviewer = "John Todd",
bibdate = "Fri Oct 20 10:34:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii Nauk SSSR",
journal-URL = "http://istina.msu.ru/journals/366838/",
keywords = "number of multiplications to evaluate a polynomial",
}
@Book{Bowman:1958:IBF,
author = "Frank Bowman",
title = "Introduction to {Bessel} Functions",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 135",
year = "1958",
LCCN = "QA408 .B68i 1958",
bibdate = "Sat Jan 15 17:24:26 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "An unabridged and unaltered republication of the first
edition.",
subject = "Bessel functions",
}
@Article{Dingle:1958:AEC,
author = "R. B. Dingle",
title = "Asymptotic Expansions and Converging Factors. {III}.
Gamma, Psi and Polygamma Functions, and {Fermi--Dirac}
and {Bose--Einstein} Integrals",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "244",
number = "1239",
pages = "484--490",
day = "22",
month = apr,
year = "1958",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
bibdate = "Mon Jun 18 07:22:24 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/100264",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series A,
Mathematical and physical sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/content/current",
}
@Article{Goldstein:1958:BFL,
author = "M. Goldstein and R. M. Thaler",
title = "{Bessel} Functions for Large Arguments",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "12",
number = "61",
pages = "18--26",
month = jan,
year = "1958",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1958-0102906-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kogbetliantz:1958:CANa,
author = "E. G. Kogbetliantz",
title = "Computation of Arctan {N} for $ - \infty < {N} < +
\infty $ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "1",
pages = "43--53",
month = jan,
year = "1958",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.21.0043",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65.3X",
MRnumber = "19,982e",
bibdate = "Wed Aug 31 13:40:00 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. B. Haselgrove",
}
@Article{Kogbetliantz:1958:CANb,
author = "E. G. Kogbetliantz",
title = "Computation of Arcsin {N} for $ 0 < {N} < 1 $ Using an
Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "3",
pages = "218--222",
month = jul,
year = "1958",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.23.0218",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65.3X",
MRnumber = "19,1197c",
bibdate = "Wed Aug 31 13:41:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. B. Haselgrove",
}
@Book{Lewin:1958:DAF,
author = "Leonard Lewin",
title = "Dilogarithms and Associated Functions",
publisher = "Macdonald",
address = "London, UK",
pages = "353",
year = "1958",
LCCN = "QA351 .L5",
bibdate = "Fri Jun 16 13:51:36 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "22-Jul-1919--13-Aug-2007",
author-url = "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
remark = "Foreword by J. C. P. Miller",
subject = "Dilogarithms",
}
@TechReport{Miller:1958:LNN,
author = "J. C. P. Miller",
title = "Lecture Notes on Numerical Analysis",
type = "Report",
institution = "Cambridge University",
address = "Cambridge, England",
year = "1958",
bibdate = "Fri Sep 20 14:46:35 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://www.youtube.com/watch?v=81YrRSeReKo",
acknowledgement = ack-nhfb,
remark-1 = "Cited in \cite[Reference 21]{Agarwal:1986:NSV} in
elefunt.bib and fparith.bib.",
remark-2 = "Page 135 of the Agarwal paper says ``Kahan has also
informed us that Miller [21] wrote about the
extra-accurate table idea in 1958.'' William M. Kahan
spent 1958--1960 in Cambridge, as a pro-forma student
of J. C. P. Miller --- Kahan already had a Ph.D. from
the University of Toronto, but it was not recognized by
Cambridge University! See the video interview in the
URL.",
}
@Article{Sugai:1958:ERR,
author = "Iwao Sugai",
title = "Extraction of Roots by Repeated Subtractions for
Digital Computers",
journal = j-CACM,
volume = "1",
number = "12",
pages = "6--8",
month = dec,
year = "1958",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/377924.377928",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sugai58;
https://www.math.utah.edu/pub/tex/bib/cacm1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Sugai58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sugai58",
}
@Article{Wadey:1958:TSR,
author = "W. G. Wadey",
title = "Two Square-Root Approximations",
journal = j-CACM,
volume = "1",
number = "11",
pages = "13--14",
month = nov,
year = "1958",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368932.368936",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Wadey58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}
@Article{Corbato:1959:GSB,
author = "Fernando J. Corbat{\'o} and Jack L. Uretsky",
title = "Generation of Spherical {Bessel} Functions in Digital
Computers",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "366--375",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Mon Dec 05 20:07:17 1994",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Davis:1959:LEI,
author = "Philip J. Davis",
title = "{Leonhard Euler}'s Integral: a Historical Profile of
the Gamma Function: In Memoriam: {Milton Abramowitz}",
journal = j-AMER-MATH-MONTHLY,
volume = "66",
number = "10",
pages = "849--869",
month = dec,
year = "1959",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2309786",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "00 (33.00)",
MRnumber = "MR0106810 (21 #5540)",
bibdate = "Mon Jun 28 12:39:33 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amermathmonthly1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2309786",
acknowledgement = ack-nhfb,
author-dates = "Philip J. Davis (2 January 1923--14 March 2018)",
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{DiDonato:1959:NFC,
author = "A. R. DiDonato and A. V. Hershey",
title = "New Formulas for Computing Incomplete Elliptic
Integrals of the First and Second Kind",
journal = j-J-ACM,
volume = "6",
number = "4",
pages = "515--526",
month = oct,
year = "1959",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320998.321005",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.00",
MRnumber = "0107353",
MRreviewer = "F. Stallmann",
bibdate = "Mon Dec 05 20:10:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Book{Emde:1959:TEF,
author = "Fritz Emde",
title = "{Tafeln Elementarer Funktionen} ({German}) [Tables of
Elementary Functions]",
publisher = "B. T. Teubner",
address = "Leipzig, Germany and Berlin, Germany",
edition = "Third",
pages = "xii + 181",
year = "1959",
LCCN = "QA47 .E5",
bibdate = "Fri Jun 11 12:34:09 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://lccn.loc.gov/61020314",
acknowledgement = ack-nhfb,
author-dates = "1873--1951",
language = "German",
}
@Article{Gautschi:1959:EIL,
author = "W. Gautschi",
title = "Exponential integral $ \int_1^\infty e^{-x t} t^{-n}
\, d t $ for large values of $n$",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "62",
number = "3",
pages = "123--125",
month = mar,
year = "1959",
DOI = "https://doi.org/10.6028/jres.062.022",
ISSN = "0091-0635",
bibdate = "Sat Feb 18 14:39:27 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
}
@Article{Goldstein:1959:RTC,
author = "M. Goldstein and R. M. Thaler",
title = "Recurrence Techniques for the Calculation of {Bessel}
Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "66",
pages = "102--108",
month = apr,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1959-0105794-5",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Greenhill:1959:AEF,
author = "Alfred George Greenhill",
title = "The Applications of Elliptic Functions",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xi + 357",
year = "1959",
bibdate = "Wed Mar 15 08:21:33 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Greenhill:1892:AEF}.",
acknowledgement = ack-nhfb,
author-dates = "1847--1927",
remark = "Reprint of \cite{Greenhill:1892:AEF}.",
}
@Article{Kogbetliantz:1959:CSC,
author = "E. G. Kogbetliantz",
title = "Computation of $ \sin {N} $, $ \cos {N} $, and $ {M} $
th Root of $ {N} $ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "3",
number = "2",
pages = "147--152",
month = apr,
year = "1959",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.32.0147",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65.00",
MRnumber = "21 \#964",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "B. A. Chartres",
}
@Article{Kreyszig:1959:RUE,
author = "Erwin Kreyszig and John Todd",
title = "The radius of univalence of the error function",
journal = j-NUM-MATH,
volume = "1",
pages = "78--89",
month = dec,
year = "1959",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 20:47:18 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Longman:1959:STT,
author = "I. M. Longman",
title = "A Short Table of $ \int^\infty_x {J}_0 (t)t^{-n} d t $
and $ \int^\infty_x {J}_1 (t) t^{-n} d t $ (in
{Technical Notes and Short Papers})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "306--311",
month = oct,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1959-0108892-5",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 6-digit values for $ n = 1, 2, \ldots {},
22 $ and for $ x = 1, 2, \ldots {}, 10 $.",
}
@Article{Luke:1959:ECH,
author = "Yudell L. Luke",
title = "Expansion of the Confluent Hypergeometric Function in
Series of {Bessel} Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "261--271",
month = oct,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1959-0107027-2",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Pan:1959:CSC,
author = "V. Ya. Pan",
title = "Certain schemes for the calculation of values of
polynomials with real coefficients",
journal = "Problemy Kibernetiki",
volume = "5",
number = "??",
pages = "17--29",
month = "????",
year = "1959",
bibdate = "Fri Oct 20 10:40:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Also available as English translation JPRS No.
11045.",
acknowledgement = ack-nhfb,
ajournal = "Probl. Kibernetiki",
keywords = "number of multiplications to evaluate a polynomial",
language = "Russian",
remark = "Check: MathSciNet does not cover this volume, or
record this paper, and the year may be wrong (based on
available volume/year list entries). Cited in
\cite[ref. 5, p. 178]{Fike:1967:MEP}.",
}
@Article{Pan:1959:SCP,
author = "V. Ya. Pan",
title = "Schemes for the computation of polynomials with real
coefficients",
journal = j-DOKL-AKAD-NAUK,
volume = "127",
number = "2",
pages = "266--269",
month = "????",
year = "1959",
CODEN = "DANKAS",
ISSN = "0002-3264",
bibdate = "Fri Oct 20 10:38:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii nauk SSSR",
journal-URL = "http://istina.msu.ru/journals/366838/",
keywords = "number of multiplications to evaluate a polynomial",
language = "Russian",
}
@Article{Sarafyan:1959:NMC,
author = "Diran Sarafyan",
title = "A New Method of Computation of Square Roots Without
Using Division",
journal = j-CACM,
volume = "2",
number = "11",
pages = "23--24",
month = nov,
year = "1959",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368481.368511",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}
@Article{Sherry:1959:CGF,
author = "M. E. Sherry and S. Fulda",
title = "Calculation of Gamma Functions to High Accuracy (in
{Technical Notes and Short Papers})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "314--315",
month = oct,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1959-0108891-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Stiefel:1959:NMT,
author = "Eduard L. Stiefel",
title = "Numerical methods of {Tchebycheff} approximation",
crossref = "Langer:1959:NAP",
pages = "217--232",
year = "1959",
MRclass = "65.00 (41.00)",
MRnumber = "0107961",
MRreviewer = "M. R. Hestenes",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
}
@Article{Strachey:1959:TSR,
author = "C. Strachey",
title = "On taking the square root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1950.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Volder:1959:CCT,
author = "Jack Volder",
title = "The {CORDIC} Computing Technique",
journal = "Proceedings of the Western Joint Computer Conference",
pages = "257--261",
year = "1959",
DOI = "https://doi.org/10.1145/1457838.1457886",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Article{Volder:1959:CTC,
author = "Jack E. Volder",
title = "The {CORDIC} Trigonometric Computing Technique",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "3",
pages = "330--334",
month = sep,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222693",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222693",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Anonymous:1960:BFP,
author = "Anonymous",
title = "{Bessel} Functions. {Part III}: {Zeros} and Associated
Values",
volume = "7",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "lx + 79",
year = "1960",
MRclass = "65.00",
MRnumber = "119441",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Prepared under the direction of the Bessel Functions
Panel of the Mathematical Tables Committee",
series = "Royal Society Mathematical Tables",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Anonymous:1960:EFG,
author = "Anonymous",
title = "Errata to {Fisher} and {Gupta}",
journal = j-TECHNOMETRICS,
volume = "2",
number = "4",
pages = "523--524",
month = nov,
year = "1960",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266462",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:29 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254224;
https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
note = "See \cite{Fisher:1960:PPD,Gupta:1960:OSG}.",
URL = "http://www.jstor.org/stable/1266462",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
subject-dates = "Sir Ronald Aylmer Fisher (17 February 1890--29 July
1962)",
}
@Article{Beam:1960:ACE,
author = "A. Beam",
title = "{Algorithm 14}: {Complex} exponential integral",
journal = j-CACM,
volume = "3",
number = "7",
pages = "406--406",
month = jul,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367349.367351",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:27 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Ei(z)$; special functions",
remark = "Fullerton: 30-line Algol procedure incorrectly
labelled algorithm 13.",
}
@Article{Fisher:1960:PPD,
author = "Ronald A. Fisher and E. A. Cornish",
title = "The Percentile Points of Distributions Having Known
Cumulants",
journal = j-TECHNOMETRICS,
volume = "2",
number = "2",
pages = "209--225",
month = may,
year = "1960",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266546",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:27 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254222;
https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
note = "See errata \cite{Anonymous:1960:EFG}.",
URL = "http://www.jstor.org/stable/1266546",
acknowledgement = ack-nhfb,
author-dates = "Sir Ronald Aylmer Fisher (17 February 1890--29 July
1962)",
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Book{Fox:1960:TWP,
author = "L. Fox",
title = "Tables of {Weber} Parabolic Cylinder Functions and
Other Functions for Large Arguments",
volume = "4",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "iii + 40",
year = "1960",
MRclass = "65.00 (33.00)",
MRnumber = "120778",
MRreviewer = "L. J. Slater",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Department of Scientific and Industrial Research",
series = "National Physical Laboratory Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Gupta:1960:OSG,
author = "Shanti S. Gupta",
title = "Order Statistics from the Gamma Distribution",
journal = j-TECHNOMETRICS,
volume = "2",
number = "2",
pages = "243--262",
month = may,
year = "1960",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266548",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
MRclass = "62.00",
MRnumber = "0112225 (22 \#3079)",
MRreviewer = "S. S. Wilks",
bibdate = "Sat Jun 21 13:17:27 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254222;
https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
note = "See errata \cite{Anonymous:1960:EFG}.",
URL = "http://www.jstor.org/stable/1266548",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Haimovici:1960:MRE,
author = "Corina Haimovici",
title = "A method of representing elementary functions in
algebras of finite order. ({Romanian})",
journal = "An. {\c{S}}ti. Univ. ``Al. I. Cuza'' Ia{\c{s}}i
Sec{\c{t}} I. (N.S.)",
volume = "6",
pages = "507--515",
year = "1960",
MRclass = "26.00",
MRnumber = "24 \#A1342",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Harumi:1960:VTN,
author = "Kasabur{\^o} Harumi and Shigetoshi Katsura and John W.
{Wrench, Jr.}",
title = "Values of {$ \frac {2}{\pi } \int^\infty_0 \Big (\frac
{\sin t}{t} \Big)^n d t $} (in {Technical Notes and
Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "72",
pages = "379--379",
month = oct,
year = "1960",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1960-0122010-7",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 10-digit table for $ n = 1, 2, \ldots {},
30 $.",
}
@InCollection{Kogbetliantz:1960:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of elementary functions",
crossref = "Ralston:1960:MMD",
pages = "7--35",
year = "1960",
MRclass = "68.00 (65.00)",
MRnumber = "22 \#8681",
MRreviewer = "J. C. P. Miller",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Lang:1960:ECC,
author = "H. A. Lang",
title = "On the Evaluation of Certain Complex Elliptic
Integrals (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "70",
pages = "195--199",
month = apr,
year = "1960",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1960-0112241-4",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Lebedev:1960:GMT,
author = "A. V. (Aleksandr Vasil'evich) Lebedev and R. M. (Rimma
Maksimova) Fedorova and Nina Mikhollovna Burunova",
title = "A Guide to Mathematical Tables",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xlvi + 586",
year = "1960",
LCCN = "Z6654.T3 L42",
bibdate = "Mon Feb 13 17:12:14 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "English edition prepared by D. G. Fry from the Russian
original.",
acknowledgement = ack-nhfb,
subject = "Mathematics; Tables; Indexes",
tableofcontents = "Front Cover \\
A Guide to Mathematical Tables \\
Copyright Page \\
Translator's Preface \\
Preface \\
Index to the Section Headings in the Table of Contents
of the Guide and the Supplement \\
Table of Contents \\
Part One: Description of the Tables \\
1. Powers, Rational and Algebraic Functions \\
Positive Whole Powers \\
Fractional Positive Powers \\
Reciprocals (Negative Whole and Fractional Powers) \\
Rational Functions \\
Algebraic Functions \\
Complex Numbers and Their Powers \\
2. Trigonometric Functions. Various Values Connected
With the Circle and the Sphere \\
Natural Values of Trigonometric Functions \\
Various Expressions Containing Trigonometric Functions
\\
Derivatives and Powers of Trigonometric Functions \\
Reciprocal Trigonometric Functions of A Complex
Variable \\
Geometric Quantities \\
Tables For Converting From One Angular Measure to
Another \\
3. Exponential and Hyperbolic Functions \\
Exponential Functions \\
Hyperbolic Functions \\
Expressions Containing Trigonometric and Hyperbolic
Functions \\
Inverse Hyperbolic Functions \\
4. Logarithms \\
Common Logarithms and Antilogarithms \\
Natural Logarithms \\
Logarithms to Base 2 \\
5. Factorials, Euler Integrals and Related Functions
\\
Factorials \\
the Gamma Function \\
the Psi Function and Its Derivatives \\
the Beta Function \\
Certain Constants \\
6. Sine and Cosine Integrals, Exponential and
Logarithmic Integrals and Related Functions \\
Sine and Cosine Integrals \\
Hyperbolic Sine and Cosine Integrals \\
Exponential Integral \\
Logarithmic Integral \\
Generalised and Composite Integral Functions \\
Integral Functions of Complex Argument \\
7. Probability Integrals and Related Functions \\
Functions of the Distribution of Probability and
Related Functions \\
Probability Integrals and Expressions Containing
Probability Integrals \\
Tables in Which the Integral Serves As the Argument \\
Probability Integrals of Complex Argument \\
Derivatives of Various Orders of Probability
Distribution Functions \\
Zeros of Probability Integrals \\
Logarithms of Probability Integrals \\
Fresnel Integrals and Related Functions \\
8. Elliptic Integrals and Elliptic Functions \\
Moduli of the Integrals \\
Complete Elliptic Integrals \\
Incomplete Elliptic Integrals \\
Elliptic Functions \\
Theta Functions \\
9. Legendre Functions and Polynomials \\
Legendre Polynomials and Legendre Functions of the
First Kind \\
Associated Legendre Functions of the First Kind \\
Roots of Legendre Functions \\
Various Expressions Containing Legendre Functions \\
10. Cylinder Functions \\
Cylinder Functions of the First and Second Kinds of
Real Argument \\
Riccati--Bessel Functions \\
Lommel Functions of Two Real Variables \\
Cylinder Functions of the Third Kind (Hankel Functions)
\\
Cylinder Functions of the First and Second Kinds of
Imaginary Argument \\
Lommel Functions of Two Imaginary Variables \\
Cylinder Functions of Complex Argument \\
Thomson Functions",
}
@Manual{Maehly:1960:ACD,
author = "Hans J. Maehly",
title = "Approximations for the {Control Data 1604}",
organization = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "ii + 44",
day = "15",
month = jan,
year = "1960",
bibdate = "Tue Nov 06 00:39:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.bitsavers.org/pdf/cdc/1604/Approximations_For_The_Control_Data_1604_Mar60.pdf",
acknowledgement = ack-nhfb,
keywords = "$\arctan(x)$; $\cos(x)$; $\exp(x)$; $\log(x)$;
$\sin(x)$; $\sqrt(x)$; $\tan(x)$; CDC 1604",
}
@Article{Philip:1960:FI,
author = "J. R. Philip",
title = "The function $ \operatorname {inverfc} \theta $",
journal = j-AUSTRALIAN-J-PHYS,
volume = "13",
number = "1",
pages = "13--20",
month = mar,
year = "1960",
CODEN = "AUJPAS",
DOI = "https://doi.org/10.1071/PH600013",
ISSN = "0004-9506 (print), 1446-5582 (electronic)",
ISSN-L = "0004-9506",
MRnumber = "22 9626",
bibdate = "Tue Sep 11 20:53:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "135.28302",
abstract = "The function inverfc $ \theta $ arises in certain
differential equations when concentration is taken as
an independent variable. It enters into a general
method of exact solution of the concentration-dependent
diffusion equation. An account is given of the
properties of this function, and of its derivatives and
integrals. The function\par
$$ B(\theta) = (2 / \pi^{1 / 2}) \exp [ - (\operatorname {inverfc} \theta)^2] $$
\noindent is intimately connected with the first
integral of inverfc $ \theta $ and with its
derivatives. Tables of $ \operatorname {inverfc} \theta
$ and $ B(\theta) $ are given.",
acknowledgement = ack-nhfb,
fjournal = "Australian Journal of Physics",
journal-URL = "http://www.publish.csiro.au/ph/content/allissues",
}
@Book{Rainville:1960:SF,
author = "Earl David Rainville",
title = "Special Functions",
publisher = pub-MACMILLAN,
address = pub-MACMILLAN:adr,
pages = "xii + 365",
year = "1960",
ISBN = "0-8284-0258-2",
ISBN-13 = "978-0-8284-0258-3",
LCCN = "QA331 R15; QA351 .R3 1971",
bibdate = "Mon Sep 3 16:04:28 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Reprinted in 1971.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Based upon the lectures on special functions which
\ldots{} [the author has] been giving at the University
of Michigan since 1946. Fullerton: All traditional
functions and polynomials are discussed in some
detail.",
shorttableofcontents = "1: Infinite Products \\
2: The Gamma and Beta Functions \\
3: Asymptotic Series \\
4: The Hypergeometric Function \\
5: Generalized Hypergeometric Functions \\
6: Bessel Functions \\
7: The Confluent Hypergeometric Function \\
8: Generating Functions \\
9: Orthogonal Polynomials \\
10: Legendre Polynomials \\
11: Hermite Polynomials \\
12: Laguerre Polynomials \\
13: The Sheffer Classification and Related Topics \\
14: Pure Recurrence Relations \\
15: Symbolic Relations \\
16: Jacobi Polynomials \\
17: Ultraspherical and Gegenbauer Polynomials \\
18: Other Polynomial Sets \\
19: Elliptic Functions \\
20: Theta Functions \\
21: Jacobian Elliptic Functions \\
Bibliography \\
Index",
subject = "Functions, Special",
tableofcontents = "1: Infinite Products \\
1. Introduction / 1 \\
2. Definition of an infinite product / 1 \\
3. A necessary condition for convergence . / 2 \\
4. The associated series of logarithms / 2 \\
5. Absolute convergence / 3 \\
6. Uniform convergence / 5 \\
\\
2: The Gamma and Beta Functions \\
7. The Euler or Mascheroni constant $\gamma$ / 8 \\
8. The Gamma function / 9 \\
9. A series for $\Gamma'(z) / \Gamma(z)$ / 10 \\
10. Evaluation of $\Gamma(1)$ and $\Gamma'(1)$ / 10 \\
11. The Euler product for $\Gamma(z)$ / 11 \\
12. The difference equation $\Gamma(z + 1) = z
\Gamma(z)$ / 12 \\
13. The order symbols $o$ and $O$ / 12 \\
14. Evaluation of certain infinite products / 13 \\
15. Euler's integral for $\Gamma(z)$ / 15 \\
16. The Beta function / 18 \\
17. The value of $\Gamma(z) \Gamma(1 - z)$ / 19 \\
18. The factorial function / 22 \\
19. Legendre's duplication formula / 23 \\
20. Gauss' multiplication theorem / 24 \\
21. A summation formula due to Euler / 26 \\
22. The behavior of $\log \Gamma(z)$ for large $|z|$ /
29 \\
\\
3: Asymptotic Series \\
23. Definition of an asymptotic expansion / 33 \\
24. Asymptotic expansions about infinity / 36 \\
25. Algebraic properties / 38 \\
26. Term-by-term integration / 39 \\
27. Uniqueness / 40 \\
28. Watson's lemma / 41 \\
\\
4: The Hypergeometric Function \\
29. The function $F(a, b; c; z)$ / 45 \\
30. A simple integral form / 47 \\
31. $F(a, b; c; 1)$ as a function of the parameters /
48 \\
32. Evaluation of $F(a, b; c; 1)$ / 48 \\
33. The contiguous function relations / 50 \\
34. The hypergeometric differential equation / 53 \\
35. Logarithmic solutions of the hypergeometric
equation / 54 \\
36. $F(a, b; c; 2)$ as a function of its parameters /
55 \\
37. Elementary series manipulations / 56 \\
38. Simple transformations / 58 \\
39. Relation between functions of $z$ and $1 - z$ / 61
\\
40. A quadratic transformation / 63 \\
41. Other quadratic transformations / 65 \\
42. A theorem due to Kummer / 68 \\
43. Additional properties / 68 \\
\\
5: Generalized Hypergeometric Functions \\
44. The function $_pF_q$ / 73 \\
45. The exponential and binomial functions / 74 \\
46. A differential equation / 74 \\
47. Other solutions of the differential equation / 76
\\
48. The contiguous function relations / 80 \\
49. A simple integral / 85 \\
50. The $_pF_q$ with unit argument / 85 \\
51. Saalsch{\"u}tz' theorem / 86 \\
52. Whipple's theorem / 88 \\
53. Dixon's theorem / 92 \\
54. Contour integrals of Barnes' type / 94 \\
55. The Barnes integrals and the function $_pF_q$ / 98
\\
56. A useful integral / 102 \\
\\
6: Bessel Functions \\
57. Remarks / 108 \\
58. Definition of $J_n(z)$ / 108 \\
59. Bessel's differential equation / 109 \\
60. Differential recurrence relations / 110 \\
61. A pure recurrence relation / 111 \\
62. A generating function / 112 \\
63. Bessel's integral / 114 \\
64. Index half an odd integer 114 , \\
65. Modified Bessel functions / 116 \\
66. Neumann polynomials / 116 \\
67. Neumann series / 119 \\
\\
7: The Confluent Hypergeometric Function \\
68. Basic properties of the $_1F_1$ / 123 \\
69. Kummer's first formula / 124 \\
70. Kummer's second formula / 125 \\
\\
8: Generating Functions \\
71. The generating function concept / 129 \\
72. Generating functions of the form $G(2 x t - t^2)$ /
131 \\
73. Sets generated by $e^t \psi(x t)$ / 132 \\
74. The generating functions $A(t) \exp[-x t / (1 -
t)]$ / 135 \\
75. Another class of generating functions / 137 \\
76. Boas and Buck generating functions / 140 \\
77. An extension / 143 \\
\\
9: Orthogonal Polynomials \\
78. Simple sets of polynomials / 147 \\
79. Orthogonality / 147 \\
80. An equivalent condition for orthogonality / 148 \\
81. Zeros of orthogonal polynomials / 149 \\
82. Expansion of polynomials / 150 \\
83. The three-term recurrence relation / 151 \\
84. The Christoffel--Darboux formula / 153 \\
85. Normalization; Bessel's inequality / 155 \\
\\
10: Legendre Polynomials \\
86. A generating function / 157 \\
87. Differential recurrence relations / 158 \\
88. The pure recurrence relation / 159 \\
89. Legendre's differential equation / 160 \\
90. The Rodrigues formula / 161 \\
91. Bateman's generating function / 162 \\
92. Additional generating functions / 163 \\
93. Hypergeometric forms of $P_n(x)$ / 163 \\
94. Brafman's generating functions / 167 \\
95. Special properties of $P_n(x)$ / 168 \\
96. More generating functions / 169 \\
97. Laplace's first integral form / 171 \\
98. Some bounds on $P_n(z)$ / 172 \\
99. Orthogonality / 173 \\
100. An expansion theorem / 176 \\
101. Expansion of $x^n$ / 179 \\
102. Expansion of analytic functions / 181 \\
\\
11: Hermite Polynomials \\
103. Definition of $H_n(x)$ / 187 \\
104. Recurrence relations / 188 \\
105. The Rodrigues formula / 189 \\
106. Other generating functions / 190 \\
107. Integrals / 190 \\
108. The Hermite polynomial as a $_2F_0$ / 191 \\
109. Orthogonality / 191 \\
110. Expansion of polynomials / 193 \\
111. More generating functions / 196 \\
\\
12: Laguerre Polynomials \\
112. The polynomial $L_n^{(\alpha)}(x)$ / 200 \\
113. Generating functions / 201 \\
114. Recurrence relations / 202 \\
115. The Rodrigues formula / 203 \\
116. The differential equation / 204 \\
117. Orthogonality / 204 \\
118. Expansion of polynomials / 206 \\
119. Special properties / 209 \\
120. Other generating functions / 211 \\
121. The simple Laguerre polynomials / 213 \\
\\
13: The Sheffer Classification and Related Topics \\
122. Differential operators and polynomial sets / 218
\\
123. Sheffer's $A$-type classification / 221 \\
124. Polynomials of Sheffer $A$-type zero / 222 \\
195. An extension of Sheffer's classification / 226 \\
126. Polynomials of $\sigma$-type zero / 228 \\
\\
14: Pure Recurrence Relations \\
127. Sister Celine's technique / 233 \\
128. A mild extension / 240 \\
\\
15: Symbolic Relations \\
129. Notation / 246 \\
130. Symbolic relations among classical polynomials /
247 \\
131. Polynomials of symbolic form $L_n(y(x))$ / 249 \\
\\
16: Jacobi Polynomials \\
132. The Jacobi polynomials / 254 \\
133. Bateman's generating function / 256 \\
134. The Rodrigues formula / 257 \\
135. Orthogonality / 258 \\
136. Differential recurrence relations / 261 \\
137. The pure recurrence relation / 263 \\
138. Mixed relations / 263 \\
139. Appell's functions of two variables / 265 \\
140. An elementary generating function / 269 \\
141. Brafman's generating functions / 271 \\
142. Expansion in series of polynomials / 272 \\
\\
17: Ultraspherical and Gegenbauer Polynomials \\
143. Definitions / 276 \\
144. The Gegenbauer polynomials / 277 \\
145. The ultraspherical polynomials / 283 \\
\\
18: Other Polynomial Sets \\
146. Bateman's $Z_n(x)$ / 285 \\
147. Rice's $H_n(\zeta, p, v)$ / 287 \\
148. Bateman's $F_n(z)$ / 289 \\
149. Sister Celine's polynomials / 290 \\
150. Bessel polynomials / 293 \\
151. Bedient's polynomials / 297 \\
152. Shively's pseudo-Laguerre and other polynomials /
298 \\
153. Bernoulli polynomials / 299 \\
154. Euler polynomials / 300 \\
155. Tchebicheff polynomials / 301 \\
\\
19: Elliptic Functions \\
156. Doubly periodic functions / 305 \\
157. Elliptic functions / 306 \\
158. Elementary properties / 306 \\
159. Order of an elliptic function / 308 \\
160. The Weierstrass function $P(z)$ / 309 \\
161. Other elliptic functions / 311 \\
162. A differential equation for $P(z)$ / 311 \\
163. Connection with elliptic integrals / 313 \\
\\
20: Theta Functions \\
164. Definitions / 314 \\
165. Elementary properties / 315 \\
166. The basic property table / 316 \\
167. Location of zeros / 319 \\
168. Relations among squares of theta functions / 322
\\
169. Pseudo addition theorems / 325 \\
170. Relation to the heat equation / 328 \\
171. The relation $\theta_1' = \theta_2 \theta_3
\theta_4$ / 329 \\
172. Infinite products / 332 \\
173. The value of $G$ / 334 \\
\\
21: Jacobian Elliptic Functions \\
174. A differential equation involving theta functions
/ 339 \\
175. The function $\sn(u)$ / 342 \\
176. The functions $\cn(u)$ and $\dn(u)$ / 343 \\
177. Relations involving squares / 344 \\
178. Relations involving derivatives / 345 \\
179. Addition theorems / 347 \\
\\
Bibliography / 349 \\
\\
Index / 359",
}
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367236.367267",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "M. Lotkin",
}
@Article{Sholander:1960:AEE,
author = "Marlow Sholander",
title = "Analytical expressions and elementary functions",
journal = j-AMER-MATH-MONTHLY,
volume = "67",
number = "3",
pages = "213--214",
month = mar,
year = "1960",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "26.00",
MRnumber = "22 \#9553",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2309678",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{Slater:1960:CHF,
author = "Lucy Joan Slater",
title = "Confluent hypergeometric functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "247",
year = "1960",
LCCN = "QA351 .S56",
bibdate = "Sat Oct 30 21:01:55 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Discussion of properties and 7 decimal
place tables of $_1 F_1 (a; b; x)$.",
subject = "Hypergeometric functions",
}
@Article{Traub:1960:CNM,
author = "J. F. Traub",
title = "Comments on a recent paper [{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = j-CACM,
volume = "3",
number = "2",
pages = "86--86",
month = feb,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366959.366989",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
abstract = "Mr. Diran Sarafyan, in his paper \booktitle{A New
Method of Computation of Square Roots Without Using
Divisions} (Communications, Nov. 1959) gave a way of
computing square roots which converges faster than the
standard Newton method. His technique can be
generalized as follows.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}
@Article{Ward:1960:CCE,
author = "Morgan Ward",
title = "The Calculation of the Complete Elliptic Integral of
the Third Kind",
journal = j-AMER-MATH-MONTHLY,
volume = "67",
number = "3",
pages = "205--213",
month = mar,
year = "1960",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2309677",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Tue Feb 6 16:32:27 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2309677",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
}
@Book{Warmus:1960:TEF,
author = "Mieczys{\l}aw Warmus",
title = "Tables of elementary functions",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "vii + 567",
year = "1960",
LCCN = "QA55 .W3 1960",
MRclass = "65.05",
MRnumber = "23 \#B1141",
MRreviewer = "J. C. P. Miller",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Pa{\'n}stwowe Wydawnictwo Naukowe, Warsaw. Separately
bound table of proportional parts, 30 pp.",
acknowledgement = ack-nhfb,
}
@Article{Wynn:1960:RAF,
author = "Peter Wynn",
title = "The Rational Approximation of Functions which are
Formally Defined by a Power Series Expansion",
journal = j-MATH-COMPUT,
volume = "14",
number = "70",
pages = "147--186",
month = apr,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Barakat:1961:EIG,
author = "Richard Barakat",
title = "Evaluation of the Incomplete Gamma Function of
Imaginary Argument by {Chebyshev} Polynomials",
journal = j-MATH-COMPUT,
volume = "15",
number = "73",
pages = "7--11",
month = jan,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Boersma:1961:TFR,
author = "J. Boersma",
title = "Two Formulas Relating to Elliptic Integrals of the
Third Kind (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "296--298",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Bowman:1961:IEF,
author = "Frank Bowman",
title = "Introduction to Elliptic Functions with Applications",
volume = "922",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "115",
year = "1961",
LCCN = "QA343 .B76 1961",
bibdate = "Wed Mar 15 06:50:49 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Unabridged and corrected republication of
\cite{Bowman:1953:IEF}.",
}
@Article{Cheney:1961:TNA,
author = "E. W. Cheney and H. L. Loeb",
title = "Two new algorithms for rational approximation",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "72--75",
month = dec,
year = "1961",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386002",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Corrington:1961:ACE,
author = "Murlan S. Corrington",
title = "Applications of the Complex Exponential Integral",
journal = j-MATH-COMPUT,
volume = "15",
number = "73",
pages = "1--6",
month = jan,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Ehrling:1961:NCI,
author = "G. Ehrling",
title = "On the Numerical Computation of Incomplete Elliptic
Integrals",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "1",
pages = "8--14",
month = mar,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01961946",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:06 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=1&spage=8",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Fields:1961:EHF,
author = "Jerry L. Fields and Jet Wimp",
title = "Expansions of Hypergeometric Functions in
Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "390--395",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Floyd:1961:ACE,
author = "Robert W. Floyd",
title = "An algorithm for coding efficient arithmetic
operations",
journal = j-CACM,
volume = "4",
number = "1",
pages = "42--51",
month = jan,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366062.366082",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:30 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/Compiler.Lins.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Robert W. Floyd (8 June 1936--25 September 2001)",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Description of binary subdivision method for computing
$n$-th powers in $ O(\log_2 (n))$ operations, as
referenced in \cite{Knuth:1962:EPC}.",
}
@Article{Froberg:1961:RCA,
author = "Carl-Erik Fr{\"o}berg",
title = "Rational {Chebyshev} Approximations of Elementary
Functions",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "4",
pages = "256--262",
month = dec,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933243",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See erratum \cite{Froberg:1963:ERC}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "elementary functions",
}
@Article{Gautschi:1961:RCR,
author = "Walter Gautschi",
title = "Recursive Computation of the Repeated Integrals of the
Error Function",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "227--232",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gray:1961:BFI,
author = "Marion C. Gray",
title = "{Bessel} functions of integral order and complex
argument",
journal = j-CACM,
volume = "4",
number = "4",
pages = "169--169",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366318",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "33.25",
MRnumber = "27\#1636",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The FORTRAN II source language [1, 2] places rather
severe restrictions on the form a subscript may take,
primarily because of the manner in which indices are
incremented in iterative loops. In the process of
constructing a compiler for a medium-sized (8008-word
memory) computer which will accept the FORTRAN II
source language, it became clear that the ``recursive
address calculation'' scheme, as used in the FORTRAN
compilers to minimize object-program running time, was
probably not the best one to use. This system,
described in some detail by Samelson and Bauer [3],
requires that the subscript expression be a linear
function of the subscripting variable. The alternative,
which requires complete evaluation of the ``storage
mapping function'', is usually rejected because of the
time required for the object program to perform the
necessary address calculation.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Bessel functions; special functions",
}
@Article{Herndon:1961:ABF,
author = "John R. Herndon",
title = "{Algorithm 57}: {Ber} or {Bei} Function",
journal = j-CACM,
volume = "4",
number = "4",
pages = "181--181",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366476",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "bei functions; ber functions; special functions",
remark = "Fullerton: 20-line Algol procedure that only sums
series.",
}
@Article{Herndon:1961:ACEa,
author = "John R. Herndon",
title = "{Algorithm 55}: {Complete} elliptic integral of the
first kind",
journal = j-CACM,
volume = "4",
number = "4",
pages = "180--180",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366454",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Herndon:1961:ACEb,
author = "John R. Herndon",
title = "{Algorithm 56}: {Complete} elliptic integral of the
second kind",
journal = j-CACM,
volume = "4",
number = "4",
pages = "180--181",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366474",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Herndon:1961:AEC,
author = "John R. Herndon",
title = "{Algorithm 46}: {Exponential} of a Complex Number",
journal = j-CACM,
volume = "4",
number = "4",
pages = "178--178",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366356",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\exp(z)$; $e^z$; elementary functions",
}
@Article{Herndon:1961:AGF,
author = "John R. Herndon",
title = "{Algorithm 54}: {Gamma} function for range $1$ to
$2$",
journal = j-CACM,
volume = "4",
number = "4",
pages = "180--180",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366453",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Gamma(x)$; special functions",
}
@Article{Herndon:1961:ASN,
author = "J. R. Herndon",
title = "{Algorithm 49}: {Spherical} {Neumann} Function",
journal = j-CACM,
volume = "4",
number = "4",
pages = "179--179",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.355579",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Coleman:1978:RSN}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Neumann functions; special functions",
}
@Book{Hochstadt:1961:SFM,
author = "Harry Hochstadt",
title = "Special functions of mathematical physics",
publisher = pub-HRW,
address = pub-HRW:adr,
pages = "viii + 81",
year = "1961",
ISBN = "0-236-73011-8",
ISBN-13 = "978-0-236-73011-7",
LCCN = "QA351 H65 1961",
bibdate = "Sat Oct 30 18:01:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
remark = "Reprinted 1966.",
}
@Article{L:1961:BRF,
author = "Y. L. L.",
title = "Book Review: {L. Fox, \booktitle{Tables of Weber
Parabolic Cylinder Functions and Other Functions for
Large Arguments}, National Physical Laboratory
Mathematical Tables Volume 4, Her Majesty's Stationery
Office, London, 1960, iii + 40 p., 28 cm.
(Paperback)}",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "310--311",
month = jul,
year = "1961",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-61-99215-8",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Nov 15 11:07:36 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2002928;
https://www.ams.org/journals/mcom/1961-15-075/S0025-5718-61-99215-8/S0025-5718-61-99215-8.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Y. L. L. == Yudell L. Luke",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Landau:1961:PSW,
author = "H. J. Landau and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {II}",
journal = j-BELL-SYST-TECH-J,
volume = "40",
number = "1",
pages = "65--84",
month = jan,
year = "1961",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.27",
MRnumber = "0140733 (25 \#4147)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-65.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Luke:1961:EHF,
author = "Yudell L. Luke and Richard L. Coleman",
title = "Expansion of Hypergeometric Functions in Series of
Other Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "233--237",
month = jul,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Rader:1961:CAC,
author = "P. J. Rader and Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 14 [not 13]}: {Complex}
exponential integral",
journal = j-CACM,
volume = "4",
number = "2",
pages = "105--105",
month = feb,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:30 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Ei(z)$; special functions",
remark = "Fullerton: It's accurate but sometimes slow.",
}
@Article{Slepian:1961:PSW,
author = "D. Slepian and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {I}",
journal = j-BELL-SYST-TECH-J,
volume = "40",
number = "1",
pages = "43--63",
month = jan,
year = "1961",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.27",
MRnumber = "0140732 (25 \#4146)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-43.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Book{Sneddon:1961:SFM,
author = "Ian Naismith Sneddon",
title = "Special Functions of Mathematical Physics and
Chemistry",
publisher = "Oliver and Boyd",
address = "Edinburgh, UK",
edition = "Ssecond",
pages = "184",
year = "1961",
LCCN = "QA331 .S65 1961",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "University mathematical texts",
acknowledgement = ack-nhfb,
remark = "See first edition \cite{Sneddon:1956:SFM} and third
edition {Sneddon:1980:SFM}",
}
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "409--417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.20",
MRnumber = "MR0134842 (24 \#B894)",
MRreviewer = "M. E. Rose",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "399--403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Weingarten:1961:TGC,
author = "Harry Weingarten and A. R. {Di Donato}",
title = "A Table of Generalized Circular Error",
journal = j-MATH-COMPUT,
volume = "15",
number = "74",
pages = "169--173",
month = apr,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Werner:1961:CAG,
author = "Helmut Werner and Robert Collinge",
title = "{Chebyshev} Approximations to the Gamma Function (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "15",
number = "74",
pages = "195--197",
month = apr,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wojcicki:1961:ABF,
author = "Maria E. Wojcicki",
title = "{Algorithm 44}: {Bessel} Functions Computed
Recursively",
journal = j-CACM,
volume = "4",
number = "4",
pages = "177--178",
month = apr,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355578.366341",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Bessel functions; special functions",
}
@Article{Albrecht:1962:FKM,
author = "J. Albrecht",
title = "{Fehlerschranken und Konvergenzbeschleunigung bei
einer monotonen oder alternierenden Iterationsfolge}.
({German}) [{Error} Bounds and Convergence Acceleration
with a Monotone or Alternating Iteration Sequence]",
journal = j-NUM-MATH,
volume = "4",
pages = "196--208",
month = dec,
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration",
language = "German",
}
@Article{Arscott:1962:BRI,
author = "F. M. Arscott",
title = "Book Review: {{\booktitle{Introduction to Elliptic
Functions with Applications}} (F. Bowman)}",
journal = j-SIAM-REVIEW,
volume = "4",
number = "4",
pages = "408--408",
month = "????",
year = "1962",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1004109",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:04:56 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/4/4;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1962",
}
@TechReport{Blanch:1962:TRR,
author = "Gertrude Blanch and Donald S. Clemm",
title = "Tables Relating to the Radial {Mathieu} Functions,
Vols. 1 \& 2",
type = "Report",
institution = "Aeronautical Research Labs. U. S. Government Printing
Office",
address = "Washington, DC, USA",
year = "1962",
bibdate = "Fri Oct 29 21:37:53 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Gertrude Blanch (1897--1996)",
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: 7-place tables.",
}
@Article{Boersma:1962:CLF,
author = "J. Boersma",
title = "On the Computation of {Lommel}'s Functions of Two
Variables (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "16",
number = "78",
pages = "232--238",
month = apr,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Lommel's functions are infinite sums
involving Bessel functions $ J_{\nu - 2m}(x) $.",
}
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "155--164",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219348",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Christiansen:1962:APC,
author = "S{\o}ren Christiansen",
title = "{Algol} Programming: Contribution no. 3: Calculation
of complementary {Fresnel} integrals",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "3",
pages = "192--194",
year = "1962",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:34:20 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: A 50-line Algol procedure is given. It
calculates $ \int_x^\infty \cos (t) / \sqrt {2 \pi t}
\, d t $ and $ \int_x^\infty \sin (t) / \sqrt {2 \pi t}
\, d t $.",
}
@Article{Cundiff:1962:AEA,
author = "John L. Cundiff",
title = "{Algorithm 88}: {Evaluation} of Asymptotic Expression
for the {Fresnel} Sine and Cosine Integrals",
journal = j-CACM,
volume = "5",
number = "5",
pages = "280--280",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: Can be used with algorithms 89 and 90.
30-line Algol procedure.",
}
@Article{Cundiff:1962:AEFa,
author = "John L. Cundiff",
title = "{Algorithm 89}: {Evaluation} of the {Fresnel} Sine
Integral",
journal = j-CACM,
volume = "5",
number = "5",
pages = "280--280",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "S(x); special functions",
remark = "Fullerton: 20-line Algol procedure that must be used
with algorithm 88.",
}
@Article{Cundiff:1962:AEFb,
author = "John L. Cundiff",
title = "{Algorithm 90}: {Evaluation} of the {Fresnel} Cosine
Integral",
journal = j-CACM,
volume = "5",
number = "5",
pages = "281--281",
month = may,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); special functions",
remark = "Fullerton: 20-line Algol procedure that must be used
with algorithm 88.",
}
@Article{DiDonato:1962:MCC,
author = "A. R. DiDonato and M. P. Jarnagin",
title = "A Method for Computing the Circular Coverage
Function",
journal = j-MATH-COMPUT,
volume = "16",
number = "79",
pages = "347--355",
month = jul,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{DiDonato:1962:MCG,
author = "A. R. DiDonato and M. P. Jamagin",
title = "A Method for Computing the Generalized Circular Error
Function and the Circular Coverage Function",
type = "NWL Report",
number = "1768",
institution = "Naval Surface Weapons Center",
address = "Dahlgren, VA 22448, USA",
day = "23",
month = jan,
year = "1962",
bibdate = "Wed Nov 12 15:56:35 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Dorn:1962:GHR,
author = "William S. Dorn",
title = "Generalizations of {Horner}'s rule for polynomial
evaluation",
journal = j-IBM-JRD,
volume = "6",
number = "2",
pages = "239--245",
month = apr,
year = "1962",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.62.0239",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65.50",
MRnumber = "24 \#B2541",
bibdate = "Tue Sep 11 16:10:28 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392358",
ZMnumber = "128.37202",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "D. H. Lehmer",
}
@Article{Fraser:1962:CRA,
author = "W. Fraser and J. F. Hart",
title = "On the computation of rational approximations to
continuous functions",
journal = j-CACM,
volume = "5",
number = "7",
pages = "401--403",
month = jul,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368273.368578",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:39 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
elementary functions; Remes algorithm; special
functions",
remark = "This paper outlines the Remes algorithm for ``for
finding polynomial approximations to the determination
of `best' rational approximations.''. It also gives
approximations for starting values of Newton--Raphson
iterations for $ \abs (x) $, $ \cos (x) $, $ \Gamma (1
+ x) $, and $ \sin (x) $.",
}
@Article{Hansen:1962:SRV,
author = "Eldon R. Hansen and Merrell L. Patrick",
title = "Some Relations and Values for the Generalized
{Riemann} Zeta Function",
journal = j-MATH-COMPUT,
volume = "16",
number = "79",
pages = "265--274",
month = jul,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Jefferson:1962:RAI,
author = "David K. Jefferson",
title = "Remark on {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "5",
number = "10",
pages = "514--514",
month = oct,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:41 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Knuth:1962:ECP,
author = "Donald E. Knuth",
title = "{Euler}'s Constant to $ 1271 $ Places",
journal = j-MATH-COMPUT,
volume = "16",
number = "79",
pages = "275--281",
month = jul,
year = "1962",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1962-0148255-X",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "10.41",
MRnumber = "26 #5763",
bibdate = "Fri Mar 22 18:03:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database; MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Knuth:1962:EPC,
author = "Donald E. Knuth",
title = "Evaluation of polynomials by computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355580.369074",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00 (12.00)",
MRnumber = "27 #970",
bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "The author reports that Motzkin (1962) showed that
Horner's rule for polynomial evaluation may not be
optimal, and develops the idea further for arbitrary
polynomials, but also observes that the coefficients of
the revised polynomials may be difficult to find. He
also asks about, but does not answer, the question of
error analysis of the various methods.",
}
@Article{Landau:1962:PSW,
author = "H. J. Landau and H. O. Pollak",
title = "Prolate spheroidal wave functions, {Fourier} analysis
and uncertainty. {III}. {The} dimension of the space of
essentially time- and band-limited signals",
journal = j-BELL-SYST-TECH-J,
volume = "41",
number = "4",
pages = "1295--1336",
month = jul,
year = "1962",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.28 (94.10)",
MRnumber = "0147686 (26 \#5200)",
MRreviewer = "I. Marx",
bibdate = "Tue Nov 9 11:15:54 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1962/BSTJ.1962.4104.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol41/bstj41-4-1295.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Merner:1962:AAC,
author = "J. N. Merner",
title = "{ACM Algorithm 149}: Complete Elliptic Integral",
journal = j-CACM,
volume = "5",
number = "12",
pages = "605",
month = dec,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Skovgaard:1978:RCE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Thacher:1962:CAB,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 57}: {$ \operatorname
{ber} $} or {$ \operatorname {bei} $} function",
journal = j-CACM,
volume = "5",
number = "8",
pages = "438--438",
month = aug,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:40 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "bei functions; ber functions; special functions",
remark = "Fullerton: The algorithm is inaccurate for large
$x$.",
}
@Article{Thacher:1962:CAH,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithms 191 and 192,
Hypergeometric and Confluent Hypergeometric
Functions}",
journal = j-CACM,
volume = "7",
number = "4",
pages = "244--244",
month = apr,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 11:27:28 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: An error in a comment is noted.",
}
@Article{Wimp:1962:PEB,
author = "Jet Wimp",
title = "Polynomial Expansions of {Bessel} Functions and Some
Associated Functions",
journal = j-MATH-COMPUT,
volume = "16",
number = "80",
pages = "446--458",
month = oct,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
note = "See corrigendum \cite{Wimp:1972:CPE}.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wynn:1962:AAP,
author = "P. Wynn",
title = "An Arsenal of {ALGOL} Procedures for Complex
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "4",
pages = "232--255",
month = dec,
year = "1962",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940171",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "ALGOL; complex arithmetic; confluence hypergeometric
function; continued fractions; incomplete beta
function; incomplete gamma function; Stieltjes
$S$-fractions; Weber parabolic cylinder function",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Barakat:1963:CES,
author = "Richard Barakat and Agnes Houston",
title = "{Chebyschev} Expansion of the Sine and Cosine
Integrals",
journal = j-J-MATH-PHYS-MIT,
volume = "42",
number = "1--4",
pages = "331--333",
month = apr,
year = "1963",
CODEN = "JMPHA9",
DOI = "https://doi.org/10.1002/sapm1963421331",
ISSN = "0097-1421",
ISSN-L = "0097-1421",
bibdate = "Sat Aug 19 13:36:07 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib",
URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1963421331",
acknowledgement = ack-nhfb,
ajournal = "J. Math. Phys. (MIT)",
fjournal = "Journal of Mathematics and Physics (MIT)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590",
onlinedate = "April 1963",
}
@Article{Burgoyne:1963:AKF,
author = "F. D. Burgoyne",
title = "Approximations to {Kelvin} Functions (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "17",
number = "83",
pages = "295--298",
month = jul,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 9-digit approximations.",
}
@Article{Carlitz:1963:IEF,
author = "L. Carlitz",
title = "The Inverse of the Error Function",
journal = j-PAC-J-MATH,
volume = "13",
number = "2",
pages = "459--470",
year = "1963",
CODEN = "PJMAAI",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
bibdate = "Thu Sep 13 21:30:05 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://pjm.math.berkeley.edu/pjm;
http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
}
@Article{Clenshaw:1963:ASF,
author = "C. W. Clenshaw and G. F. Miller and M. Woodger",
title = "Algorithms for Special Functions {I}",
journal = j-NUM-MATH,
volume = "4",
pages = "403--419",
month = dec,
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:21:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
remark = "Fullerton: ALGOL 60 procedures with accuracy $ \approx
10^{-15} $ for $ \exp $, $ \ln $, $ \sin $, $ \cos $, $
\tan $, $ \arcsin $, $ \arctan $, $ \gamma $, $ \Ei $
and $ \erf $. See G. F. Miller (1965) for
corrections.",
}
@Article{Eisman:1963:PER,
author = "S. H. Eisman",
title = "Polynomial Evaluation Revisited",
journal = j-CACM,
volume = "6",
number = "7",
pages = "384--385",
month = jul,
year = "1963",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366663.366668",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Erdelyi:1963:AEC,
author = "A. Erd{\'e}lyi and M. Wyman",
title = "The asymptotic evaluation of certain integrals",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "14",
number = "1",
pages = "217--260",
month = jan,
year = "1963",
CODEN = "AVRMAW",
DOI = "https://doi.org/10.1007/BF00250704",
ISSN = "0003-9527 (print), 1432-0673 (electronic)",
ISSN-L = "0003-9527",
bibdate = "Sat Feb 18 14:53:08 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/BF00250704",
acknowledgement = ack-nhfb,
fjournal = "Archive for rational mechanics and analysis",
journal-URL = "http://link.springer.com/journal/205",
keywords = "incomplete gamma function",
}
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting Approximations for the Iterative Calculation
of Square Roots",
journal = j-COMP-J,
volume = "6",
number = "3",
pages = "274--276",
month = nov,
year = "1963",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/6.3.274",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:30 MST 2012",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://comjnl.oxfordjournals.org/content/6/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Several starting approximations are given which, in
conjunction with a well-known iterative process, lead
to square root approximations, with a relative error in
the range $ (2^{-55}, 2^{-45}) $, at the expense of
three divisions. More accurate approximations are given
which require in addition a single multiplication.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fettis:1963:AMH,
author = "Henry E. Fettis",
title = "{Algorithm 163}: {Modified} {Hankel} function",
journal = j-CACM,
volume = "6",
number = "4",
pages = "161--162",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Hankel functions; special functions",
remark = "Fullerton: A 25-line Algol procedure for $ e^x K_p(x)
$.",
}
@Article{Froberg:1963:APC,
author = "Carl-Erik Fr{\"o}berg",
title = "{Algol} Programming: Contribution no. 5: Computation
of the {Fermi} function",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "3",
number = "2",
pages = "141--142",
year = "1963",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: The Fermi function depends on several
physical parameters of the atomic nucleus.",
}
@Article{Froberg:1963:ERC,
author = "C.-E. Fr{\"o}berg",
title = "Erratum: {``Rational Chebyshev Approximations of
Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261,
line 12]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "3",
number = "1",
pages = "68--68",
month = mar,
year = "1963",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01963538",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Froberg:1961:RCA}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "elementary functions",
}
@InProceedings{Gautschi:1963:RCS,
author = "Walter Gautschi",
editor = "????",
booktitle = "{The University of Michigan Engineering Summer
Conferences, Numerical Analysis, Summer 1963}",
title = "Recursive computation of special functions",
publisher = "????",
address = "????",
pages = "??--??",
year = "1963",
bibdate = "Fri Aug 21 11:08:35 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gray:1963:AFI,
author = "Malcolm D. Gray",
title = "{Algorithm 213}: {Fresnel} Integrals",
journal = j-CACM,
volume = "6",
number = "10",
pages = "617--617",
month = oct,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:49 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Gray:1964:CAF} and related
remark \cite{Gray:1963:RAE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); S(x); special functions",
}
@Article{Gray:1963:RAE,
author = "Malcolm D. Gray",
title = "Remark on Algorithms 88, 89, and 90 evaluation of the
{Fresnel} integrals",
journal = j-CACM,
volume = "6",
number = "10",
pages = "618--618",
month = oct,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:49 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: An error is noted.",
}
@Article{Hofsommer:1963:NCE,
author = "D. J. Hofsommer and R. van de Riet",
title = "On the numerical calculation of elliptic integrals of
the first and second kind and the elliptic functions of
{Jacobi}",
journal = j-NUM-MATH,
volume = "5",
pages = "291--302",
month = dec,
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Ibbetson:1963:AG,
author = "D. Ibbetson",
title = "{Algorithm 209}: {Gauss}",
journal = j-CACM,
volume = "6",
number = "10",
pages = "616--616",
month = oct,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:49 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Knuth:1963:LEE,
author = "Donald E. Knuth",
title = "Letter to the {Editor}: {Evaluation} of polynomials by
computer",
journal = j-CACM,
volume = "6",
number = "2",
pages = "51--51",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Dec 26 16:31:38 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Knuth:1962:EPC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Lee-Whiting:1963:EFC,
author = "G. E. Lee-Whiting",
title = "Erratum: ``{Formulas} for Computing Incomplete
Elliptic Integrals of the First and Second Kinds''",
journal = j-J-ACM,
volume = "10",
pages = "412--412",
year = "1963",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Dec 10 15:59:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Lee-Whiting:1963:FCI}.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
xxmonth = "none",
xxnumber = "none",
}
@Article{Lee-Whiting:1963:FCI,
author = "G. E. Lee-Whiting",
title = "Formulas for Computing Incomplete Elliptic Integrals
of the First and Second Kinds",
journal = j-J-ACM,
volume = "10",
number = "2",
pages = "126--130",
month = apr,
year = "1963",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Nov 05 22:55:28 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Lee-Whiting:1963:EFC}.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Book{Ljusternik:1963:MVF,
author = "L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R.
Janpol{\'s}ki{{\u{\i}}}",
title = "{{\cyr Matematicheski{\u{\i}}analiz. Vychislenie
{\`e}lementarnykh funktsi{\u{\i}}}}. [Mathematical
analysis. {Computation} of the elementary functions]",
publisher = "Gosudarstv. Izdat. Fiz-Mat. Lit.",
address = "Moscow, USSR",
pages = "247",
year = "1963",
MRclass = "65.25",
MRnumber = "28 \#1733",
MRreviewer = "John Todd",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ludwig:1963:AIB,
author = "Oliver G. Ludwig",
title = "{Algorithm 179}: {Incomplete} beta ratio",
journal = j-CACM,
volume = "6",
number = "6",
pages = "314--314",
month = jun,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Pike:1976:RIB,Bosten:1974:RAI}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: This algorithm is the basis for a modern
treatment by Bosten and Battiste.",
}
@Article{Meyer:1963:CAI,
author = "Noelle A. Meyer",
title = "Certification of {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "6",
number = "2",
pages = "69--69",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:44 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Newman:1963:ICS,
author = "J. N. Newman and W. Frank",
title = "An Integral Containing the Square of a {Bessel}
Function",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "64--70",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: The integral $ I_n^m(x) = \int_0^{\pi / 2}
\frac {J_n^2(x \cos (\theta))}{(x \cos (\theta))^{2m}}
\, d \theta $, where $m$ and $n$ are either integers or
half integers, is considered.",
}
@Article{Peuizulaev:1963:AEF,
author = "{\v{S}}. I. Pe{\u{\i}}zulaev",
title = "An approximation by elementary functions.
({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
volume = "3",
pages = "769--770",
year = "1963",
MRclass = "41.30",
MRnumber = "28 \#398",
MRreviewer = "D. D. Stancu",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Relph:1963:AAH,
author = "A. P. Relph",
title = "{ACM Algorithm 191}: Hypergeometric",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--389",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:32:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Koppelaar:1974:CRA}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Relph:1963:ACH,
author = "A. P. Relph",
title = "{Algorithm 192}: {Confluent} hypergeometric",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--388",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: 30-line Algol procedure for complex args.
The work of Luke supersedes this.",
}
@Article{Relph:1963:AH,
author = "A. P. Relph",
title = "{Algorithm 191}: {Hypergeometric}",
journal = j-CACM,
volume = "6",
number = "7",
pages = "388--388",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Koppelaar:1974:CRA}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: 30-line Algol procedure. The work of Luke
is better.",
}
@Article{Rutishauser:1963:BQG,
author = "H. Rutishauser",
title = "{Betrachtungen zur Quadratwurzeliteration}. ({German})
[{Considerations} on square root iteration]",
journal = j-MONAT-MATH,
volume = "67",
pages = "452--464",
year = "1963",
CODEN = "MNMTA2",
DOI = "https://doi.org/10.1007/BF01295091",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
MRclass = "65.50",
MRnumber = "158532",
MRreviewer = "A. S. Householder",
bibdate = "Mon Aug 24 21:56:15 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Heinz Rutishauser (30 January 1918--10 November
1970)",
fjournal = "Monatshefte f{\"u}r Mathematik",
journal-URL = "http://link.springer.com/journal/605",
language = "German",
}
@Book{Sneddon:1963:SFM,
author = "Ian Naismith Sneddon",
title = "{Spezielle Funktionen der mathematischen Physik und
Chemie. Mathematische Formelsammlung II}. ({German})
[Special {functions} of mathematical physics and
chemistry. {Mathematical} formula collection {II}]",
volume = "54",
publisher = pub-BIBLIO-INST,
address = pub-BIBLIO-INST:adr,
pages = "166",
year = "1963",
LCCN = "QA351 .S6415",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "B. I.-Hochschultaschenb{\"u}cher",
acknowledgement = ack-nhfb,
language = "German",
remark = "German translation of \cite{Sneddon:1961:SFM}.",
subject = "Functions; Mathematical physics",
}
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
title = "A circuit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}
@Article{Sweeney:1963:CEC,
author = "Dura W. Sweeney",
title = "On the Computation of {Euler}'s Constant",
journal = j-MATH-COMPUT,
volume = "17",
number = "82",
pages = "170--178",
month = apr,
year = "1963",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1963-0160308-X",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 3566 digits should be enough.",
}
@Article{Thacher:1963:ACEa,
author = "Henry C. {Thacher, Jr.}",
title = "{Algorithm 165}: {Complete} elliptic integrals",
journal = j-CACM,
volume = "6",
number = "4",
pages = "163--164",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Thacher:1963:CACa,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 55}: {Complete} elliptic
integral of the first kind",
journal = j-CACM,
volume = "6",
number = "4",
pages = "166--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Thacher:1963:CACb,
author = "Henry C. {Thacher, Jr.}",
title = "Certification of {Algorithm 149}: {Complete} elliptic
integral",
journal = j-CACM,
volume = "6",
number = "4",
pages = "166--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Book{Tocher:1963:AS,
author = "K. D. Tocher",
title = "The Art of Simulation",
publisher = "Van Nostrand",
address = "Princeton, NJ, USA",
pages = "viii + 184",
year = "1963",
LCCN = "TA177 .T6",
bibdate = "Sat Dec 16 17:47:12 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Simulation methods",
}
@Article{vandeRiet:1963:CAI,
author = "R. P. van de Riet",
title = "Certification of {Algorithm 73}: {Incomplete} elliptic
integrals",
journal = j-CACM,
volume = "6",
number = "4",
pages = "167--167",
month = apr,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:46 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Werner:1963:AFI,
author = "H. Werner and G. Raymann",
title = "An Approximation to the {Fermi} Integral {$ F_{1 /
2}(x) $}",
journal = j-MATH-COMPUT,
volume = "17",
number = "82",
pages = "193--194",
month = apr,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2003641",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors of $ 5 \times 10^{-4} $.",
}
@Article{Whittlesey:1963:IGF,
author = "John R. B. Whittlesey",
title = "Incomplete Gamma Functions for Evaluating {Erlang}
Process Probabilities",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "11--17",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InCollection{Abramowitz:1964:CWF,
author = "Milton Abramowitz",
title = "{Coulomb} Wave Functions",
crossref = "Abramowitz:1964:HMF",
pages = "537--554",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Abramowitz:1964:SFR,
author = "Milton Abramowitz",
title = "{Struve} Functions and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "495--502",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
title = "Proposed automatic calculating machine",
journal = j-IEEE-SPECTRUM,
volume = "1",
number = "8",
pages = "62--69",
month = aug,
year = "1964",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1964.6500770",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Tue Jan 14 11:14:17 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
abstract = "Here presented is the memorandum that 20 years ago
initiated a series of events whose revolutionary
implications are only beginning to manifest themselves
a description of the first large-scale general-purpose
automatic digital computer. Twenty years ago, on August
7, 1944, Mark I, the first large-scale general-purpose
automatic digital computer ever to be put in operation
was dedicated at Harvard University by James B. Conant,
then president of Harvard, and the late Thomas J.
Watson, founder of IBM.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
remark = "Pages 66--69 discuss computation of the elementary
functions with minimal intermediate storage: recipes
are given for integral and fractional power, log,
exponential, trigonometric, inverse trigonometric,
hyperbolic, and inverse hyperbolic. Mention is also
made of the probability integral, elliptic functions,
and Bessel functions, but the text says they will be
discussed later (meaning, in a future publication). The
methods involve recurrences and series summations, and
thus, can be regarded as precision independent.",
xxnote = "Previously unpublished memorandum written by Aiken and
dated by an unknown recipient as 4 November 1937.
Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
}
@InCollection{Antosiewicz:1964:BFF,
author = "H. A. Antosiewicz",
title = "{Bessel} Functions of Fractional Order",
crossref = "Abramowitz:1964:HMF",
pages = "435--478",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Blanch:1964:MF,
author = "Gertrude Blanch",
title = "{Mathieu} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "721--750",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "1897--1996",
citedby = "Fullerton:1980:BEM",
}
@Article{Bray:1964:CAGa,
author = "T. A. Bray",
title = "Certification of {Algorithm 225}: {Gamma} function
with controlled accuracy",
journal = j-CACM,
volume = "7",
number = "10",
pages = "586--586",
month = oct,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Gamma(x)$; special functions",
remark = "Fullerton: No corrections were necessary.",
}
@Article{Burgoyne:1964:GTF,
author = "F. D. Burgoyne",
title = "Generalized Trigonometric Functions (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "18",
number = "86",
pages = "314--316",
month = apr,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1964:DPS,
author = "William J. {Cody, Jr.}",
title = "Double-Precision Square Root for the {CDC-3600}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "715--718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:57 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC-1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has built-in
double-precision floating-point arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a double-precision subroutine for the
3600.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$sqrt(x)$; CDC 3600; elementary functions;
floating-point arithmetic",
}
@Article{Cowgill:1964:LEB,
author = "D. Cowgill",
title = "Logic Equations for a Built-In Square Root Method",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "156--157",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263791",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Curtiss:1964:EIB,
author = "C. F. Curtiss",
title = "Expansions of Integrals of {Bessel} Functions of Large
Order",
journal = j-J-MATH-PHYS,
volume = "5",
number = "4",
pages = "561--564",
month = apr,
year = "1964",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1704149",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 08:40:12 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v5/i4/p561_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "22 December 2004",
pagecount = "4",
}
@Article{Cyvin:1964:AGF,
author = "S. J. Cyvin and B. N. Cyvin",
title = "{Algorithm 225}: {Gamma} function with controlled
accuracy",
journal = j-CACM,
volume = "7",
number = "5",
pages = "295--295",
month = may,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:53 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Gamma(x)$; special functions",
remark = "Fullerton: 30-line Algol procedure based on
out-of-date method.",
}
@Article{Cyvin:1964:AND,
author = "S. J. Cyvin",
title = "{Algorithm 226}: {Normal} distribution function",
journal = j-CACM,
volume = "7",
number = "5",
pages = "295--295",
month = may,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/364099.364315",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:53 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
}
@InCollection{Davis:1964:GFR,
author = "Philip J. Davis",
title = "Gamma Function and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "253--294",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Eve:1964:EP,
author = "J. Eve",
title = "The evaluation of polynomials",
journal = j-NUM-MATH,
volume = "6",
number = "1",
pages = "17--21",
month = dec,
year = "1964",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386049",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "number of multiplications to evaluate a polynomial",
remark = "From the first two paragraphs: ``Ostrowski [5] has
shown that the $ 2 n $ operations required by this
algorithm [Horner's] are minimal for $ n \leq 4 $.
Motzkin [4] (see also Todd [8]) and Knuth [3] have
given methods whereby polynomials with $ 4 \leq n \leq
6 $ can be evaluated in $ [(1 / 2)(n + 3)] $
multiplications and not more than $ n + 1 $ additions.
Similar methods effecting a reduction in the number of
multiplications have been described by Pan [6] for $ n
\leq 12 $. Each of these methods is valid only for a
particular value of $n$.\par A general method due to
Pan [7] applicable to all polynomials with $ n \geq 5 $
results in an evaluation involving $ [(1 / 2) (n + 4)]
$ multiplications and $ n + 1 $ additions. Knuth has
also given a method applicable to all polynomials with
$ n \geq 3 $ in which $ n + 1 $ additions are required
while the number of multiplications varies between $
[(1 / 2) (n + 3)] $ and approximately $ (3 / 4)n $.''",
}
@TechReport{Fisherkeller:1964:TCE,
author = "M. A. Fisherkeller and W. J. {Cody, Jr.}",
title = "Tables of the Complete Elliptic Integrals $ {K} $, $
{K}' $, $ {E} $, and $ {E}' $",
type = "Technical Memo",
number = "ANL AMD 71",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "14",
year = "1964",
bibdate = "Thu Nov 17 10:44:21 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See review by John W. Wrench in Mathematics of
Computation, {\bf 19}(89--92), 342, 1965.",
acknowledgement = ack-nhfb,
}
@Article{Gargantini:1964:RCA,
author = "I. Gargantini and T. Pomentale",
title = "Rational {Chebyshev} approximations to the {Bessel}
function integrals {$ K i_s(x) $}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "727--730",
month = dec,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "31\#863",
bibdate = "Fri Nov 25 18:19:57 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The second Remes algorithm is used to approximate the
integrals $ K i_s $ by rational functions. The related
coefficients for the approximations of $ K i_1, K i_2,
K i_3 $ are given for different precisions.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Bessel functions; Kis(x); special functions",
remark = "Fullerton: Approximations for repeated integrals $
\operatorname {Ki}_s(x) $ of $ K(x) $ for $ s = 1, 2, 3
$ are given for accuracies down to $ 10^{-5} $ for $ s
= 1 $ and to $ 10^{-7} $ for $ s = 2, 3 $.",
}
@Article{Gautschi:1964:AAB,
author = "W. Gautschi",
title = "{ACM Algorithm 236}: {Bessel} Functions of the First
Kind [{S17}]",
journal = j-CACM,
volume = "7",
number = "8",
pages = "479--480",
month = aug,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355586.355587",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:55 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See remark \cite{Skovgaard:1975:RBF}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$J_n(x)$; Bessel functions of the first kind; special
functions",
}
@Article{Gautschi:1964:AGF,
author = "Walter Gautschi",
title = "{Algorithm 221}: {Gamma} functions",
journal = j-CACM,
volume = "7",
number = "3",
pages = "143--143",
month = mar,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:52 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\Gamma(x)$; special functions",
}
@Article{Gautschi:1964:AIB,
author = "Walter Gautschi",
title = "{Algorithm 222}: {Incomplete} beta functions ratios",
journal = j-CACM,
volume = "7",
number = "3",
pages = "143--143",
month = mar,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:52 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "beta functions; special functions",
remark = "Fullerton: 200-line Algol procedure.",
}
@Article{Gautschi:1964:CAI,
author = "Walter Gautschi",
title = "Certification of {Algorithm 222}: {Incomplete} beta
function ratios",
journal = j-CACM,
volume = "7",
number = "4",
pages = "244--244",
month = apr,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:53 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "beta functions; special functions",
remark = "Fullerton: A typographical error is noted.",
}
@InCollection{Gautschi:1964:EFF,
author = "Walter Gautschi",
title = "Error Function and {Fresnel} Integrals",
crossref = "Abramowitz:1964:HMF",
pages = "295--330",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Gautschi:1964:EIR,
author = "Walter Gautschi and William F. Cahill",
title = "Exponential Integral and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "227--252",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Gray:1964:CAF,
author = "Malcolm Gray",
title = "Certification of {Algorithm 213}: {Fresnel}
integrals",
journal = j-CACM,
volume = "7",
number = "11",
pages = "661--661",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gray:1963:AFI,Gray:1963:RAE}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); S(x); special functions",
remark = "Fullerton: Several corrections are given.",
}
@InCollection{Haynsworth:1964:BEP,
author = "Emilie V. Haynsworth and Karl Goldberg",
title = "{Bernoulli} and {Euler} Polynomials, {Riemann Zeta}
Function",
crossref = "Abramowitz:1964:HMF",
pages = "803--820",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Hochstrasser:1964:OP,
author = "Urs W. Hochstrasser",
title = "Orthogonal Polynomials",
crossref = "Abramowitz:1964:HMF",
pages = "771--802",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Hummer:1964:EDF,
author = "David G. Hummer",
title = "Expansions of {Dawson}'s Function in a Series of
{Chebyshev} Polynomials (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "18",
number = "86",
pages = "317--319",
month = apr,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Almost l5-digit approximations.",
}
@Article{Lanczos:1964:PAG,
author = "Cornelius Lanczos",
title = "A Precision Approximation of the Gamma Function",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "1",
number = "1",
pages = "86--96",
month = "????",
year = "1964",
DOI = "https://doi.org/10.1137/0701008",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
ISSN-L = "0887-459X",
MRclass = "33.15",
MRnumber = "0176115 (31 \#390)",
MRreviewer = "S. C. van Veen",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2949767",
ZMnumber = "Zbl 0136.05201",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics: Series B, Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
}
@Article{Lotsch:1964:AFI,
author = "Helmut Lotsch and Malcolm Gray",
title = "{Algorithm 244}: {Fresnel} Integrals [{S20}]",
journal = j-CACM,
volume = "7",
number = "11",
pages = "660--661",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:56 MST 2005",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "This procedure computes the Fresnel sine and cosine
integrals $ C(w) = \int_0^\infty \cos [(\pi / 2)t^2] \,
d t $ and $ S(w) = \int_0^w \sin [(\pi / 2)t^2] \, d t
$. It is a modification of Algorithm 213 (Comm. ACM, 6
(Oct. 1963), 617) such that the accuracy, expressed by
\textit{eps}, is improved. eps can arbitrarily be
chosen up to $ \textit {eps} = 10^{-6} $ for a computer
with sufficient word length as, for example, the
Burroughs B5000 which has 11--12 significant digits.
Referring to the formulas of Algorithm 213: if $ |w| <
\sqrt {(26.20 / \pi)} $ the series expansions $ C(w) $
and $ S(w) $ are terminated when the absolute value of
the relative change in two successive terms is $ \leq
\textit {eps} $. If $ |w| \geq \sqrt {(26.20 / \pi)} $
the series $ Q(x) $ and $ P(x) $ are terminated when
the absolute value of the terms is $ \leq \textit {eps}
/ 2 $. However, this truncation point is not
necessarily valid for the range $ \sqrt {(26.20 / \pi)}
\leq |w| < \sqrt {(28.50 / \pi)} $ when $ \textit {eps}
= 10^{-6} $, since the asymptotic series must be
terminated before arriving at the minimum. In this
range the ignored terms of the series expansions are $
< 3 \times 10^6 $, and for larger arguments $ < 10^{-6}
$. This accuracy may be improved if desired: the
switch-over point from the regular to the asymptotic
series expansions has to be displaced to larger
arguments.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "C(x); Fresnel integrals; S(x); special functions",
remark = "Fullerton: 100-line Algol procedure.",
}
@InCollection{Lowan:1964:SWF,
author = "Arnold N. Lowan",
title = "Spheroidal Wave Functions",
crossref = "Abramowitz:1964:HMF",
pages = "751--770",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Luke:1964:IBF,
author = "Yudell L. Luke",
title = "Integrals of {Bessel} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "479--494",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Book{Meinardus:1964:AFI,
author = "Gunter Meinardus",
title = "{Approximation von Funktionen und ihre numerische
Behandlung}. ({German}) [{Approximation} of functions
and their numerical treatment]",
volume = "4",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 180",
year = "1964",
DOI = "https://doi.org/10.1007/978-3-642-85646-4",
ISBN = "3-540-03219-3, 3-642-85646-2, 3-642-85647-0 (print)",
ISBN-13 = "978-3-540-03219-9, 978-3-642-85646-4,
978-3-642-85647-1 (print)",
LCCN = "QA320 .M4",
bibdate = "Thu Oct 19 17:00:27 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Springer tracts in natural philosophy",
abstract = "[numerous OCR errors to be corrected] Erst in den
letzten Jahren hat sich derjenige Tell der
Approximations theorie, der sich auf numerische
Fragestellungen anwenden l{\"a}{\ss}t, starker
entwickelt. Das Prinzip der in einem gewissen Sinne
besten Ann{\"a}herung von Funktionen gewann
insbesondere durch die Verwendung elektronischer
Rechenmaschinen an Bedeutung. Einige der theoretischen
Grundlagen, die zur Behandlung der auftretenden
Probleme herange zogen werden mussen, finden sich
verstreut in wenigen Buchern. Der weitaus gro{\ss}te
Teil der theoretischen und praktischen Untersuchungen
ist jedoch nur in den Originalarbeiten nachzulesen.
Hieraus ergab sich die Zielsetzung des vorliegenden
Buches: Es sollte eine Zusammen stellung der
wesentlichen Ergebnisse der Approximationstheorie
gegeben werden, die einerseits ein rasches Eindringen
in die modernen Entwicklungen dieses Gebietes
ermoglicht und andererseits eine gewisse
Vollst{\"a}ndigkeit auf dem Problemkreis der
Tschebyscheff-Approximationen bietet, womit keineswegs
gemeint ist, da{\ss} eine vollst{\"a}ndige Literatur
{\"u}bersicht angestrebt wurde. Die Auswahl erfolgte
stets nach dem immer noch subjektiven Gesichtspunkt der
Bedeutung f{\"u}r die Anwendungen. Dies gilt z. B. auch
f{\"u}r die asymptotischen Untersuchungen des {\S} 3,
denn ich bin der Meinung, da{\ss} man sich auch
beinumerischen Approximationen {\"u}ber die, wenigstens
asymptotisch zu erwartende Genauigkeit Gedanken machen
sollte. Fast ausschlie{\ss}lich habe ich mich auf die
Theorie der gleich m{\"a}{\ss}igen Approximation
beschr{\"a}nkt, da diese die weitaus gro{\ss}te
praktische Bedeutung besitzt. Das erste Kapitel
behandelt lineare Approximationen. Der {\S} 3
enth{\"a}lt wohl den heute k{\"u}rzesten Zugang zur
linearen Theorie.",
acknowledgement = ack-nhfb,
author-dates = "1926--",
language = "German",
subject = "Aproximaciones",
tableofcontents = "I Lineare Approximationen \\
I.1. Das allgemeine lineare Approximationsproblem \\
I.2. Dichte Systeme \\
I.3. Allgemeine Theorie linearer
Tschebyscheff-Approximationen \\
I.4. Spezielle Tschebyscheff-Approximationen \\
I.5. Absch{\"a}tzungen der Gr{\"o}{\ss}enordnung des
Fehlers bei trigonometrischer und bei polynomialer
Approximation \\
I.6. Polynomapproximationen \\
I.7. Numerische Verfahren bei linearen
Tschebyscheff-Approximationen \\
II Nicht-lineare Approximationen \\
II.8. Allgemeine Theorie nicht-linearer
Tschebyscheff-Approximationen \\
II.9. Rationale Approximationen \\
II.10. Exponentialapproximationen",
}
@InCollection{Miller:1964:PCF,
author = "J. C. P. Miller",
title = "Parabolic Cylinder Functions",
crossref = "Abramowitz:1964:HMF",
pages = "685--720",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Milne-Thomson:1964:EI,
author = "L. M. Milne-Thomson",
title = "Elliptic Integrals",
crossref = "Abramowitz:1964:HMF",
pages = "587--626",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Milne-Thomson:1964:JEF,
author = "L. M. Milne-Thomson",
title = "{Jacobian} Elliptic Functions and Theta Functions",
crossref = "Abramowitz:1964:HMF",
pages = "567--586",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Morelock:1964:AAE,
author = "J. C. Morelock",
title = "{ACM} Algorithm 229: Elementary Functions by Continued
Fractions",
journal = j-CACM,
volume = "7",
number = "5",
pages = "296",
month = may,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:32:21 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@InCollection{Oberhettinger:1964:HF,
author = "Frtiz Oberhettinger",
title = "Hypergeometric Functions",
crossref = "Abramowitz:1964:HMF",
pages = "555--566",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Olver:1964:BFI,
author = "F. W. J. Olver",
title = "{Bessel} Functions of Integer Order",
crossref = "Abramowitz:1964:HMF",
pages = "355--434",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Schmidt:1964:AEC,
author = "Paul W. Schmidt",
title = "Asymptotic Expansion of Certain Integrals Containing
the {Bessel} Function {$ J_0 (x) $}",
journal = j-J-MATH-PHYS,
volume = "5",
number = "8",
pages = "1183--1184",
month = aug,
year = "1964",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1704223",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 08:40:15 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v5/i8/p1183_s1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "22 December 2004",
pagecount = "2",
}
@Article{Simauti:1964:AFS,
author = "Takakazu Simauti",
title = "Approximation formulas for some elementary functions",
journal = "Comment. Math. Univ. St. Paul.",
volume = "12",
pages = "23--35",
year = "1964",
CODEN = "COMAAC",
ISSN = "0010-258X",
MRclass = "65.25",
MRnumber = "28 \#5552",
MRreviewer = "John Todd",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Slater:1964:CHF,
author = "Lucy Joan Slater",
title = "Confluent Hvpergeometric Functions",
crossref = "Abramowitz:1964:HMF",
pages = "503--536",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Slepian:1964:PSW,
author = "David Slepian",
title = "Prolate Spheroidal Wave Functions, {Fourier} Analysis
and Uncertainty --- {IV}: Extensions to Many
Dimensions; Generalized Prolate Spheroidal Functions",
journal = j-BELL-SYST-TECH-J,
volume = "43",
number = "6",
pages = "3009--3057",
month = nov,
year = "1964",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "33.28",
MRnumber = "0181766 (31 \#5993)",
MRreviewer = "J. Meixner",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1964/BSTJ.1964.4306.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol43/bstj43-6-3009.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@InCollection{Southard:1964:WER,
author = "Thomas H. Southard",
title = "{Weierstrass} Elliptic and Related Functions",
crossref = "Abramowitz:1964:HMF",
pages = "627--684",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Stegun:1964:LF,
author = "Irene A. Stegun",
title = "{Legendre} Functions",
crossref = "Abramowitz:1964:HMF",
pages = "331--354",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Stegun:1964:MF,
author = "Irene A. Stegun",
title = "Miscellaneous Functions",
crossref = "Abramowitz:1964:HMF",
pages = "997--1010",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
keywords = "Clausen's integral; Clebsch--Gordan coefficients;
Debye function; Dilogarithm (Spence's integral);
Einstein function; Planck function; Sievert and related
integrals",
remark = "Fullerton: Debye, Planck and Einstein functions.
Sievert and related integrals. Dilogarithm (Spence's
integral). Clausen's integral. Clebsch--Gordan
coefficients.",
}
@Article{Wengert:1964:SAD,
author = "R. E. Wengert",
title = "A simple automatic derivative evaluation program",
journal = j-CACM,
volume = "7",
number = "8",
pages = "463--464",
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A procedure for automatic evaluation of total and
partial derivatives of arbitrary algebraic functions is
presented. The numerical values of derivatives are
computed without developing analytic expressions for
the derivatives. The function is decomposed into a
sequence of elementary expressions A library is
provided for differentiating of elementary functions.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "computer program.; differentiation arithmetic; point
algorithm",
referred = "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a];
[Kala83b]; [Laws88a]; [Laws91a]; [Neid87a]; [Neid89a];
[Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a];
[Wilk64a].",
}
@InCollection{Zelen:1964:PF,
author = "Marvin Zelen and Norman C. Severo",
title = "Probability Functions",
crossref = "Abramowitz:1964:HMF",
pages = "925--996",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@InCollection{Zucker:1964:ETF,
author = "Ruth Zucker",
title = "Elementary Transcendental Functions. {Logarithmic},
Exponential, Circular and Hyperbolic Functions",
crossref = "Abramowitz:1964:HMF",
pages = "65--226",
year = "1964",
bibdate = "Sat Oct 30 19:37:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
}
@Article{Bingulac:1965:ACG,
author = "S. P. Bingulac and E. A. Humo",
title = "Analog Computer Generation of {Bessel} Functions of
Arbitrary Order",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "886--889",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264084",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038609",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Braess:1965:MIG,
author = "Dietrich Braess",
title = "{Monotone Iterationsfolgen bei Gleichungssystemen mit
fehlerhaften Koeffizienten und
Iterationsbeschleunigung}. ({German}) [{Monotone}
Iteration Sequences for Equation Systems with
Coefficients Having Errors, and Iteration
Acceleration]",
journal = j-NUM-MATH,
volume = "7",
number = "1",
pages = "32--41",
month = feb,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration",
language = "German",
}
@Article{Bulirsch:1965:NCEa,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions",
journal = j-NUM-MATH,
volume = "7",
number = "1",
pages = "78--90",
month = feb,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Handbook Series Special functions",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bulirsch:1965:NCEb,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions. {II}",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "353--354",
month = aug,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Christiansen:1965:APE,
author = "S. Christiansen",
title = "{Algol} programming: Error Integral with Complex
Argument",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "4",
pages = "287--293",
month = dec,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01937509",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=4&spage=287",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: A 75-line Algol procedure with maximum
absolute error about $ 2 \times 10^{-6} $ is given for
$ w(z) = e^{-z^2} \erfc ( - i z) $.",
}
@Article{Cochran:1965:ZHF,
author = "J. A. Cochran",
title = "The zeros of {Hankel} functions as functions of their
order",
journal = j-NUM-MATH,
volume = "7",
number = "3",
pages = "238--250",
month = jun,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 18 10:06:00 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Cody:1965:CAC,
author = "W. J. {Cody, Jr.}",
title = "{Chebyshev} Approximations for the Complete Elliptic
Integrals {$K$} and {$E$}",
journal = j-MATH-COMPUT,
volume = "19",
number = "89--92",
pages = "105--112",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.05",
MRnumber = "30\#1601",
bibdate = "Fri Oct 23 11:10:16 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Cody:1966:CCA}.",
URL = "http://www.jstor.org/stable/2004103",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 4 \times 10^{-18}
$.",
}
@Article{Cody:1965:CPE,
author = "W. J. {Cody, Jr.}",
title = "{Chebyshev} Polynomial Expansions of Complete Elliptic
Integrals",
journal = j-MATH-COMPUT,
volume = "19",
number = "89--92",
pages = "249--259",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "31\#2820",
bibdate = "Fri Oct 23 11:10:33 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2003350",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 25-digit approximations.",
}
@Article{Combet:1965:CBT,
author = "M. Combet and H. {Van Zonneveld} and L. Verbeek",
title = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "863--867",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dahlquist:1965:CAP,
author = "Germund Dahlquist and Sven-{\AA}ke Gustafson and
K{\'a}roly Sikl{\'o}si",
title = "Convergence Acceleration from the Point of View of
Linear Programming",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "1",
pages = "1--16",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01975719",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=1",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "convergence acceleration",
}
@Article{Fettis:1965:CEI,
author = "Henry E. Fettis",
title = "Calculation of Elliptic Integrals of the Third Kind by
Means of {Gauss}' Transformation",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "97--104",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004102",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fields:1965:RAG,
author = "Jerry L. Fields",
title = "Rational Approximations to Generalized Hypergeometric
Functions",
journal = j-MATH-COMPUT,
volume = "19",
number = "92",
pages = "606--624",
month = oct,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Franke:1965:NEE,
author = "Charles H. Franke",
title = "Numerical Evaluation of the Elliptic Integral of the
Third Kind (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "494--496",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fraser:1965:SMC,
author = "W. Fraser",
title = "A Survey of Methods for Computing Minimax and
Near-Minimax Polynomial Approximations for Functions of
a Single Independent Variable",
journal = j-J-ACM,
volume = "12",
number = "3",
pages = "295--314",
month = jul,
year = "1965",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321281.321282",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "Methods are described for the derivation of minimax
and near-minimax polynomial approximations. For minimax
approximations techniques are considered for both
analytically defined functions and functions defined by
a table of values. For near-minimax approximations
methods of determining the coefficients of the
Fourier--Chebyshev expansion are first described. These
consist of the rearrangement of the coefficients of a
power polynomial, and also direct determination of the
coefficients from the integral which defines them, or
the differential equation which defines the function.
Finally there is given a convenient modification of an
interpolation scheme which finds coefficients of a
near-minimax approximation without requiring numerical
integration or the numerical solution of a system of
equations.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Gautschi:1965:ALF,
author = "W. Gautschi",
title = "{Algorithm 259}: {Legendre} Functions for Arguments
Larger than One [{S16}]",
journal = j-CACM,
volume = "8",
number = "8",
pages = "488--492",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Jansen:1977:RLF}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Legendre functions; special functions",
remark = "Fullerton: Long Algol procedures for the associated
Legendre functions of the first and second kinds: $
P_a^n(x) $ and $ Q_n^m $.",
}
@Article{Gautschi:1965:CAS,
author = "Walter Gautschi",
title = "Certification of {Algorithm 236} [{S17}]: {Bessel}
functions of the first kind",
journal = j-CACM,
volume = "8",
number = "2",
pages = "105--106",
month = feb,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:58 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$J_n(x)$; Bessel functions of the first kind; special
functions",
}
@Article{Gunn:1965:ASa,
author = "J. H. Gunn",
title = "{Algorithm 260}: {6-$J$} symbols",
journal = j-CACM,
volume = "8",
number = "8",
pages = "492--492",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Gunn:1965:ASb,
author = "J. H. Gunn",
title = "{Algorithm 261}: {9-$J$} symbols",
journal = j-CACM,
volume = "8",
number = "8",
pages = "492--493",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Gunn:1965:AZV,
author = "J. H. Gunn",
title = "{Algorithm 252} [{Z}]: {Vector} coupling or
{Clebsch--Gordan} coefficients",
journal = j-CACM,
volume = "8",
number = "4",
pages = "217--217",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:59 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Heatley:1965:ETT,
author = "A. H. Heatley",
title = "An Extension of the Table of the {Toronto} Function
(in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "118--123",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Some 5 and 7-digit values.",
}
@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kazangapov:1965:REF,
author = "A. N. Kazangapov",
title = "Representation of elementary function in the system of
residual classes. ({Russian})",
journal = "Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk",
volume = "3",
pages = "79--84",
year = "1965",
MRclass = "65.25",
MRnumber = "33 \#5090",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{King:1965:LED,
author = "R. King",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Book{Lebedev:1965:SFT,
author = "N. N. (Nikola{\u\i}i Nikolaevich) Lebedev",
title = "Special Functions and Their Applications",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 308",
year = "1965",
LCCN = "QA351 .L3613",
bibdate = "Sat Apr 1 14:42:46 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Revised English edition translated and edited by
Richard A. Silverman.",
series = "Selected Russian publications in the mathematical
sciences",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Mathematical physics",
}
@Book{Lyusternik:1965:HCE,
author = "L. A. Lyusternik and O. A. Chervonenkis and A. R.
Yanpol{\'s}kii",
title = "Handbook for Computing Elementary Functions",
volume = "76",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xiii + 251",
year = "1965",
LCCN = "QA221.L513",
MRclass = "65.25",
MRnumber = "32 \#584",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Translated from the Russian by G. J. Tee. Translation
edited by K. L. Stewart.",
series = "International series of monographs on pure and applied
mathematics",
acknowledgement = ack-nhfb,
}
@Article{MacLaren:1965:APN,
author = "M. D. MacLaren",
title = "{Algorithm 272}: {Procedure} for the Normal
Distribution Functions [{S15}]",
journal = j-CACM,
volume = "8",
number = "12",
pages = "789--790",
month = dec,
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/365691.365957",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:03 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remarks \cite{Hill:1967:RAS,MacLaren:1968:RAP}.",
abstract = "The procedure gives $ \Phi (a) = \sqrt {1 / (2 \pi)}
\int_{- \infty }^a \exp ( - t^2 / 2) \, d t $ and $
\Phi *(a) = 2 (\Phi (|a|) - 0.5) = \sqrt {2 / \pi }
\int_0^{|a|} \exp ( - t^2 / 2) \, d t $.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
}
@Article{Maklovic:1965:IIC,
author = "S. T. Maklovi{\v{c}}",
title = "Investigation of integrals containing {Bessel} and
elementary functions. ({Russian})",
journal = "Ki{\v{s}}inev. Gos. Univ. U{\v{c}}en. Zap.",
volume = "82",
pages = "75--81",
year = "1965",
MRclass = "33.25",
MRnumber = "34 \#387",
MRreviewer = "H. A. Lauwerier",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Markman:1965:RZF,
author = "B. Markman",
title = "The {Riemann} Zeta Function",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "2",
pages = "138--141",
year = "1965",
bibdate = "Sat Oct 30 08:53:17 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: A 25-line Algol procedure for evaluating $
\zeta (s) $ for all $ s \neq 1 $ is given.",
}
@Article{Medhurst:1965:EI,
author = "R. G. Medhurst and J. H. Roberts",
title = "Evaluation of the Integral $ {I}_n(b) = \frac {2}{\pi
} \int^\infty_0 \bigg (\frac {\sin x}{x} \bigg)^n \cos
(b x) d x $",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "113--117",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Metze:1965:MSR,
author = "Gernot Metze",
title = "Minimal Square Rooting",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "181--185",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.263963",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Miller:1965:ASF,
author = "G. F. Miller",
title = "Algorithms for Special Functions {II}",
journal = j-NUM-MATH,
volume = "7",
pages = "194--196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
remark = "Fullerton: Corrections and simplifications of the $
\sin $, $ \cos $ and $ \tan $ routines given in paper
I. See Clenshaw (1963).",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Nemeth:1965:CEF,
author = "G. N{\'e}meth",
title = "{Chebyshev} expansions for {Fresnel} integrals",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "310--312",
month = aug,
year = "1965",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01436524",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 20:47:18 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
remark = "Fullerton: Two series of 12-digit coefficients are
given to cover the range $ 0 \leq x < \infty $.",
}
@Article{Rice:1965:CPR,
author = "John R. Rice",
title = "On the Conditioning of Polynomial and Rational Forms",
journal = j-NUM-MATH,
volume = "7",
number = "5",
pages = "426--435",
month = oct,
year = "1965",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01436257",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.99",
MRnumber = "MR0189283 (32 \#6710)",
MRreviewer = "James H. Wilkinson",
bibdate = "Sun Oct 16 17:22:04 GMT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "number of multiplications to evaluate a polynomial",
}
@Article{Slepian:1965:EAP,
author = "David Slepian and Estelle Sonnenblick",
title = "Eigenvalues associated with prolate spheroidal wave
functions of zero order",
journal = j-BELL-SYST-TECH-J,
volume = "44",
number = "8",
pages = "1745--1759",
month = oct,
year = "1965",
CODEN = "BSTJAN",
ISSN = "0005-8580",
MRclass = "65.25",
MRnumber = "0183103 (32 \#585)",
MRreviewer = "R. Nicolovius",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1965/BSTJ.1965.4408.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol44/bstj44-8-1745.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Slepian:1965:SAE,
author = "David Slepian",
title = "Some Asymptotic Expansions for Prolate Spheroidal Wave
Functions",
journal = "J. Math. and Physics {XLIV(2)}",
volume = "??",
number = "??",
pages = "99--140",
month = jun,
year = "1965",
bibdate = "Sat Oct 30 10:46:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=189661",
acknowledgement = ack-nhfb,
author-dates = "1923--2007",
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Several complicated expansions are derived
and presented.",
}
@Article{Swarztrauber:1965:LED,
author = "P. N. Swarztrauber",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Aug 31 14:02:19 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Thompson:1965:AEI,
author = "G. T. Thompson",
title = "The Asymptotic Expansion of the Integrals Psi and Chi
in Terms of {Tchebycheff} Polynomials (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "92",
pages = "661--663",
month = oct,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Doppler Broadening",
}
@Book{Clenshaw:1966:CSB,
author = "C. W. Clenshaw and Susan M. Picken",
title = "{Chebyshev} series for {Bessel} functions of
fractional order",
volume = "8",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "iii + 53",
year = "1966",
MRclass = "33.25",
MRnumber = "203095",
MRreviewer = "L. J. Slater",
bibdate = "Sun Nov 12 06:18:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "National Physical Laboratory. Mathematical tables",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
xxpages = "51",
xxpages = "iii + 54",
}
@Article{Cody:1966:CCA,
author = "W. J. {Cody, Jr.}",
title = "Corrigenda: ``{Chebyshev} Approximations for the
Complete Elliptic Integrals $ {K} $ and $ {E} $''",
journal = j-MATH-COMPUT,
volume = "20",
number = "93",
pages = "207--207",
month = jan,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri Oct 23 11:13:58 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Cody:1965:CAC}.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Doring:1966:CZC,
author = "Boro Doring",
title = "Complex Zeros of Cylinder Functions",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "215--222",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fike:1966:SAS,
author = "C. T. Fike",
title = "Starting Approximations for Square Root Calculation on
{IBM System\slash 360}",
journal = j-CACM,
volume = "9",
number = "4",
pages = "297--299",
month = apr,
year = "1966",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/365278.365556",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
abstract = "Several starting approximations for square root
calculation by Newton's method are presented in a form
to facilitate their use in IBM System/360 square root
routines. These approximations include several for the
range [1/16, 1], which is the interval of primary
interest on IBM System/360.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; IBM S/360",
}
@Article{Filippi:1966:BEE,
author = "S. Filippi",
title = "{Die Berechnung einiger elementarer transzendenter
Funktionen mit Hilfe des Richardson-Algorithmus}
\toenglish {The Computation of Some Elementary
Transcendental Functions by Means of the Richardson
Algorithm} \endtoenglish",
journal = j-COMPUTING,
volume = "1",
number = "2",
pages = "127--132",
month = jun,
year = "1966",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02342622",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Gautschi:1966:AD,
author = "Walter Gautschi",
title = "{Algorithm 282}: {Derivatives} of $ e^x / x $, $ \cos
(x) / x $, and $ \sin (x) / x $",
journal = j-CACM,
volume = "9",
number = "4",
pages = "272--272",
month = apr,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:05 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Gautschi:1970:RAD}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\cos(x)/x$; $\sin(x)/x$; $e^x/x$; elementary
functions",
}
@Article{Gautschi:1966:ARC,
author = "Walter Gautschi",
title = "{Algorithm 292}: {Regular} {Coulomb} Wave Functions",
journal = j-CACM,
volume = "9",
number = "11",
pages = "793--795",
month = nov,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:10 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
}
@Article{Glasser:1966:ESI,
author = "M. L. Glasser",
title = "Evaluation of Some Integrals Involving the $ \psi
$-Function (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "332--333",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gustafson:1966:CAM,
author = "Sven-{\AA}ke Gustafson",
title = "Convergence Acceleration by Means of Numerical
Quadrature",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "2",
pages = "117--128",
month = jun,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933103",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=2&spage=117",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "convergence acceleration",
}
@Article{Hart:1966:CAR,
author = "Roger G. Hart",
title = "A Close Approximation Related to the Error Function
(in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "600--602",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Hastings:1966:RCB,
author = "C. W. Hastings",
title = "{R66-78} Computation of the Base Two Logarithm of
Binary Number",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "6",
pages = "956--957",
month = dec,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264517",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038956",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Book{Jurimae:1966:KFT,
author = "E. J{\"u}rim{\"a}e",
title = "Kompleksmuutuja funktsioonide teooria. {I}:
Elementaarsed funktsioonid. ({Estonian}) [Theory of
functions of a complex variable. {I}: Elementary
functions]",
publisher = "Tartu Riiklik {\"U}likool",
address = "Tartu, Estonia",
pages = "131",
year = "1966",
MRclass = "30.00",
MRnumber = "40 \#5827a",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Kogbetliantz:1966:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of Elementary Functions",
crossref = "Ralston:1960:MMD",
pages = "7--35",
year = "1966",
bibdate = "Sat Dec 09 14:09:27 1995",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@TechReport{Kuki:1966:CAE,
author = "H. Kuki",
title = "Comments on the {ANL} Evaluation of the {OS\slash 360
FORTRAN} Math Function Library",
type = "????",
number = "SSD 169, C4773",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "47--53",
year = "1966",
bibdate = "Wed Feb 14 19:13:50 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Larssen:1966:CAC,
author = "Gerhard Meidell Larssen",
title = "Certification of {Algorithm 56}: {Complete} elliptic
integral of the second kind",
journal = j-CACM,
volume = "9",
number = "1",
pages = "12--12",
month = jan,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:04 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Mechel:1966:CMB,
author = "Fr. Mechel",
title = "Calculation of the Modified {Bessel} Functions of the
Second Kind with Complex Argument",
journal = j-MATH-COMPUT,
volume = "20",
number = "95",
pages = "407--412",
month = jul,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Nellis:1966:REE,
author = "W. J. Nellis and B. C. Carlson",
title = "Reduction and Evaluation of Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "223--231",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Pike:1966:ALG,
author = "M. C. Pike and I. D. Hill",
title = "{Algorithm 291}: {Logarithm} of Gamma Function",
journal = j-CACM,
volume = "9",
number = "9",
pages = "684--684",
month = sep,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:09 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\log(\Gamma(x))$; special functions",
remark = "Fullerton: Short Algol procedure valid only for $ x >
0 $. Accurate to 10 digits.",
}
@TechReport{Price:1966:NAR,
author = "James F. Price",
title = "Numerical Analysis and Related Literature for
Scientific Computer Users",
type = "Mathematical Note",
number = "456 (D1-82-0517)",
institution = "Mathematics Research Laboratory, Boeing Scientific
Research Laboratories",
address = "Seattle, WA, USA",
edition = "Second",
pages = "ix + 191",
month = mar,
year = "1966",
bibdate = "Mon Jun 18 06:55:22 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.dtic.mil/dtic/tr/fulltext/u2/632244.pdf",
abstract = "The Second Edition of this annotated bibliography
lists the contents of over 150 books in English on
numerical analysis and related literature. It is meant
for the general scientific computer user and not for
the research numerical analyst; the descriptions and
suggestions are given with this in mind. It is expected
that the most useful section will be the 27-page index
which tells in which books various topics may be found.
There is also a section describing how to look up
further information on such topics which may be found
in the literature.",
acknowledgement = ack-nhfb,
tableofcontents = "Introduction / iv \\
I. Numerical Procedures in Books / 1 \\
II. How to Find What You Want / 157 \\
A. Bibliographies, lists of books, abstracting journals
/ 157 \\
B. Looking for Tables of Various Functions / 161 \\
C. Keeping Up with Some of the New Literature / 163 \\
III. Subject Index / 165",
}
@Book{Slater:1966:GHF,
author = "Lucy Joan Slater",
title = "Generalized Hypergeometric Functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiii + 273",
year = "1966",
LCCN = "QA351 .S565",
bibdate = "Sat Oct 30 21:01:55 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Takenaga:1966:EIG,
author = "Roy Takenaga",
title = "On the Evaluation of the Incomplete Gamma Function (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "606--610",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Thompson:1966:ESI,
author = "Rory Thompson",
title = "Evaluation of $ {I}_n(b) = 2 \pi^{-1} \int^\infty_0
\big (\frac {sin x}{x} \big)^n \cos (b x) d x $ and of
Similar Integrals (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "94",
pages = "330--332",
month = apr,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Tolke:1966:PFT,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 2. Theta-Funktionen und
spezielle Weierstrasssche Funktionen}. ({German})
[{Practical} functional theory. 2. {Theta} functions
and special {Weierstrass} functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vii + 248",
year = "1966",
ISBN = "",
ISBN-13 = "",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Tricomi:1966:RUS,
author = "F. G. Tricomi",
title = "Lectures on the use of special functions by
calculations with electronic computers",
type = "Lecture Series",
number = "47",
institution = "The Institute for Fluid Dynamics and Applied
Mathematics, University of Maryland, College Park",
address = "College Park, MD, USA",
year = "1966",
bibdate = "Tue Mar 14 18:48:58 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Watson:1966:TTB,
author = "G. N. Watson",
title = "A Treatise on the Theory of {Bessel} Functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "vi + 804",
year = "1966",
ISBN = "0-521-09382-1",
ISBN-13 = "978-0-521-09382-8",
LCCN = "QA 408 W33t 1966",
bibdate = "Fri Nov 24 13:53:35 MST 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/matched-field-proc.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
alias = "Watson 66a",
sthbib = "M2 Wat 82 55",
}
@Article{Wood:1966:DBI,
author = "Van E. Wood and R. P. Kenan and M. L. Glasser",
title = "{Doppler} Broadening Integrals (in {Technical Notes
and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "610--611",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Anonymous:1967:CAP,
author = "Anonymous",
title = "Convergence acceleration from the point of view of
linear programming",
journal = j-BIT,
volume = "7",
number = "3",
pages = "256--256",
month = sep,
year = "1967",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939269",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:10 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=3&spage=256",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "convergence acceleration",
}
@Article{Bond:1967:AAF,
author = "Gillian Bond and M. L. V. Pitteway",
title = "{Algorithm 301}: {Airy} Function",
journal = j-CACM,
volume = "10",
number = "5",
pages = "291--292",
month = may,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Airy functions; special functions",
remark = "Fullerton: 100-line Algol program for $ \operatorname
{Ai} $, $ \operatorname {Bi} $. and their
derivatives.",
}
@Article{Cody:1967:CAN,
author = "W. J. Cody and K. E. Hillstrom",
title = "{Chebyshev} Approximations for the Natural Logarithm
of the Gamma Function",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "198--203",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 10^{-17} $.",
}
@Article{Cody:1967:CRC,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "Corrigendum: ``{Rational Chebyshev approximations for
Fermi--Dirac integrals of orders $ - 1 / 2 $, $ 1 / 2
$, and $ 3 / 2 $''}",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "525--525",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Sep 26 19:36:03 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Cody:1967:RCA}.",
URL = "http://www.jstor.org/stable/2003289",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
xxmonth = "(none)",
}
@Article{Cody:1967:LEA,
author = "William J. {Cody, Jr.}",
title = "Letter to the {Editor}: Another Aspect of Economical
Polynomials",
journal = j-CACM,
volume = "10",
number = "9",
pages = "531--531",
month = sep,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363566.363577",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Nov 17 10:20:03 1994",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fike:1967:MEP}.",
abstract = "In his paper ``Methods of Evaluating Polynomial
Approximations in Function Evaluation Routines'' [Comm.
ACM 10, (March 1967)], C. T. Fike fails to discuss one
very important aspect of the ``economical'' methods for
polynomials. Since these evaluation methods involve a
decreased number of arithmetic operations over the
usual Horner's method (or at least replace a
multiplication by an addition) the implication is that
they are faster to execute. Dr. Fike points out that
these methods can be poorly conditioned for particular
polynomials, thus requiring extended precision or
fixed-point arithmetic to maintain accuracy and costing
more in time than Horner's method. But even if we
assume the methods are well conditioned, the need to
store away and retrieve intermediate results in some
machines with only one floating-point arithmetic
register can wipe out the time savings effected by a
reduction in the number of arithmetic operations. On
many of today's high-performance computers the time
required to store away and retrieve a result is about
the same as the time required for a floating-point
addition. It is no longer sufficient to estimate the
efficiency of a method by a count of arithmetic
operations alone.",
acknowledgement = ack-wjc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic",
}
@Article{Cody:1967:RCA,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "Rational {Chebyshev} approximations for {Fermi--Dirac}
integrals of orders $ - 1 / 2 $, $ 1 / 2 $, and $ 3 / 2
$",
journal = j-MATH-COMPUT,
volume = "21",
number = "97",
pages = "30--40",
month = jan,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Sep 26 19:23:19 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Cody:1967:CRC}.",
URL = "http://www.jstor.org/stable/2003468",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 10^{-9} $.",
}
@Article{DiDonato:1967:ECI,
author = "A. R. DiDonato and M. P. Jarnagin",
title = "The Efficient Calculation of the Incomplete
Beta-Function Ratio for Half-Integer Values of the
Parameters $ a, b $",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "652--662",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fair:1967:RAI,
author = "Wyman G. Fair and Yudell L. Luke",
title = "Rational Approximations to the Incomplete Elliptic
Integrals of the First and Second Kinds",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "418--422",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fettis:1967:MCI,
author = "Henry E. Fettis",
title = "More on the Calculation of the Integral $ {I}_n(b) =
\frac {2}{\pi } \int^\infty_0 \big (\frac {\sin x}{x}
\big)^n \cos b x \, d x $ (in {Technical Notes and
Short Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "727--730",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fike:1967:LER,
author = "C. T. Fike",
title = "Letter to the {Editor}: {A} rational approximation
optimal by {Moursund}'s criterion",
journal = j-CACM,
volume = "10",
number = "11",
pages = "683--684",
month = nov,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363790.363795",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:16 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "elementary function; square root",
remark = "Gives a starting value for $ \sqrt {x} $ ($x$ on $ [1
/ 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x +
0.84106293)$, with an error of $ 2^{-12.496}$.",
}
@Article{Fike:1967:MEP,
author = "C. T. Fike",
title = "Methods of Evaluating Polynomial Approximations in
Function Evaluation Routines",
journal = j-CACM,
volume = "10",
number = "3",
pages = "175--178",
month = mar,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363162.363200",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remark on efficiency \cite{Cody:1967:LEA}.",
abstract = "The method of nested multiplication is commonly used
in function evaluation routines to evaluate
approximation polynomials. New polynomial evaluation
methods have been developed in recent years which
require fewer multiplications than nested
multiplication and may therefore be preferable for use
in function evaluation routines. Although some of these
methods do not appear to be practically useful because
of rounding-error difficulties, several methods of
evaluating low-degree polynomials have been found to be
satisfactory. Three such methods are described and
illustrated.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
received = "August 1966 (revised December 1966)",
}
@Article{Friedland:1967:AAV,
author = "Paul Friedland",
title = "{Algorithm 312}: {Absolute} Value and Square Root of a
Complex Number",
journal = j-CACM,
volume = "10",
number = "10",
pages = "665--665",
month = oct,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363717.363780",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(z)$; $\sqrt(z)$; elementary functions",
}
@Article{Gautschi:1967:CAT,
author = "Walter Gautschi",
title = "Computational Aspects of Three-Term Recurrence
Relations",
journal = j-SIAM-REVIEW,
volume = "9",
number = "1",
pages = "24--82",
month = jan,
year = "1967",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1009002",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:42 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/9/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://link.aip.org/link/?SIR/9/24/1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "Bessel functions; continued fractions; Coulomb wave
functions; Fourier coefficients; incomplete beta
functions; incomplete gamma functions; Legendre
functions; Sturm--Liouville boundary value problems;
three-term recurrence relations",
onlinedate = "January 1967",
remark = "This paper is frequently cited in later work on
continued fractions, three-term recurrence relations,
and special functions.",
}
@Article{Goldstein:1967:CSB,
author = "Max Goldstein and C. W. Clenshaw and Susan M. Picken",
title = "{Chebyshev} Series for {Bessel} Functions of
Fractional Order",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "509--??",
month = jul,
year = "1967",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2003271",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sun Nov 12 09:25:35 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "TO DO: Why is this missing from journal bibliography
file, mathcomp1970.bib?",
}
@Article{Gunn:1967:ACW,
author = "J. H. Gunn",
title = "{Algorithm 300}: {Coulomb} Wave Functions",
journal = j-CACM,
volume = "10",
number = "4",
pages = "244--245",
month = apr,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Vos:1973:RAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: 150-line Algol procedure that is superseded
by other routines in the physics literature.",
}
@Article{Hill:1967:ACS,
author = "I. D. Hill and M. C. Pike",
title = "{Algorithm 299}: {Chi}-Squared Integral",
journal = j-CACM,
volume = "10",
number = "4",
pages = "243--244",
month = apr,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Hill:1985:RCS,elLozy:1976:RAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "chi-squared; probability functions",
remark = "Fullerton: Short Algol procedure.",
}
@Article{Hill:1967:ANCa,
author = "I. D. Hill and S. A. Joyce",
title = "{Algorithm 304}: {Normal} Curve Integral",
journal = j-CACM,
volume = "10",
number = "6",
pages = "374--375",
month = jun,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363332.363411",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remarks \cite{Hill:1967:RAS,Bergson:1968:ACR}.",
abstract = "{\tt normal(x,upper)} calculates the curve, i.e., tail
area of the standardized normal curve, i.e., $ (1 /
\sqrt {2 \pi }) \int \exp ( - t^2 / 2) \, d t $. If
{\tt upper} is {\tt true}, the limits of integration
are $x$ and $ \infty $. If {\tt upper} is {\tt false},
the limits of integration are $ - \infty $ and $x$.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
remark = "Fullerton: 75-line Algol procedure that is superseded
by numerous $ \erf $ routines.",
}
@Article{Hill:1967:RAS,
author = "I. D. Hill and S. A. Joyce",
title = "Remarks on {Algorithm 123} [{S15}]: {Real} error
function, {{\tt ERF(x)}}; {Algorithm 180} [{S15}]:
{Error} Function --- Large $ {X} $; {Algorithm 181}
[{S15}]: {Complementary} Error Function --- Large $ {X}
$; {Algorithm 209} [{S15}]: {Gauss}; {Algorithm 226}
[{S15}]: {Normal} Distribution Function; {Algorithm
272} [{S15}]: {Procedure} for the Normal Distribution
Functions; {Algorithm 304} [{S15}]: {Normal} Curve
Integral",
journal = j-CACM,
volume = "10",
number = "6",
pages = "377--378",
month = jun,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363332.365433",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Cyvin:1964:AND,MacLaren:1965:APN,Hill:1967:ANCa}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\erf(x)$; $\erfc(x)$; probability functions; special
functions",
}
@Article{Kilpatrick:1967:CIP,
author = "J. E. Kilpatrick and Shigetoshi Katsura and Yuji
Inoue",
title = "Calculations of Integrals of Products of {Bessel}
Functions",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "407--412",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Knuth:1967:CTE,
author = "Donald E. Knuth and Thomas J. Buckholtz",
title = "Computation of Tangent, {Euler}, and {Bernoulli}
Numbers",
journal = j-MATH-COMPUT,
volume = "21",
number = "100",
pages = "663--688",
month = oct,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "36 #4787",
bibdate = "Fri Mar 22 18:03:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database; MathSciNet database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: The first 119. 120 and 250 tangent, Euler
and Bernoulli numbers, respectively.",
}
@Book{MacRobert:1967:SHE,
author = "Thomas Murray MacRobert and Ian Naismith Sneddon",
title = "Spherical harmonics; an elementary treatise on
harmonic functions, with applications",
volume = "98",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
edition = "Third",
pages = "xviii + 349",
year = "1967",
LCCN = "QA406 .M3 1967",
bibdate = "Sat Oct 30 21:22:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "International series of monographs in pure and applied
mathematics",
acknowledgement = ack-nhfb,
author-dates = "1884--1962",
subject = "Spherical harmonics",
}
@Book{Meinardus:1967:AFT,
author = "G{\"u}nter Meinardus",
title = "Approximation of functions: Theory and numerical
methods",
volume = "13",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 198",
year = "1967",
ISBN = "0-387-03985-6, 3-540-03985-6",
ISBN-13 = "978-0-387-03985-5, 978-3-540-03985-3",
ISSN = "0081-3877",
LCCN = "QA221 .M3813",
bibdate = "Thu Oct 19 17:07:54 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Springer Tracts in Natural Philosophy",
URL = "http://catalogue.bnf.fr/ark:/12148/cb37378349d",
acknowledgement = ack-nhfb,
author-dates = "(1926--2007)",
remark = "Translation by Larry L. Schumaker of
\cite{Meinardus:1964:AFI}.",
subject = "Approximation theory; Numerical analysis; Th{\'e}orie
de l'approximation; Analyse num{\'e}rique; Fonctions
(math{\'e}matiques); Approximation, Th{\'e}orie de l';
Analyse num{\'e}rique; Approximation theory; Numerical
analysis; Approximation; Funktion; Mathematik",
tableofcontents = "Part I. Linear Approximation \\
1. The General Linear Approximation Problem / 1 \\
1.1. Statement of the Problem. Existence Theorem / 1
\\
1.2. Strictly Convex Spaces. Hilbert Space / 2 \\
1.3. Maximal Linear Functionals / 4 \\
2. Dense Systems / 5 \\
2.1. A General Criterion of Banach / 5 \\
2.2. Approximation Theorems of Weierstrass and Muntz /
6 \\
2.3. Approximation Theorems in the Complex Plane / 10
\\
3. General Theory of Linear Tchebycheff Approximation /
13 \\
3.1. Fundamentals. The Theorem of Kolmogoroff / 13 \\
3.2. The Haar Uniqueness Theorem. Linear Functionals
and Alternants / 16 \\
3.3. Further Uniqueness Results / 24 \\
3.4. Invariants / 26 \\
3.5. Vector-valued Functions / 28 \\
4. Special Tchebycheff Approximations / 28 \\
4.1. Tchebycheff Systems / 28 \\
4.2. Tchebycheff Polynomials / 31 \\
4.3. The Function ?? / 33 \\
4.4. A Problem of Bernstein and Achieser / 36 \\
4.5 Zolotareff's Problem / 41 \\
5. Estimating the Magnitude of Error in Trigonometric
and Polynomial Approximation / 45 \\
5.1. Projection Operators. Linear Polynomial Operators
/ 45 \\
5.2. The Connection between Trigonometric and
Polynomial Approximation / 45 \\
5.3. The Fej{\'e}r Operator / 47 \\
5.4. The Korovkin Operators / 50 \\
5.5. The Theorems of D. Jackson / 52 \\
5.6. The Theorems of Bernstein and Zygmund / 57 \\
5.7. Supplements / 65 \\
6. Approximation by Polynomials and Related Functions /
72 \\
6.1. Foundations / 72 \\
6.2. Upper Bounds for En (??) / 77 \\
6.3. Lower Bounds for En (??) / 82 \\
6.4. Dependence of the Approximation on the Interval /
85 \\
6.5. Regular Haar Systems / 87 \\
6.6. Asymptotic Results / 90 \\
6.7. Results for tho Alternants / 101 \\
7. Numerical Methods for Linear Tchebycheff
Approximation / 105 \\
7.1. The Iterative Methods of Remez / 105 \\
7.2. Initial Approximations / 116 \\
7.3. Direct Methods / 122 \\
7.4. Discretization. Other Methods / 124 \\
Part II. Non-linear Approximation \\
8. General Theory of Non-linear Tchebycheff
Approximation / 131 \\
8.1. Survey of the Problem. A Generalization of the
Kolmogoroff Theorem / 131 \\
8.2. The Haar Uniqueness Theorem. Alternants / 141 \\
8.3. The Investigations of Rice / 148 \\
8.4. The Newton Iteration Method / 149 \\
8.5. H-Sets / 153 \\
9. Rational Approximation / 154 \\
9.1. Existence. Invariants. A Theorem of Walsh / 154
\\
9.2. Theorems on Alternants. Anomalies. Continuity.
Examples / 160 \\
9.3. Asymptotic Results. Small Intervals / 167 \\
9.4. Numerical Methods / 170 \\
10. Exponential Approximation / 176 \\
10.1. The Results of Rice / 176 \\
10.2. An Anomaly Theorem. Constructive Methods / 179
\\
11. Segment Approximation / 183 \\
11.1. Statement of the Problem. Hypotheses / 183 \\
11.2. The principle of Lawson / 184 \\
H.3. Equidegree Polynomial Approximation / 188 \\
Bibliography / 189 \\
Subject Index / 197",
}
@Article{Moody:1967:ADF,
author = "William T. Moody",
title = "Approximations for the Psi (Digamma) Function (in
Technical Notes and Short Notices)",
journal = j-MATH-COMPUT,
volume = "21",
number = "97",
pages = "112--112",
month = jan,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Moursund:1967:OSV,
author = "David G. Moursund",
title = "Optimal starting values for {Newton--Raphson}
calculation of $ \sqrt {x} $",
journal = j-CACM,
volume = "10",
number = "7",
pages = "430--432",
month = jul,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363427.363454",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "39\#2297",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
abstract = "The problem of obtaining starting values for the
Newton-Raphson calculation of $ \sqrt {x} $ on a
digital computer is considered. It is shown that the
conventionally used best uniform approximations to $
\sqrt {x} $ do not provide optimal starting values. The
problem of obtaining optimal starting values is stated,
and several basic results are proved. A table of
optimal polynomial starting values is given.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
remark = "Title of article has incorrect $ \sqrt (x^{1 / 2}) $:
the article discusses computation of {\tt sqrt(x)}.",
}
@Article{Olver:1967:BSS,
author = "F. W. J. Olver",
title = "Bounds for the Solutions of Second-Order Linear
Difference Equations [{Anger--Weber} and {Struve}
Functions]",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "71B",
number = "4",
pages = "161--166",
month = oct,
year = "1967",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 09:37:44 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Truncation error estimates of an earlier
published algorithm.",
}
@Article{Olver:1967:NSS,
author = "F. W. J. Olver",
title = "Numerical solution of second-order linear difference
equations",
journal = j-J-RES-NATL-BUR-STAND-B,
volume = "71B",
number = "2--3",
pages = "111--129",
month = apr,
year = "1967",
CODEN = "JNBBAU",
DOI = "https://doi.org/10.6028/jres.071B.018",
ISSN = "0022-4340",
MRclass = "65.70",
MRnumber = "221789",
MRreviewer = "G. N. Lance",
bibdate = "Sun Nov 5 09:03:34 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/jres/71B/jresv71Bn2-3p111_A1b.pdf",
abstract = "A new algorithm is given for computing the solution of
any second-order linear difference equation which is
applicable when simple recurrence procedures cannot be
used because of instability. Compared with the
well-known Miller algorithm the new method has the
advantages of (i) automatically determining the correct
number of recurrence steps. (ii) applying to
inhomogeneous difference equations, (iii) enabling more
powerful error analyses to be constructed.\par
The method is illustrated by numerical computations,
including error analyses of Anger--Weber, Struve, and
Bessel functions, and the solution of a differential
equation in Chebyshev series",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
fjournal = "Journal of Research of the National Bureau of
Standards. Section B. Mathematics and Mathematical
Physics",
journal-URL = "http://www.nist.gov/nvl/jrespastpapers.cfm",
keywords = "Chebyshev series; difference equations; error
analysis; Miller algorithm. recurrence methods; special
functions",
}
@Article{Pike:1967:RAI,
author = "M. C. Pike and I. D. Hill",
title = "Remark on {Algorithm 179}: {Incomplete} {Beta} ratio",
journal = j-CACM,
volume = "10",
number = "6",
pages = "375--376",
month = jun,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$B(z,w)$; beta function; special functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Article{Pitteway:1967:RAA,
author = "M. L. V. Pitteway",
title = "Remark on {Algorithm 301}: {Airy} function",
journal = j-CACM,
volume = "10",
number = "7",
pages = "453--453",
month = jul,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:14 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Airy functions; special functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Book{Sen:1967:TSF,
author = "Bibhutibhusan Sen",
title = "A treatise on special functions, for scientists and
engineers",
publisher = "Allied Publishers",
address = "Bombay, India",
pages = "164",
year = "1967",
LCCN = "QA351 .S45",
bibdate = "Fri Oct 29 21:30:38 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Spherical harmonics",
}
@Book{Tolke:1967:PFE,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 4. Elliptische
Integralgruppen und Jacobische elliptische Funktionen
im Komplexen}. ({German}) [{Practical} functional
theory. 4. {Elliptical} integral groups and {Jacobian}
elliptic functions in the complex plane]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 191",
year = "1967",
DOI = "https://doi.org/10.1007/978-3-662-36381-2",
ISBN = "3-662-36381-X, 3-662-35552-3 (print), 3-662-36381-X
(e-book)",
ISBN-13 = "978-3-662-36381-2, 978-3-662-35552-7 (print),
978-3-662-36381-2 (e-book)",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/978-3-662-36381-2",
acknowledgement = ack-nhfb,
language = "German",
}
@Book{Tolke:1967:PFJ,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 3. Jacobische elliptische
Funktionen, Legendresche elliptische Normalintegrale
und spezielle Weierstrasssche Zeta- und
Sigma-Funktionen}. ({German}) [{Practical} functional
theory. 3. {Jacobian} elliptic functions, Legendre
elliptical normal Integrals and special {Weierstrass}
zeta- and sigma functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 180",
year = "1967",
DOI = "https://doi.org/10.1007/978-3-662-36379-9",
ISBN = "3-642-50264-4, 3-662-36379-8, 3-662-35550-7 (print),
3-662-36379-8 (e-book)",
ISBN-13 = "978-3-642-50264-4, 978-3-662-36379-9,
978-3-662-35550-3 (print), 978-3-662-36379-9 (e-book)",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/content/978-3-662-36379-9",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "5 Jacobische elliptische Funktionen und
zugeh{\"o}rige logarithmische Ableitungen \\
108. Definitionen \\
109. Funktionalgleichungen \\
110. Periodenverhalten und Substitutionen \\
111. Funktionswerte an den Stellen $ 0, \pm
\frac{1}{2}, \pm \frac{ix}{2}, \pm \frac{1}{2}, \pm
\frac{ix}{2} $ bzw. $ 0, \pm K, \pm iK', \pm K \pm iK'
$ \\
112. Trigonometrische und hyperbolische
Reihenentwicklungen \\
113. Potenzreihen-Entwicklungen \\
114. Imagin{\"a}re Argumenttransformation, reziproke
Modultransformation und imagin{\"a}re
Modultransformation \\
115. Ableitungen \\
116. Gausssche und Landensche Transformation.
Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und
$\zeta \pm \frac{ix}{4} $ \\
117. Additionstheoreme. Transformationsgleichungen
f{\"u}r doppeltes und halbes Argument. Weitere
Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und
$\zeta \pm \frac{ix}{4}$ sowie f{\"u}r $\zeta \pm
\frac{1}{4} \pm \frac{ix}{4} $ \\
118. Die Logarithmen der logarithmischen Ableitungen
der Jacobischen elliptischen Funktionen \\
119. {\"U}berg{\"a}nge vom (?,?)-System auf das $(z,
k)$-System \\
120. Funktionsverlauf der Jacobischen elliptischen
Funktionen und der zugeh{\"o}rigen Ableitungen und
logarithmischen Ableitungen im Reellen. Ausartungen \\
121. Differentialgleichungen erster und zweiter Ordnung
\\
122. Die Integrale der Jacobischen elliptischen
Funktionen \\
123. Die Integrale der logarithmischen Ableitungen der
Jacobischen elliptischen Funktionen \\
6 Umkehrfunktionen der Jacobischen elliptischen
Funktionen und elliptische Normalintegrale erster
Gattung. Elliptische Amplitudenfunktion sowie
Legendresche $F$- und $E$-Funktion. Elliptische
Normalintegrale zweiter Gattung. Jacobische Zeta- und
Heumansche Lambda-Funktion \\
124. Die 18 Umkehrfunktionen der Jacobischen
elliptischen Funktionen und ihrer logarithmischen
Ableitungen. (Elliptische Normalintegrale erster
Gattung.) Additionstheoreme der Umkehrfunktionen \\
125. Elliptische Normalintegrale erster Gattung in
hyperbolischer Form \\
126. Potenzreihen-Entwicklungen der Umkehrfunktionen
\\
127. Die elliptische Amplitudenfunktion $? = \am(z, k)$
und ihre Umkehrfunktion $z = F(?, k)$. Die vier
trigonometrischen Legendreschen Normalintegrale erster
Gattung \\
128. Darstellung der 18 Umkehrfunktionen und der
elliptischen Normalintegrale erster Gattung durch die
Funktion F. Die vier hyperbolischen Legendreschen
Normalintegrale erster Gattung und die Funktion $F$
f{\"u}r imagin{\"a}res Argument \\
129. Die Legendresche $E$-Funktion f{\"u}r reelles und
imagin{\"a}res Argument \\
130. Die 18 Integrale der Quadrate der Jacobischen
elliptischen Funktionen und ihrer logarithmischen
Ableitungen, die 12 durch Umformung der letzteren
entstehenden hyperbolischen Integrale, die 24
Normalintegrale zweiter Gattung und die acht
trigonometrischen und hyperbolischen Legendreschen
Normalintegrale zweiter Gattung \\
131. Die 46 Normalintegrale erster und zweiter Gattung
mit linearen trigonometrischen und hyperbolischen
Funktionen \\
132. Jacobische Zeta-Funktion und Heumansche
Lambda-Funktion \\
7 Normalintegrale dritter Gattung. Legendresche
$\Pi$-Funktion. Zur{\"u}ckf{\"u}hrung des allgemeinen
elliptischen Integrals auf Normalintegrale erster,
zweiter und dritter Gattung \\
133. Die 96 Normalintegrale dritter Gattung in
Jacobischer Form \\
134. Die acht zu den logarithmischen Ableitungen der
Jacobischen elliptischen Funktionen geh{\"o}rigen
Normalintegrale dritter Gattung \\
135. 48 Quotientenintegrale und 48 spezielle
Normalintegrale dritter Gattung in der Jacobischen Form
\\
136. Algebraische Form der elliptischen Normalintegrale
dritter Gattung \\
137. Darstellung der vollst{\"a}ndigen Normalintegrale
dritter Gattung durch Jacobische Zeta- und Heumansche
Lambda-Funktionen \\
138. Die $\Pi$-Funktion und die Integrale dritter
Gattung in trigonometrischer Form \\
139. Die 48 speziellen Normalintegrale dritter Gattung
in algebraischer Form \\
140. Weitere sechs spezielle Normalintegrale dritter
Gattung \\
141. Zur{\"u}ckf{\"u}hrung des allgemeinen elliptischen
Integrals in der Legendreschen Form auf Normalintegrale
erster, zweiter und dritter Gattung \\
8 Spezielle Weierstra{\ss}sche Zeta-Funktionen \\
142. Definitions- und Funktionalgleichungen \\
143. Substitutionen \\
144. Relatives Periodenverhalten. Spezielle
Funktionswerte. Funktionsverlauf \\
145. Lineare Beziehungen zu den logarithmischen
Ableitungen der Jacobischen elliptischen Funktionen und
deren Ableitungen \\
146. Integrale der $\Pi$-Funktionen als Weierstrasssche
Zeta-Funktionen und Ableitungen der Zeta-Funktionen \\
147. Differentialtransformationen f{\"u}r doppelte und
halbe Parameter \\
148. Gausssche und Landensche Transformation \\
149. Additionstheoreme und Transformationsgleichungen
f{\"u}r doppeltes und halbes Argument \\
150. Trigonometrische, hyperbolische und
Potenzreihen-Entwicklungen \\
151. Homogenit{\"a}tstransformation der Funktionen",
}
@Article{Verma:1967:NSG,
author = "Arun Verma",
title = "A Note on the Summation of the Generalised
Hypergeometric Functions (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "232--236",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wigner:1967:BRW,
author = "Eugene P. Wigner",
title = "Book Review: {Wilhelm Magnus, Fritz Oberhettinger, and
R. P. Soni, \booktitle{Formulas and Theorems for the
Special Functions of Mathematical Physics}}",
journal = j-PHYS-TODAY,
volume = "20",
number = "12",
pages = "81--81",
month = dec,
year = "1967",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.3034082",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Sat Jul 28 07:53:52 MDT 2012",
bibsource = "http://www.physicstoday.org/search;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.aip.org/link/phtoad/v20/i12/p81/s1",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
}
@Article{Wood:1967:CEI,
author = "Van E. Wood",
title = "{Chebyshev} Expansions for Integrals of the Error
Function (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "99",
pages = "494--496",
month = jul,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 7-digit approximations for $ i^n \erfc (x),
n = 1, 2 $.",
}
@Article{Yarbrough:1967:PCC,
author = "Lynn Yarbrough",
title = "Precision calculations of $e$ and $ \pi $ constants",
journal = j-CACM,
volume = "10",
number = "9",
pages = "537--537",
month = sep,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363566.363578",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; number base conversion",
remark = "Gives decimal, octal, and hexadecimal values of $e$
and $ \pi $ to 100 digits, and notes ``The difficulty
arises because assemblers and compilers are hardly ever
designed to convert decimal constants to a precision of
more than a dozen or so digits. Thus, if calculations
to greater precision are to be done, constants usually
must be input in octal or other binary-derived
representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Anonymous:1968:ISA,
author = "Anonymous",
title = "Index by Subject to Algorithms, 1960--1968",
journal = j-CACM,
volume = "11",
number = "12",
pages = "827--830",
month = dec,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 09:29:34 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Book{Arsenin:1968:BES,
author = "V. Ja. (Vasilii Jakovlevich) Arsenin",
title = "Basic equations and special functions of mathematical
physics",
publisher = "Iliffe",
address = "London, UK",
pages = "7 + 361",
year = "1968",
ISBN = "0-592-05035-1",
ISBN-13 = "978-0-592-05035-5",
LCCN = "QC20 .A693",
bibdate = "Sat Oct 30 18:25:22 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Translation by S. Chomet, Kings College, London of
Matematicheska{\"e}i{\`\i}a fizika.",
acknowledgement = ack-nhfb,
subject = "Mathematical physics",
}
@Article{Ascari:1968:LRG,
author = "A. Ascari and P. G. Novario",
title = "L'algoritmo {$ Q D $} di {Rutishauser} e la
generazione di funzioni speciali nel calcolo
automatico. ({Italian}) [{The} {$ Q D $} algorithm of
{Rutishauser} and the generation of special functions
in automatic calculation]",
journal = j-CALCOLO,
volume = "5",
number = "1",
pages = "162--173",
month = "????",
year = "1968",
CODEN = "CALOBK",
DOI = "https://doi.org/10.1007/BF02576063",
ISSN = "0008-0624 (print), 1126-5434 (electronic)",
ISSN-L = "0008-0624",
bibdate = "Mon Aug 24 21:37:24 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://link.springer.com/article/10.1007/BF02576063",
acknowledgement = ack-nhfb,
fjournal = "Calcolo: a quarterly on numerical analysis and theory
of computation",
journal-URL = "http://link.springer.com/journal/10092",
language = "Italian",
subject-dates = "Heinz Rutishauser (30 January 1918--10 November
1970)",
}
@Book{Bell:1968:SFS,
author = "W. W. (William Wallace) Bell",
title = "Special functions for scientists and engineers",
publisher = "Van Nostrand",
address = "London, UK",
pages = "xiv + 247",
year = "1968",
LCCN = "QA351 .B4",
bibdate = "Fri Oct 29 21:30:38 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
remark = "Fullerton: Gamma, Beta, Legendre, Bessel, and
Hypergeometric functions as well as orthogonal
polynomials. Reprinted in \cite{Bell:2004:SFS}.",
subject = "Functions, Special",
}
@Article{Bergson:1968:ACR,
author = "A. Bergson",
title = "Certification of and remark on {Algorithm 304}
[{S15}]: {Normal} curve integral",
journal = j-CACM,
volume = "11",
number = "4",
pages = "271--271",
month = apr,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362991.363048",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:19 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Hill:1967:ANCa,Hill:1967:RAS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
remark = "Fullerton: 50-line Algol Program that is superceded by
numerous {\tt erf} routines.",
}
@Article{Bingulac:1968:RAA,
author = "S. P. Bingulac",
title = "{R68-38} Accurate Analog Computer Generation of
{Bessel} Functions for Large Ranges",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "8",
pages = "819--819",
month = aug,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229133",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687462",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chiarella:1968:EIR,
author = "C. Chiarella and A. Reichel",
title = "On the Evaluation of Integrals Related to the Error
Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "137--143",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1968:RCAa,
author = "W. J. Cody and H. C. {Thacher, Jr.}",
title = "Rational {Chebyshev} approximations for the
exponential integral {$ E_1 (x) $}",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "641--649",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "38\#6745",
bibdate = "Wed Jan 17 08:57:34 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 10^{-21} $.",
}
@Article{Dorrer:1968:ADS,
author = "Egon Dorrer",
title = "{Algorithm 322}: {$F$}-Distribution [{S14}]",
journal = j-CACM,
volume = "11",
number = "2",
pages = "116--117",
month = feb,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:18 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: 50-line Algol Program.",
}
@Book{Fike:1968:CEM,
author = "C. T. Fike",
title = "Computer Evaluation of Mathematical Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 227",
year = "1968",
LCCN = "QA297 .F5",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Fleckner:1968:MCF,
author = "Oscar L. Fleckner",
title = "A Method for the Computation of the {Fresnel}
Integrals and Related Functions",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "635--640",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Fox:1968:CPN,
author = "L. Fox and I. B. Parker",
title = "{Chebyshev} Polynomials in Numerical Analysis",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "ix + 205",
year = "1968",
ISBN = "0-19-859614-6",
ISBN-13 = "978-0-19-859614-1",
LCCN = "QA297 .F65",
MRclass = "65.10",
MRnumber = "228149",
MRreviewer = "G. N. Lance",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
note = "Reprinted in 1972 with corrections, but same ISBN.",
series = "Oxford mathematical handbooks",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
mynote = "JRUL: 517",
series-editor = "John Crank and C. C. Ritchie",
subject = "Chebyshev polynomials; Numerical analysis",
tableofcontents = "TO DO: find this!",
xxauthor = "L. (Leslie) Fox and I. B. (Ian Bax) Parker",
}
@Article{Galant:1968:HAG,
author = "D. C. Galant and P. F. Byrd",
title = "High Accuracy Gamma Function Values for Some Rational
Arguments (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "104",
pages = "885--887",
month = oct,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Hart:1968:CAa,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-88275-642-7",
ISBN-13 = "978-0-88275-642-4",
LCCN = "QA 297 C64 1978",
bibdate = "Tue Dec 14 22:55:11 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Reprinted 1978 with corrections.",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
2: General Methods of Computing Functions / 10 \\
3: Least Maximum Approximations / 42 \\
4: The Choice and Application of Approximations / 58
\\
5: Description and Use of the Tables / 82 \\
6: Function Notes / 89 \\
7: Tables of Coefficients / 155 \\
Appendix A: Conversion Algorithms / 307 \\
Appendix B: Bibliography of Approximations / 313 \\
Appendix C: Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
tableofcontents = "1: The Design of a Function Subroutine / 1 \\
1.1 Introduction / 1 \\
1.2 General Considerations in Writing a Function
Subroutine / 2 \\
1.3 Relation of the Function Subroutine to the Computer
System / 3 \\
1.4 The Three Main Types of Function Subroutine / 4 \\
1.5 Special Programming Techniques / 7 \\
1.6 Subroutine Errors / 7 \\
1.7 Final Steps / 9 \\
2: General Methods of Computing Functions / 10 \\
2.1 Introduction / 10 \\
2.2 Application of Infinite Expansions / 11 \\
2.3 Recurrence and Difference Relations / 23 \\
2.4 Iterative Techniques / 27 \\
2.5 Integral Representations / 28 \\
2.6 Differential Equations / 29 \\
2.7 Tabular Data / 32 \\
2.8 Convergence Acceleration / 33 \\
3: Least Maximum Approximations / 42 \\
3.1 Introduction / 42 \\
3.2 Properties of Least Maximum Approximations / 43 \\
3.3 Nearly Least Maximum Approximations / 46 \\
3.4 Rational Approximation / 51 \\
3.5 Segmented Approximation / 54 \\
3.6 Computation of the Tables / 55 \\
4: The Choice and Application of Approximations / 58
\\
4.1 Introduction / 5 8 \\
4.2 Domain Considerations / 58 \\
4.3 Machine Considerations / 62 \\
4.4 Conditioning of Approximations / 65 \\
4.5 Polynomial Forms / 67 \\
4.6 Rational Forms / 73 \\
4.7 Transformation Algorithms / 78 \\
5: Description and Use of the Tables / 82 \\
5.1 Introduction / 22 \\
5.2 Function Notes / 82 \\
5.3 Accuracy of the Coefficients / 83 \\
5.4 How to Use the Tables / 86 \\
5.5 Preparation of the Tables / 88 \\
6: Function Notes / 89 \\
6.1 Square Root, Cube Root / 89 \\
6.2 Exponential and Hyperbolic Functions / 96 \\
6.3 The Logarithm Function / 105 \\
6.4 Trigonometric Functions / 112 \\
6.5 The Inverse Trigonometric Functions / 120 \\
6.6 The Gamma Function and Its Logarithm / 130 \\
6.7 The Error Function / 136 \\
6.8 Bessel Functions / 141 \\
6.9 Complete Elliptic Integrals / 150 \\
7: Tables of Coefficients / 155 \\
Appendix A Conversion Algorithms / 307 \\
Appendix B Bibliography of Approximations / 313 \\
Appendix C Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
}
@Book{Hart:1968:CAb,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-471-35630-1",
ISBN-13 = "978-0-471-35630-1",
LCCN = "QA297 .C64",
bibdate = "Sat Jan 14 14:53:06 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "The SIAM series in applied mathematics",
acknowledgement = ack-nhfb,
}
@Article{Kolbig:1968:ADS,
author = "K. S. K{\"o}lbig",
title = "{Algorithm 327}: {Dilogarithm} [{S22}]",
journal = j-CACM,
volume = "11",
number = "4",
pages = "270--271",
month = apr,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362991.363043",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:19 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$d(x) = \int_0^x (\ln|1-y|/y)\,dy$; dilogarithm;
special functions",
}
@Article{Luke:1968:AEI,
author = "Yudell L. Luke",
title = "Approximations for Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "627--634",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{MacLaren:1968:RAP,
author = "M. D. MacLaren",
title = "Remark on {Algorithm 272}: {Procedure} for the normal
distribution functions",
journal = j-CACM,
volume = "11",
number = "7",
pages = "498--498",
month = jul,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363397.363553",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:20 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{MacLaren:1965:APN}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "probability functions",
}
@Article{Mavromatis:1968:IFP,
author = "H. A. Mavromatis and K. Schilcher",
title = "Inverse Functions of the Products of Two {Bessel}
Functions and Applications to Potential Scattering",
journal = j-J-MATH-PHYS,
volume = "9",
number = "10",
pages = "1627--1632",
month = oct,
year = "1968",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1664492",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 11:55:17 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v9/i10/p1627_s1",
acknowledgement = ack-nhfb,
classification = "A0380 (General theory of scattering)",
corpsource = "Dept. Physics, American Univ. Beirut, Lebanon",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "functions; mathematics; scattering",
onlinedate = "28 October 2003",
pagecount = "6",
}
@Article{Mechel:1968:IRT,
author = "Fr. Mechel",
title = "Improvement in Recurrence Techniques for the
Computation of {Bessel} Functions of Integral Order (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "202--205",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Miller:1968:LTS,
author = "Willard Miller",
title = "{Lie} theory and special functions",
volume = "43",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 338",
year = "1968",
ISBN = "0-12-497450-3",
ISBN-13 = "978-0-12-497450-0",
LCCN = "QA387 .M55 1968eb",
bibdate = "Sat Oct 30 19:07:04 MDT 2010",
bibsource = "catalog.library.cornell.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in science and engineering",
acknowledgement = ack-nhfb,
remark = "Reprinted 1979 with same ISBN.",
subject = "Lie groups; Functions, Special",
}
@Article{Nagashima:1968:EFN,
author = "Takashi Nagashima",
title = "On elementary functions of natural numbers",
journal = "Hitotsubashi J. Arts Sci.",
volume = "9",
pages = "50--58",
year = "1968",
ISSN = "0073-2788",
MRclass = "02.72",
MRnumber = "MR0232678 (38 \#1001)",
MRreviewer = "R. L. Goodstein",
bibdate = "Mon Oct 24 11:33:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Hitotsubashi Journal of Arts \& Sciences",
}
@Article{Ng:1968:DSS,
author = "Edward W. Ng",
title = "On the direct summation of series involving higher
transcendental functions",
journal = j-J-COMPUT-PHYS,
volume = "3",
number = "2",
pages = "334--338",
month = oct,
year = "1968",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(68)90029-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 08:28:02 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999168900296",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{OBrien:1968:CAC,
author = "William M. O'Brien and Joan Wood",
title = "Certification of {Algorithm 299} [{S15}]:
{Chi-squared} integral",
journal = j-CACM,
volume = "11",
number = "4",
pages = "271--271",
month = apr,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:19 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "chi-squared; probability functions",
remark = "Fullerton: Corrections to an Algol procedure.",
}
@Article{Osborn:1968:IBF,
author = "David Osborn and Richard Madey",
title = "The Incomplete Beta Function and its Ratio to the
Complete Beta Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "159--162",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Richardson:1968:SUP,
author = "Daniel Richardson",
title = "Some Undecidable Problems Involving Elementary
Functions of a Real Variable",
journal = j-J-SYMBOLIC-LOGIC,
volume = "33",
number = "4",
pages = "514--520",
month = dec,
year = "1968",
CODEN = "JSYLA6",
ISSN = "0022-4812 (print), 1943-5886 (electronic)",
ISSN-L = "0022-4812",
MRclass = "02.75",
MRnumber = "39 #1330",
bibdate = "Mon May 19 13:04:20 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Logic",
journal-URL = "http://projecteuclid.org/euclid.jsl;
http://www.jstor.org/journal/jsymboliclogic",
}
@Article{Schmidt:1968:AEK,
author = "Jochen W. Schmidt",
title = "{Asymptotische Einschlie{\ss}ung bei
konvergenzbeschleunigenden Verfahren. II}. ({German})
[{Asymptotic enclosure with convergence acceleration
method. II}]",
journal = j-NUM-MATH,
volume = "11",
number = "1",
pages = "53--56",
month = jan,
year = "1968",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration",
language = "German",
}
@Article{Strecok:1968:CIE,
author = "Anthony J. Strecok",
title = "On the Calculation of the Inverse of the Error
Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "144--158",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004772",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 18-digit approximations.",
}
@Book{Talman:1968:SFG,
author = "James D. Talman",
title = "Special Functions: a Group Theoretic Approach Based on
Lectures by {Eugene P. Wigner}",
publisher = pub-BENJAMIN,
address = pub-BENJAMIN:adr,
pages = "xii + 260",
year = "1968",
LCCN = "????",
bibdate = "Sat Oct 30 16:57:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "With an introduction by Eugene P. Wigner.",
series = "The mathematical physics monograph series",
acknowledgement = ack-nhfb,
keywords = "group theory; mathematical function; special
functions",
}
@Book{Tolke:1968:PFA,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 5. Allgemeine
Weierstrasssche Funktionen und Ableitungen nach dem
Parameter: Integrale der Theta-Funktionen und
Bilinear-Entwicklungen}. ({German}) [{Practical}
functional theory. 5. {General} information on
{Weierstrass} functions and derivatives according to
the parameters: integrals of theta functions and
bilinear developments]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 158",
year = "1968",
ISBN = "3-662-11121-7, 3-662-11120-9",
ISBN-13 = "978-3-662-11121-5, 978-3-662-11120-8",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "12 Allgemeine Weierstra{\ss}sche Funktionen.
Doppelreihen-Entwicklungen \\
13 Die Ableitungen nach dem Parameter und dem Modul \\
14 Integrale von Theta-Funktionen (D-Funktionen) \\
15 Mehrdimensionale Theta- und D-Funktionen \\
16 Theta- und D-Funktionen mit imagin{\"a}ren
Parametern \\
17 Greensche Funktionen und Bilinear-Entwicklungen",
xxISBN = "3-662-11031-8",
xxISBN-13 = "978-3-662-11031-7",
}
@Article{Tooper:1968:SCP,
author = "Robert F. Tooper and John Mark",
title = "Simplified Calculation of {$ \operatorname {Ei}(x) $}
for Positive Arguments, and a Short Table of $
\operatorname {Shi}(x) $ (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "102",
pages = "448--449",
month = apr,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "exponential integral ($\operatorname{Ei}(x)$);
hyperbolic sine integral ($\operatorname{Shi}(x)$)",
}
@Article{Wilcox:1968:ZTN,
author = "Peter H. Wilcox",
title = "The Zeros of $ {P}^1_\nu (\cos \theta) $ and $ \frac
{\partial }{\partial \theta } {P}^1_\mu (\cos \theta) $
(in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "22",
number = "101",
pages = "205--208",
month = jan,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2004783",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: $ P_\nu^1 $ are Legendre functions.",
}
@Article{Wimp:1968:RFH,
author = "Jet Wimp",
title = "Recursion Formulae of Hypergeometric Functions",
journal = j-MATH-COMPUT,
volume = "22",
number = "102",
pages = "363--373",
month = apr,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Witte:1968:AAJ,
author = "B. F. W. Witte",
title = "{ACM Algorithm 332}: {Jacobi} Polynomials",
journal = j-CACM,
volume = "11",
number = "6",
pages = "436--437",
month = jun,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:33:08 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Skovgaard:1975:RAJ}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Wrench:1968:CTS,
author = "John W. {Wrench, Jr.}",
title = "Concerning Two Series for the Gamma Function",
journal = j-MATH-COMPUT,
volume = "22",
number = "103",
pages = "617--626",
month = jul,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRnumber = "MR 0237078 (38:5371)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Aharoni:1969:C,
author = "Amikam Aharoni",
title = "Computation of {$ K_p(x) $}",
journal = j-J-COMPUT-PHYS,
volume = "4",
number = "2",
pages = "270--271",
month = aug,
year = "1969",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(69)90072-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 08:28:03 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999169900722",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Boersma:1969:ECW,
author = "J. Boersma",
title = "Expansions for {Coulomb} Wave Functions",
journal = j-MATH-COMPUT,
volume = "23",
number = "105",
pages = "51--59",
month = jan,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Buchholz:1969:CHF,
author = "Herbert Buchholz",
title = "The confluent hypergeometric function with special
emphasis on its applications",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xviii + 238",
year = "1969",
LCCN = "QA351 .B813",
bibdate = "Sat Oct 30 21:06:31 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
note = "Translation by H. Lichtblau and K. Wetzel to English
from German ``Die konfluente hypergeometrische
Funktion.''",
series = "Springer tracts in natural philosophy",
acknowledgement = ack-nhfb,
subject = "Hypergeometric functions",
}
@Article{Bulirsch:1969:EBT,
author = "R. Bulirsch",
title = "An extension of the {Bartky}-transformation to
incomplete elliptic integrals of the third kind",
journal = j-NUM-MATH,
volume = "13",
number = "3",
pages = "266--284",
month = jul,
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bulirsch:1969:NCE,
author = "R. Bulirsch",
title = "Numerical calculation of elliptic integrals and
elliptic functions. {III}",
journal = j-NUM-MATH,
volume = "13",
number = "4",
pages = "305--315",
month = aug,
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Carlson:1969:CBE,
author = "B. C. Carlson",
title = "A connection between elementary functions and higher
transcendental functions",
journal = j-SIAM-J-APPL-MATH,
volume = "17",
pages = "116--148",
year = "1969",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
MRclass = "33.20 (30.00)",
MRnumber = "40 \#408",
MRreviewer = "S. K. Bose",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
}
@InProceedings{Clark:1969:SCE,
author = "N. W. Clark and W. J. Cody",
title = "Self-contained exponentiation",
crossref = "AFIPS:1969:ACPb",
pages = "701--706",
year = "1969",
bibdate = "Wed Sep 07 10:49:33 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Clemm:1969:ACV,
author = "Donald S. Clemm",
title = "{Algorithm 352}: {Characteristic} Values and
Associated Solutions of {Mathieu}'s Differential
Equation [{S22}]",
journal = j-CACM,
volume = "12",
number = "7",
pages = "399--407",
month = jul,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:27 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4170 (Differential equations); C7300 (Natural
sciences computing)",
corpsource = "Wright-Patterson Air Force Base, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "differential equations; function evaluation;
subroutines",
remark = "Fullerton: Long set of FORTRAN routines to evaluate
Mathieu functions as well as several Bessel
functions.",
}
@Article{Cobb:1969:CAS,
author = "S. M. Cobb",
title = "Certification of {Algorithm 47} [{S16}]: {Associated}
{Legendre} functions of the first kind for real or
imaginary arguments",
journal = j-CACM,
volume = "12",
number = "11",
pages = "635--636",
month = nov,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:28 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "associated Legendre functions of the first kind;
special functions",
remark = "Fullerton: Numerous additional corrections and changes
to an Algol procedure.",
}
@Article{Cody:1969:CAE,
author = "W. J. Cody and Henry C. {Thacher, Jr.}",
title = "{Chebyshev} Approximations for the Exponential
Integral {$ \hbox {Ei}(x) $}",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "289--303",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "39\#3680",
bibdate = "Wed Jan 17 08:57:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1969:CRA,
author = "W. J. Cody and G. Meinardus and R. S. Varga",
title = "{Chebyshev} rational approximations to $ e^{-x} $ on $
[0, \infty) $ and applications to heat conduction
problems",
journal = j-J-APPROX-THEORY,
volume = "2",
number = "??",
pages = "50--65",
month = "??",
year = "1969",
CODEN = "JAXTAZ",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "65.67 (41.00)",
MRnumber = "40\#999",
bibdate = "Wed Jan 17 08:57:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
}
@Article{Cody:1969:RCA,
author = "W. J. Cody",
title = "Rational {Chebyshev} Approximations for the Error
Function",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "631--637",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Farkas:1969:CAS,
author = "I. Farkas",
title = "Certification of {Algorithm 165} [{S21}]: {Complete}
elliptic integrals",
journal = j-CACM,
volume = "12",
number = "1",
pages = "38--38",
month = jan,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "special functions",
}
@Article{Gautschi:1969:ACE,
author = "Walter Gautschi",
title = "{Algorithm 363}: {Complex} Error Function [{S15}]",
journal = j-CACM,
volume = "12",
number = "11",
pages = "635--635",
month = nov,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:28 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Kolbig:1972:CAC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\erf(z)$; special functions",
remark = "Fullerton: 50-line Algol procedure with accuracy to 10
decimal places.",
}
@Article{Gautschi:1969:RAS,
author = "Walter Gautschi",
title = "Remark on {Algorithm 292} [{S22}]: {Regular} {Coulomb}
wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "280--280",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: The first of many remarks.",
}
@Article{Herman:1969:NHE,
author = "G. T. Herman",
title = "A new hierarchy of elementary functions",
journal = j-PROC-AM-MATH-SOC,
volume = "20",
pages = "557--562",
year = "1969",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "02.77",
MRnumber = "40 \#4110",
MRreviewer = "G. E. Sacks",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{Holzwarth:1969:VBB,
author = "A. Holzwarth",
title = "{Ein Verfahren zur Bestimmung bester
Tscheb\-y\-scheff-Ap\-prox\-i\-ma\-tion\-en der
Quadratwurzelfunktion}. ({German}) {A Method for
Determination of Best Chebyshev Approximations to the
Square Root Function}",
journal = j-COMPUTING,
volume = "4",
number = "2",
pages = "168--177",
month = jun,
year = "1969",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "T{\"u}bingen, West Germany",
classification = "C4130",
description = "Chebyshev approximation; numerical analysis",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{King:1969:LEN,
author = "Richard F. King and David L. Phillips",
title = "The Logarithmic Error and {Newton}'s Method for the
Square Root",
journal = j-CACM,
volume = "12",
number = "2",
pages = "87--88",
month = feb,
year = "1969",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362848.362861",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2333",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The problem of obtaining optimal starting values for
the calculation of the square root using Newton's
method is considered. It has been pointed out elsewhere
that if relative error is used as the measure of
goodness of fit, optimal results are not obtained when
the initial approximation is a best fit. It is shown
here that if, instead, the so-called logarithmic error
is used, then a best initial fit is optimal for both
types of error. Moreover, use of the logarithmic error
appears to simplify the problem of determining the
optimal initial approximation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Argonne Nat. Lab., Argonne, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; function evaluation;
iterative methods",
}
@Article{Kolbig:1969:CASa,
author = "K. S. K{\"o}lbig",
title = "Certification of {Algorithm 292} [{S22}]: {Regular}
{Coulomb} wave functions and of remark on {Algorithm
292} [{S22}]: {Regular} {Coulomb} wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "278--279",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: Tests of an Algol procedure.",
}
@Article{Kolbig:1969:CASb,
author = "K. S. K{\"o}lbig",
title = "Certification of {Algorithm 300} [{S22}]: {Coulomb}
wave functions",
journal = j-CACM,
volume = "12",
number = "5",
pages = "279--280",
month = may,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: The first of many remarks.",
}
@Article{Kolbig:1969:RAS,
author = "K. S. K{\"o}lbig",
title = "Remark on {Algorithm 300} [{S22}]: {Coulomb} wave
functions",
journal = j-CACM,
volume = "12",
number = "12",
pages = "692--692",
month = dec,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; special functions",
remark = "Fullerton: One of many remarks.",
}
@Article{Lardner:1969:RBB,
author = "Thomas J. Lardner",
title = "Relations Between {${}_0 F_3 $} and {Bessel}
Functions",
journal = j-SIAM-REVIEW,
volume = "11",
number = "1",
pages = "69--72",
month = "????",
year = "1969",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1011007",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:04 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/11/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1969",
}
@Article{Lewis:1969:FII,
author = "Richard L. Lewis",
title = "On Finite Integrals Involving Trigonometric, {Bessel},
and {Legendre} Functions",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "259--273",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Luke:1969:SFTa,
author = "Yudell L. Luke",
title = "The Special Functions and Their Approximations",
volume = "I",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xx + 349",
year = "1969",
ISBN = "0-12-459901-X",
ISBN-13 = "978-0-12-459901-7",
LCCN = "QA351 .L94 1969",
bibdate = "Wed Dec 15 17:55:35 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Mathematics in Science and Engineering, Volume 53-I,
Editor: Richard Bellman",
acknowledgement = ack-nhfb,
}
@Book{Luke:1969:SFTb,
author = "Yudell L. Luke",
title = "The Special Functions and Their Approximations",
volume = "II",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xx + 485",
year = "1969",
ISBN = "0-12-459902-8",
ISBN-13 = "978-0-12-459902-4",
LCCN = "QA351 .L797",
bibdate = "Wed Dec 15 17:55:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Mathematics in Science and Engineering, Volume 53-II,
Editor: Richard Bellman",
URL = "http://www.sciencedirect.com/science/book/9780124599024",
acknowledgement = ack-nhfb,
tableofcontents = "Dedication / v \\
Preface / vii--ix \\
Contents of Volume I / xv \\
Introduction / xvii--xx \\
IX: Expansions of Generalized Hypergeometric Functions
in Series of Functions of the Same Kind / 1--65 \\
X: The $\tau$-Method / 66--91 \\
XI: Polynomial and Rational Approximations to
Generalized Hypergeometric Functions / 92--132 \\
XII: Recursion Formulas for Polynomials and Functions
which Occur in Infinite Series and Rational
Approximations to Generalized Hypergeometric Functions
/ 133--166 \\
XIII: Polynomial and Rational Approximations for $E(z)
= _2F_1(1, \sigma; \rho + 1; 1/z)$ / 167--185 \\
XIV: Polynomial and Rational Approximations for the
Incomplete Gamma Function / 186--213 \\
XV: Trapezoidal Rule Integration Formulas / 214--226
\\
XVI: Applications / 227--281 \\
XVII: Tables of Coefficients / 282--452 \\
Bibliography / 453--461 \\
Notation Index / 463--467 \\
Subject Index to Volumes I and II / 468--485",
}
@TechReport{Moses:1969:ICS,
author = "Joel Moses",
title = "The integration of a class of special functions with
the {Risch} algorithm",
type = "{AI} Memo (180)",
number = "MAC-M-421",
institution = "Artificial Intelligence Laboratory, Massachusetts
Institute of Technology",
address = "Cambridge, MA, USA",
pages = "13 + 1",
year = "1969",
LCCN = "Q334 M533 no. 180",
bibdate = "Sat Oct 30 18:37:28 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Ng:1969:CPE,
author = "Edward W. Ng and C. J. Devine and R. F. Tooper",
title = "{Chebyshev} Polynomial Expansion of {Bose--Einstein}
Functions of Orders $1$ to $ 10$",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "639--643",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: $ B_p(\eta) = \frac {1}{\Gamma (p - 1)}
\int_0^\infty \frac {x^p}{e^{x - \eta } - 1} \, d t $.
Relative errors down to $ 3 \times 10^{-19} $.",
}
@Article{Reichel:1969:IPV,
author = "Alex Reichel",
title = "The Integral of the $n$ th Power of the {Voigt}
Function",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "645--649",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: The function $ \chi_n(t) = \int_{- \infty
}^\infty \{ U_0 (x, t) \}^n \, d x $, where $ U_0 (x,
t) = \frac {1}{\sqrt {4 \pi t}} \frac {\exp [ - (x -
y)^2 / 4 t]}{1 + y^2} \, d y $ is considered.",
}
@Article{Robertson:1969:CNC,
author = "G. H. Robertson",
title = "Computation of the Noncentral Chi-Square
Distribution",
journal = j-BELL-SYST-TECH-J,
volume = "48",
number = "1",
pages = "201--207",
month = jan,
year = "1969",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1969/BSTJ.1969.4801.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol48/bstj48-1-201.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Sollfrey:1969:IFP,
author = "William Sollfrey",
title = "Inverse Functions of the Products of Two {Bessel}
Functions",
journal = j-J-MATH-PHYS,
volume = "10",
number = "8",
pages = "1429--1430",
month = aug,
year = "1969",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1664985",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 11:55:26 MDT 2011",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v10/i8/p1429_s1",
acknowledgement = ack-nhfb,
classification = "A0200 (Mathematical methods in physics)",
corpsource = "RAND Corp., Santa Monica, CA, USA",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "functions",
onlinedate = "4 November 2003",
pagecount = "2",
}
@Article{TadeudeMedeiros:1969:APF,
author = "Adilson {Tadeu de Medeiros} and Georges Schwachheim",
title = "{Algorithm 349}: {Polygamma} Functions with Arbitrary
Precision [{S14}]",
journal = j-CACM,
volume = "12",
number = "4",
pages = "213--214",
month = apr,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:25 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See certification \cite{Lewis:1975:CPF}.",
abstract = "This procedure assigns to polygam the value of the
polygamma function of order n for any real argument
$z$. For $ n = 0$, we have the psi or digamma function,
for $ n = 1$ the trigamma function, for $ n = 2$ the
tetragamma function, and so on.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7300 (Natural sciences computing)",
corpsource = "Centro Brasileiro de Pesquisas Fisicas, Rio de
Janeiro, Brazil",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "digamma function; mathematics; polygamma function; psi
function; special functions; subroutines; tetragamma
function; trigamma function",
remark = "Fullerton: 150-line Algol procedure.",
}
@InProceedings{Tesler:1969:AEF,
author = "G. S. Tesler",
booktitle = "Mathematical provisioning of electronic digital
computers and effective organization of the computing
process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2",
title = "The approximation of elementary functions by means of
polynomials of degree zero and one. ({Russian})",
publisher = "Akad. Nauk Ukrain. SSR",
address = "Kiev, USSR",
pages = "75--88",
year = "1969",
MRclass = "65D15",
MRnumber = "45 \#4600",
MRreviewer = "I. Selihova",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Book{Tolke:1969:PFT,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet
der Theta-Funktionen und der elliptischen Funtionen}.
({German}) [{Practical} functional theory. 6. {Tables}
from the field of theta functions and elliptic
functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "lxxxii + 449 (vol. 1)",
year = "1969",
ISBN = "",
ISBN-13 = "",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Two volumes",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Turner:1969:DSC,
author = "L. R. Turner",
title = "Difficulty in {$ \sin $ \slash$ \cos $} Routine",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "13--13",
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Feb 15 15:23:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{VandeVel:1969:SEM,
author = "H. {Van de Vel}",
title = "On the Series Expansion Method for Computing
Incomplete Elliptic Integrals of the First and Second
Kinds",
journal = j-MATH-COMPUT,
volume = "23",
number = "105",
pages = "61--69",
month = jan,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Zaker:1969:CCE,
author = "T. A. Zaker",
title = "Calculation of the complementary error function of
complex argument",
journal = j-J-COMPUT-PHYS,
volume = "4",
number = "3",
pages = "427--430",
month = oct,
year = "1969",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(69)90011-4",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Thu Dec 04 16:20:39 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Bray:1970:CAR,
author = "T. Bray",
title = "Certification of {Algorithm 22, Ricatti--Bessel
Functions of First and Second Kind}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "448--448",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Oct 29 21:49:15 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: An error in an Algol procedure is
reported.",
}
@Article{Carlitz:1970:SRF,
author = "L. Carlitz",
title = "Some Reduction Formulas for Generalized Hypergeometric
Functions",
journal = j-SIAM-J-MATH-ANA,
volume = "1",
number = "2",
pages = "243--245",
month = may,
year = "1970",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sun Nov 28 19:21:58 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/2;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Carlson:1970:HSS,
author = "B. C. Carlson",
title = "Hidden Symmetries of Special Functions",
journal = j-SIAM-REVIEW,
volume = "12",
number = "3",
pages = "332--345",
month = jul,
year = "1970",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1012078",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:20 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/12/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://www.jstor.org/stable/2028552",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1970",
}
@Article{Chen:1970:CGI,
author = "Reuven Chen",
title = "On the Computation of the Generalized Integral in Glow
Curve Theory",
journal = j-J-COMPUT-PHYS,
volume = "6",
number = "2",
pages = "314--316",
month = oct,
year = "1970",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(70)90027-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Fri Oct 29 22:09:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Cochran:1970:NTF,
author = "James Alan Cochran and Judith N. Hoffspiegel",
title = "Numerical Techniques for Finding $ \nu $-Zeros of
{Hankel} Functions",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "413--422",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1970:CAC,
author = "W. J. Cody and K. E. Hillstrom",
title = "{Chebyshev} Approximations for the {Coulomb} Phase
Shift",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "671--677",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.25",
MRnumber = "42\#8661",
bibdate = "Wed Jan 17 08:57:04 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Relative errors down to $ 4 \times 10^{-19}
$.",
}
@Article{Cody:1970:CAD,
author = "W. J. Cody and Kathleen A. Paciorek and Henry C.
{Thacher, Jr.}",
title = "{Chebyshev} approximations for {Dawson}'s integral",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "171--178",
month = jan,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.20",
MRnumber = "41\#2883",
bibdate = "Wed Jan 17 08:57:30 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1970:RAC,
author = "W. J. Cody and Kathleen A. Paciorek",
title = "Remark on {Algorithm} 292 [{S22}]: Regular {Coulomb}
Wave Functions",
journal = j-CACM,
volume = "13",
number = "9",
pages = "573",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Nov 16 23:58:51 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: More modifications to an Algol procedure.",
}
@Article{Darlington:1970:AAA,
author = "Sidney Darlington",
title = "Analytical Approximations to Approximations in the
{Chebyshev} Sense",
journal = j-BELL-SYST-TECH-J,
volume = "49",
number = "1",
pages = "1--32",
month = jan,
year = "1970",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4901.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-1-1.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@TechReport{DeLugish:1970:CAA,
author = "Bruce Gene DeLugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Functions in a Binary Computer",
number = "399",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, Illinois",
pages = "191",
year = "1970",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Gautschi:1970:RAD,
author = "Walter Gautschi and Bruce J. Klein",
title = "Remark on {Algorithm 282, Derivatives of $ e^x / x $,
$ \cos (x) / x $, and $ \sin (x) / x $}",
journal = j-CACM,
volume = "13",
number = "1",
pages = "53--54",
month = jan,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 07:27:17 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gautschi:1966:AD}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Corrections are given for several Algol
procedures.",
}
@Article{Gautschi:1970:RCC,
author = "Walter Gautschi and Bruce J. Klein",
title = "Recursive computation of certain derivatives --- a
study of error propagation",
journal = j-CACM,
volume = "13",
number = "1",
pages = "7--9",
month = jan,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65Q05",
MRnumber = "46 1115",
MRreviewer = "D. F. Mayers",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "A brief study is made of the propagation of errors in
linear first-order difference equations. The recursive
computation of successive derivatives of $ (e^x) / x $
and $ (\cos x) / x $ is considered as an
illustration.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4110 (Error analysis in numerical methods)",
corpsource = "Purdue Univ., Lafayette, IN, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "difference equations; error analysis; error
propagation; recursive computation; successive
derivatives",
remark = "Fullerton: Recursive calculation of derivatives of $
e^x / x $ and $ \cos (x) / x $ is considered.",
}
@Article{Hill:1970:AASa,
author = "G. W. Hill",
title = "{ACM Algorithm 395}: {Student}'s $t$-Distribution",
journal = j-CACM,
volume = "13",
number = "10",
pages = "617--619",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "statistics; subroutines",
remark = "Fullerton: Description of a 50-line Algol procedure.",
}
@Article{Hill:1970:AASb,
author = "G. W. Hill",
title = "{ACM Algorithm 396}: {Student}'s $t$-Quantiles",
journal = j-CACM,
volume = "13",
number = "10",
pages = "619--620",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also
\cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "function evaluation; statistics; subroutines",
remark = "Fullerton: Description of a 50-line Algol procedure.",
}
@Article{Holmgren:1970:RAN,
author = "Bo Holmgren",
title = "Remark on {Algorithm 304, Normal Curve Integral}",
journal = j-CACM,
volume = "13",
number = "10",
pages = "624--624",
month = oct,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 08:18:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Jones:1970:GHF,
author = "Alan L. Jones",
title = "The generalized hypergeometric function",
journal = j-SIGPLAN,
volume = "5",
number = "3",
pages = "26--27",
month = mar,
year = "1970",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 25 06:40:57 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Kolbig:1970:CZI,
author = "K. S. Kolbig",
title = "Complex Zeros of an Incomplete {Riemann} Zeta Function
and of the Incomplete Gamma Function",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "679--696",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lehman:1970:DZR,
author = "R. S. Lehman",
title = "On the distribution of zeros of the {Riemann}
zeta-function",
journal = j-PROC-LONDON-MATH-SOC-1,
volume = "3",
number = "20",
pages = "303--320",
month = "????",
year = "1970",
ISSN = "0024-6115 (print), 1460-244X (electronic)",
ISSN-L = "0024-6115",
MRnumber = "MR0258768 (41:3414)",
bibdate = "Mon Oct 24 12:42:07 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "This paper corrects several errors in
\cite{Turing:1953:SCR}. See also
\cite{Trudgian:2011:ITM}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the London Mathematical Society. First
Series",
journal-URL = "http://plms.oxfordjournals.org/content/by/year",
}
@TechReport{Lugish:1970:CAA,
author = "B. G. de Lugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Function in a Binary Computer",
type = "Report",
number = "399",
institution = "Department of Computer Science, University of
Illinois",
pages = "????",
month = jun,
year = "1970",
bibdate = "Fri Sep 02 22:49:20 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Luke:1970:FAE,
author = "Yudell L. Luke",
title = "Further Approximations for Elliptic Integrals",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "191--198",
month = jan,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Minton:1970:GHF,
author = "Barry M. Minton",
title = "Generalized Hypergeometric Function of Unit Argument",
journal = j-J-MATH-PHYS,
volume = "11",
number = "4",
pages = "1375--1376",
month = apr,
year = "1970",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1665270",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 16:39:25 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v11/i4/p1375_s1",
acknowledgement = ack-nhfb,
classification = "A0200 (Mathematical methods in physics)",
corpsource = "Univ. Calgary, Alta., Canada",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "functions",
onlinedate = "28 October 2003",
pagecount = "2",
}
@Article{Ng:1970:CAE,
author = "E. N. Ng",
title = "Certification of {Algorithm 385, Exponential Integral
$ \operatorname {Ei}(x) $}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "448--449",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 09:18:14 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Comments on a FORTRAN routine.",
}
@Article{Ng:1970:CDF,
author = "E. W. Ng and C. J. Devine",
title = "On the Computation of {Debye} Functions of Integer
Orders",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "405--407",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Debye functions are incomplete Riemann zeta
functions. $ \overbar {D}_p(x) = \frac {1}{\Gamma (p -
1)} \int_0^x \frac {t^p}{e^t - 1} \, d t $ and the
complementary integral are calculated to 20 digits.",
}
@Article{Ninomiya:1970:BRS,
author = "Ichizo Ninomiya",
title = "Best Rational Starting Approximations and Improved
{Newton} Iteration for the Square Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "391--404",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Nagoya Univ., Chikua ku, Japan",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computing procedure; function approximation; iterative
methods; Newton iteration; rational approximation;
square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Paciorek:1970:AEI,
author = "K. A. Paciorek",
title = "{Algorithm 385}: {Exponential} Integral {$
\operatorname {Ei}(x) $}",
journal = j-CACM,
volume = "13",
number = "7",
pages = "446--447",
month = jul,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Redish:1970:RAE,Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation);
C7300 (Natural sciences computing)",
corpsource = "Argonne Nat. Lab., IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "integration; subroutines",
remark = "Fullerton: A 100-line FORTRAN routine for both $
\operatorname {E1}(x) $ and $ \operatorname {Ei}(x)
$.",
}
@Article{Raff:1970:CGF,
author = "Morton S. Raff",
title = "On Calculating the Gamma Function of Non-Integral
Arguments",
journal = j-AMER-STAT,
volume = "24",
number = "2",
pages = "22--24",
month = apr,
year = "1970",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 10:52:18 MST 2012",
bibsource = "http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326364;
https://www.math.utah.edu/pub/tex/bib/amstat1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.jstor.org/stable/2681926",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Redish:1970:RAE,
author = "K. A. Redish",
title = "Remark on {Algorithm 385, Exponential Integral $
\operatorname {Ei}(x) $}",
journal = j-CACM,
volume = "13",
number = "12",
pages = "750--750",
month = dec,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Oct 30 09:56:59 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Paciorek:1970:AEI}",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Minor corrections to a FORTRAN routine.",
}
@TechReport{Rothmaier:1970:BQN,
author = "B. Rothmaier",
title = "{Die Berechnung der Quadratwurzel nebst Schranken auf
Dualmaschinen} \toenglish {The Computation of the
Square Root together with [Interval] Bounds on Binary
Machines} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/17",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rothmaier:1970:DSB,
author = "B. Rothmaier",
title = "{Dokumentation der Standardfunktionen des
Betriebssystems Hydra X8} \toenglish {Documentation} of
the Elementary Functions of the Operating System {Hydra
X8} \endtoenglish",
type = "Interner {Bericht}",
number = "Nr. 70/8",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1970",
bibdate = "Fri Jun 11 12:37:53 1999",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Smith:1970:ASH,
author = "Robert R. Smith and Dennis McCall",
title = "{Algorithm 392}: {Systems} of Hyperbolic {P.D.E.}",
journal = j-CACM,
volume = "13",
number = "9",
pages = "567--570",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See remark \cite{Frisch:1972:RAR}.",
acknowledgement = ack-nhfb,
classcodes = "C4170 (Differential equations); C7310 (Mathematics
computing)",
corpsource = "US Naval Electronics Lab. Center, San Diego, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "boundary-value problems; partial differential
equations",
}
@Book{Spain:1970:FMP,
author = "Barry Spain and M. G. (Michael Gambier) Smith",
title = "Functions of Mathematical Physics",
publisher = pub-VAN-NOSTRAND-REINHOLD,
address = pub-VAN-NOSTRAND-REINHOLD:adr,
pages = "xi + 208",
year = "1970",
ISBN = "0-442-07871-4, 0-442-07876-5 (hardcover)",
ISBN-13 = "978-0-442-07871-3, 978-0-442-07876-8 (hardcover)",
LCCN = "QA351 .S69",
bibdate = "Tue Dec 5 10:54:45 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "The New university mathematics series",
URL = "http://books.google.com/books?id=kYgZAQAAIAAJ",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Mathematical physics; Fonctions
sp{\'e}ciales; Physique math{\'e}matique; Functions,
Special; Mathematical physics; Functions, Special;
Fonctions",
tableofcontents = "1: Series solution of second-order linear
homogeneous equations \\
2: Contour integral solutions of an ordinary linear
differential equation \\
3: Oscillation Theorems and Sturm--Liouville Theory \\
4: Asymptotics \\
5: The Gamma function \\
6: The Hypergeometric Equation \\
7: The confluent hypergeometric function \\
8: The Legendre Functions \\
9: Bessel Functions \\
10: Laguerre Polynomials \\
11: Hermite Polynomials \\
Appendix 1: The Laplace and Helmholtz Equations \\
Appendix 2: The Schr{\"o}dinger Equation \\
References \\
Index",
}
@Article{Squire:1970:RAI,
author = "William Squire",
title = "A Rational Approximation to an Integral Appearing in
Glow Curve Theory",
journal = j-J-COMPUT-PHYS,
volume = "6",
number = "1",
pages = "152--253",
month = aug,
year = "1970",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(70)90016-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sat Oct 30 10:57:00 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Srivastava:1970:CRI,
author = "H. M. Srivastava",
title = "Certain Results Involving Generalized Hypergeometric
Functions",
journal = j-SIAM-J-MATH-ANA,
volume = "1",
number = "1",
pages = "75--81",
month = feb,
year = "1970",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
bibdate = "Sun Nov 28 19:21:56 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/1;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Stegun:1970:ACM,
author = "I. A. Stegun and R. Zucker",
title = "Automatic Computing Methods for Special Functions.
Part 1. {Error}, Probability, and Related Functions",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "74B",
number = "3",
pages = "211--224",
month = jul,
year = "1970",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:58:39 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Adjustable double precision FORTRAN
routines for $ \erf $ and $ \erfc $.",
}
@Book{Tolke:1970:PFT,
author = "Friedrich T{\"o}lke",
title = "{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet
der Theta-Funktionen und der elliptischen Funtionen}.
({German}) [{Practical} functional theory. 6. {Tables}
from the field of theta functions and elliptic
functions]",
publisher = pub-SV,
address = pub-SV:adr,
pages = "452--1047 (vol. 2)",
year = "1970",
ISBN = "3-662-13079-3 (print), 3-662-13078-5",
ISBN-13 = "978-3-662-13079-7 (print), 978-3-662-13078-0",
LCCN = "????",
bibdate = "Mon Feb 13 19:01:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Two volumes",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "Sechsstellige Tafel III der Theta-Funktionen und
ihrer logarithmischen Ableitungen, der Jacobischen
elliptischen Funktionen und ihrer logarithmischen
Ableitungen sowie der Weierstrassschen $z$, $?$, und
$?$-Funktionen einschlie{\ss}lich einiger
Parameterfunktionen f{\"u}r $? = z/2K$ als Argument und
bzw. $1/?$ als Parameter $2$ H{\"a}lfte,
Parameterbereich $1 ? 1 / ? 0$ \\
Neunstellige Tafel IV der Legendreschen Normalintegrale
erster und zweiter Gattung sowie der Jacobischen
Zeta-Funktion und der abgewandelten Heumanschen
Lambda-Funktion \\
Sechsstellige Tafel V der $D$-Funktionen erster bis
vierter Ordnung f{\"u}r die Charakteristiken 1 bis 4
\\
Sechsstellige Tafel VI der Legendreschen
Normalintegrale erster und zweiter Gattung sowie der
Funktion \\
\ldots{}",
}
@Article{Wilson:1970:OSA,
author = "M. Wayne Wilson",
title = "Optimal Starting Approximations for Generating Square
Root for Slow or No Divide",
journal = j-CACM,
volume = "13",
number = "9",
pages = "559--560",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2338",
MRreviewer = "J. E. {Dennis, Jr.}",
bibdate = "Tue Apr 08 20:38:30 1997",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "On computing machines with slow or no division, it is
preferable to use an iterative scheme for the square
root different from the classical Heron scheme. The
problem of optimal initial approximants is considered,
and some optimal polynomial initial approximations are
tabulated.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, Houston, TX, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "CACMA; digital arithmetic; ele; iterative methods;
mathematics; numerical methods; optimisation",
}
@Article{Winograd:1970:NMN,
author = "Shmuel Winograd",
title = "On the number of multiplications necessary to compute
certain functions",
journal = j-COMM-PURE-APPL-MATH,
volume = "23",
number = "2",
pages = "165--179",
month = mar,
year = "1970",
CODEN = "CPAMAT, CPMAMV",
DOI = "https://doi.org/10.1002/cpa.3160230204",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
bibdate = "Sat Oct 21 12:05:50 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "Comm. Pure Appl. Math.",
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
keywords = "number of multiplications to evaluate a polynomial",
remark = "From the second paragraph: ``Motzkin [3] introduced
the notion of preconditioning of the coefficients.
Motzkin showed that if, in the course of computing $
P_n(x) = \sum_{i = 0}^n a_i x^i $, operations which
depend only the $ a_i $ are not counted, then only
about $ n / 2 $ multiplications are necessary to
evaluate $ P_n(x) $. The obvious application of this
result is when the same polynomial $ P_n(x) $ has to be
evaluated at many different points.''.",
}
@TechReport{Yohe:1970:RBC,
author = "J. M. Yohe",
title = "Rigorous Bounds on Computed Approximations to Square
Roots and Cube Roots",
type = "MRC Technical Summary",
number = "1088",
institution = "University of Wisconsin, Madison",
year = "1970",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-jr,
}
@Article{Yong:1970:GBA,
author = "Lam Lay Yong",
title = "The Geometrical Basis of the {Ancient Chinese}
Square-Root Method",
journal = j-ISIS,
volume = "61",
number = "1",
pages = "92--102",
month = "Spring",
year = "1970",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:28:39 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302287;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
URL = "http://www.jstor.org/stable/229151",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Zill:1970:SEI,
author = "D. G. Zill and B. C. Carlson",
title = "Symmetric Elliptic Integrals of the Third Kind",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "199--214",
month = jan,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bohan:1971:ADC,
author = "K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov",
title = "The analytic definition of certain elementary
functions. ({Russian}) Questions of modern mathematics
and methods of teaching it at institutions of higher
learning",
journal = "Leningrad. Gos. Ped. Inst. U{\v{c}}en. Zap.",
volume = "404",
pages = "59--78",
year = "1971",
MRclass = "26A09",
MRnumber = "55 \#10612",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Book{Byrd:1971:HEI,
author = "Paul F. Byrd and Morris D. Friedman",
title = "Handbook of Elliptic Integrals for Engineers and
Scientists",
volume = "67",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xvi + 358",
year = "1971",
DOI = "https://doi.org/10.1007/978-3-642-65138-0",
ISBN = "0-387-05318-2 (New York)",
ISBN-13 = "978-0-387-05318-9 (New York)",
LCCN = "QA343 .B95 1971",
bibdate = "Mon Oct 15 16:40:14 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
series = "Die Grundlehren der mathematischen Wissenschaften in
Einzeldarstellungen",
acknowledgement = ack-nhfb,
subject = "Elliptic functions",
tableofcontents = "Introduction / 1--7 \\
Definitions and Fundamental Relations / 8--41 \\
Reduction of Algebraic Integrands to Jacobian Elliptic
Functions / 42--161 \\
Reduction of Trigonometric Integrands to Jacobian
Elliptic Functions / 162--181 \\
Reduction of Hyperbolic Integrands to Jacobian Elliptic
Functions / 182--190 \\
Table of Integrals of Jacobian Elliptic Functions /
191--222 \\
Elliptic Integrals of the Third Kind / 223--239 \\
Miscellaneous Elliptic Integrals Involving
Trigonometric and Hyperbolic Integrands / 240--248 \\
Elliptic Integrals Resulting from Laplace
Transformations / 249--251 \\
Hyperelliptic Integrals / 252--271 \\
Integrals of the Elliptic Integrals / 272--281 \\
Derivatives / 282--287 \\
Miscellaneous Integrals and Formulas / 288--297 \\
Expansions in Series / 298--307 \\
Appendix / 308 \\
Bibliography / 351 \\
Supplemental Bibliography / 353 \\
Index / 355",
}
@Misc{Chen:1971:BAU,
author = "Tien Chi Chen",
title = "Binary arithmetic unit implementing a multiplicative
iteration for the exponential, logarithm, quotient and
square root functions",
howpublished = "United States Patent 3,631,230",
day = "28",
month = dec,
year = "1971",
bibdate = "Tue Jan 08 21:54:11 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/3631230.html",
abstract = "Apparatus and a method is described for efficiently
achieving arithmetic evaluations for functions such as
exponential, logarithm, quotient, and square root with
a minimum use of multiplications or divisions.
Basically, use is made of the fact that $ x(1 \pm
2^{-m}) $ can be evaluated by a shift followed by an
add. A pair of numbers $ (x_k, y_k) $ can represent a
function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
y_n) = y_n $ for logarithm, quotient and square root.
Then, multiplication by shifting is applied to $ x_k $
with suitable adjustments on $ y_k $, until $ x_k $ is
close to unity, at which time $ y_k $ represents the
desired answer. The exponential is computed by
essentially reversing the logarithm procedure. A
termination algorithm further improves accuracy. The
apparatus involves two registers for $ x_k $ and $ y_k
$, a local memory, an adder and a shift register.",
acknowledgement = ack-nhfb,
}
@Article{Choong:1971:RA,
author = "K. Y. Choong and D. E. Daykin and C. R. Rathbone",
title = "Rational Approximations to $ \pi $",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "387--392",
month = apr,
year = "1971",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1971-0300981-0",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
database",
note = "See errata \cite{Shanks:1976:TER}.",
URL = "http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0300981-0",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Cody:1971:CAR,
author = "W. J. Cody and K. E. Hillstrom and Henry C. {Thatcher,
Jr.}",
title = "{Chebyshev} approximations for the {Riemann} zeta
function",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "537--547",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20",
MRnumber = "47 2785",
bibdate = "Wed Jan 17 08:57:00 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-wjc,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: 20-digit approximations for either $ \zeta
(s) $ or $ \zeta (s) - 1 $.",
}
@InCollection{Cody:1971:SEF,
author = "W. J. Cody",
title = "Software for the Elementary Functions",
crossref = "Rice:1971:MS",
pages = "171--186",
year = "1971",
bibdate = "Thu Sep 15 18:56:47 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Glasser:1971:CFE,
author = "M. L. Glasser and V. E. Wood",
title = "A Closed Form Evaluation of the Elliptic Integral",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "535--536",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Glasser:1971:EII,
author = "M. L. Glasser",
title = "An Elliptic Integral Identity",
journal = j-MATH-COMPUT,
volume = "25",
number = "115",
pages = "533--534",
month = jul,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Herman:1971:EDH,
author = "G. T. Herman",
title = "The equivalence of different hierarchies of elementary
functions",
journal = "Z. Math. Logik Grundlagen Math.",
volume = "17",
pages = "219--224",
year = "1971",
MRclass = "02.77 (68.00)",
MRnumber = "44 \#6494",
MRreviewer = "D. A. Clarke",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Book{Hochstadt:1971:FMP,
author = "Harry Hochstadt",
title = "The Functions of Mathematical Physics",
volume = "XXIII",
publisher = pub-WI,
address = pub-WI:adr,
pages = "xi + 322",
year = "1971",
ISBN = "0-471-40170-6 (hardcover)",
ISBN-13 = "978-0-471-40170-4 (hardcover)",
LCCN = "QA351 .H68",
bibdate = "Tue Dec 5 10:48:41 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
series = "Pure and applied mathematics: a series of texts and
monographs",
acknowledgement = ack-nhfb,
subject = "Functions, Special; Fonctions sp{\'e}ciales; Fonctions
(math{\'e}matiques)",
tableofcontents = "1: Orthogonal Polynomials \\
1 Linear Spaces / 1 \\
2 Orthogonal Polynomials / 6 \\
3 The Recurrence Formula / 8 \\
4 The Christoffel--Darboux Formula / 9 \\
5 The Weierstrass Approximation Theorem / 11 \\
6 The Zeros of the Orthogonal Polynomials / 14 \\
7 Approximation Theory / 16 \\
8 More about the Zeros of the Orthonormal Polynomials /
23 \\
9 The completeness of the Orthonormal Polynomials in
the Space of Square-Integrable Functions / 27 \\
10 Generalizations and an Application to Conformal
Mappings / 32 \\
\\
2: The Classical Orthogonal Polynomials 1 Rodrigues'
Formula and the Classical Orthogonal Polynomials / 39
\\
2 The Differential Equations Satisfied by the Classical
Orthogonal Polynomials / 43 \\
3 On the Zeros of the Jacobi Polynomials / 45 \\
4 An Alternative Approach to the Tchebicheff
Polynomials / 46 \\
5 An Application of the Hermite Polynomials to Quantum
Mechanics / 49 \\
6 The Completeness of the Hermite and Laguerre
Polynomials / 53 \\
7 Generating Functions / 57 \\
\\
3: The Gamma Function 1 Definitions and Basic
Properties / 61 \\
2 Analytic Continuation and Integral Representations /
65 \\
3 Asymptotic Expansions / 69 \\
4 Beta Functions / 75 \\
5 The Logarithmic Derivative of the Gamma Function / 77
\\
6 Mellin--Barnes Integrals / 78 \\
7 Mellin Transforms / 80 \\
8 Applications to Algebraic Equations / 81 \\
\\
4: Hypergeometric Functions 1 Review of Linear
Differential Equations with Regular Singular Points /
88 \\
2 The Hypergeometric Differential Equation / 90 \\
3 The Hypergeometric Function / 93 \\
4 A General Method for Finding Integral Representations
/ 100 \\
5 Integral Representations for the Hypergeometric
Function / 105 \\
6 The Twenty-four Solutions of the Hypergeometric /
Equation / 106 \\
7 The Schwarz--Christoffel Transformation / 112 \\
8 Mappings of Curvilinear Triangles / 119 \\
9 Group Theoretic Discussion of the Case $ \pi(\alpha_1
+ \alpha_2 + \alpha_3) > \pi$ / 130 \\
10 Nonlinear Transformations of Hypergeometric
Functions / 132 \\
\\
5: The Legendre Functions 1 Laplace's Differential
Equation / 138 \\
2 Maxwell's Theory of Poles / 140 \\
3 Relationship to the Hypergeometric Functions / 141
\\
4 Expansion Formulas / 147 \\
5 The Addition Theorem / 149 \\
6 Green's Functions / 153 \\
7 The Complete Solution of Legendre's Differential
Equation / 156 \\
8 Asymptotic Formulas / 161 \\
\\
6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous
Polynomials / 168 \\
2 Orthogonality of Spherical Harmonics / 171 \\
3 Legendre Polynomials / 175 \\
4 Applications to Boundary Value Problems / 183 \\
\\
7: Confluent Hypergeometric Functions 1 Relationship to
the Hypergeometric Functions / 189 \\
2 Applications of These Functions in Mathematical
Physics / 191 \\
3 Integral Representations / 195 \\
4 Asymptotic Representations / 198 \\
\\
8: Bessel Functions 1 Basic Definitions / 200 \\
2 Integral Representations / 203 \\
3 Relationship to the Legendre Functions / 205 \\
4 The Generating Function of the Bessel Function / 207
\\
5 More Integral Representations / 210 \\
6 Addition Theorems / 216 \\
7 The Complete Solution of Bessel's Equation / 223 \\
8 Asymptotic Expansions for Large Argument / 225 \\
9 Airy Functions / 230 \\
10 Asymptotic Expansions for Large Indices and Large
Arguments / 235 \\
11 Some Applications of Bessel Functions in Physical
Optics / 241 \\
12 The Zeros of Bessel Functions / 249 \\
13 Fourier--Bessel Expansions / 257 \\
14 Applications in Mathematical Physics / 266 \\
15 Discontinuous Integrals / 269 \\
\\
9: Hill's Equation 1 Mathieu's Equation / 281 \\
2 Hill's Equation / 282 \\
3 The Discriminant / 287 \\
4 Expansion Theorems / 299 \\
5 Inverse Problems / 305 \\
6 Hill's Equations with Even Coefficients / 309 \\
7 Mathieu's Equation Revisited / 310 \\
8 Energy Bands in Crystals / 313 \\
Appendix / 314 \\
\\
Bibliography / 318 \\
\\
Index / 321",
}
@Article{Honey:1971:CCD,
author = "D. W. Honey",
title = "Correspondence: Calculation of a double-length square
root from a double length number using single precision
techniques",
journal = j-COMP-J,
volume = "14",
number = "4",
pages = "443--443",
month = nov,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:58 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Kuki:1971:FEP,
author = "H. Kuki and J. Ascoly",
title = "{FORTRAN} extended-precision library",
journal = j-IBM-SYS-J,
volume = "10",
number = "1",
pages = "39--61",
year = "1971",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:51:32 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
acknowledgement = ack-nj,
fjournal = "IBM Systems Journal",
xxmonth = "(none)",
}
@InCollection{Kuki:1971:MFS,
author = "H. Kuki",
title = "Mathematical Function Subprograms for Basic System
Libraries{}\emdash Objectives, Constraints, and
Trade-Off",
crossref = "Rice:1971:MS",
pages = "187--199",
year = "1971",
bibdate = "Fri Sep 16 16:27:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Lehmer:1971:CCM,
author = "D. H. Lehmer",
title = "On the compounding of certain means",
journal = j-J-MATH-ANAL-APPL,
volume = "36",
number = "1",
pages = "183--200",
month = oct,
year = "1971",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247x(71)90029-1",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
bibdate = "Tue Mar 14 18:52:11 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "arithmetic--geometric mean (AGM) iteration; complete
elliptic integrals of the first and second kinds.
Landen s transformation",
}
@Article{Liron:1971:ISR,
author = "N. Liron",
title = "Infinite Sums of Roots for a Class of Transcendental
Equations and {Bessel} Functions of Order One-Half",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "769--781",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lucas:1971:AAC,
author = "C. W. {Lucas, Jr.} and C. W. Terrill",
title = "{ACM Algorithm 404}: Complex Gamma Function [{S14}]",
journal = j-CACM,
volume = "14",
number = "1",
pages = "48--49",
month = jan,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:00:03 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#LucasT71;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "Coll. William and Mary, Williamsburg, VA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; CGAMMA; complex gamma function evaluation;
formula; function evaluation; poles of gamma function;
recursion formula; reflection; Stirling's asymptotic
series; subroutine in ALGOL; subroutines",
oldlabel = "LucasT71",
remark = "Fullerton: Fortran routine with machine-dependent
constants.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/LucasT71",
}
@Article{Luke:1971:MTBa,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "323--330",
month = apr,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Luke:1971:MTBb,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions, {II}",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "789--795",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Majithia:1971:CAN,
author = "J. C. Majithia and R. Kitai",
title = "A Cellular Array for the Nonrestoring Extraction of
Square Roots",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1617--1618",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223191",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Matta:1971:UCE,
author = "F. Matta and A. Reichel",
title = "Uniform Computation of the Error Function and Other
Related Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "339--344",
month = apr,
year = "1971",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1971-0295538-4",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
URL = "http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0295538-4",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@PhdThesis{Rothmaier:1971:BEF,
author = "B. Rothmaier",
title = "{Die Berechnung der elementaren Funktionen mit
beliebiger Genauigkeit} \toenglish {The Computation of
Elementary Functions with Arbitrary Accuracy}
\endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "????",
year = "1971",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Sarkar:1971:EPP,
author = "B. P. Sarkar and E. V. Krishnamurthy",
title = "Economic Pseudodivision Processes for Obtaining Square
Root, Logarithm, and Arctan",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1589--1593",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223178",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 01 10:32:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Scarton:1971:DPF,
author = "Henry A. Scarton",
title = "Double precision {FORTRAN} subroutines to compute both
ordinary and modified {Bessel} functions of the first
kind and of integer order with arbitrary complex
argument: {$ J_n(x + j y) $} and {$ I_n(x + j y) $}",
journal = j-J-COMPUT-PHYS,
volume = "8",
number = "2",
pages = "295--299",
month = oct,
year = "1971",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(71)90010-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:04 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999171900106",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Shenton:1971:CFP,
author = "L. R. Shenton and K. O. Bowman",
title = "Continued Fractions for the Psi Function and its
Derivatives",
journal = j-SIAM-J-APPL-MATH,
volume = "20",
number = "4",
pages = "547--554",
month = jun,
year = "1971",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2099856",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
}
@Article{Shipman:1971:HSE,
author = "L. L. Shipman and R. E. Christoffersen",
title = "High Speed Evaluation of {$ F_0 (x) $}",
journal = j-COMP-PHYS-COMM,
volume = "2",
number = "4",
pages = "201--206",
month = may # "\slash " # jun,
year = "1971",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(71)90053-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:40:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465571900531",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "Fullerton: $ F_0 (x) = \int_0^1 \exp ( - x u^2) \, d u
$, which is simply related to $ \erf $ for $ x > 0 $
and to Dawson's function for $ x < 0 $.",
}
@Article{Spellucci:1971:DPA,
author = "P. Spellucci",
title = "Double precision approximations to the elementary
functions using {Jacobi-fractions}",
journal = j-NUM-MATH,
volume = "18",
pages = "127--143",
year = "1971/1972",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D20",
MRnumber = "45 \#7938",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Spira:1971:CGF,
author = "Robert Spira",
title = "Calculation of the Gamma Function by {Stirling}'s
Formula",
journal = j-MATH-COMPUT,
volume = "25",
number = "114",
pages = "317--322",
month = apr,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Sundblad:1971:AFT,
author = "Y. Sundblad",
title = "The {Ackermann} Function. {A} Theoretical,
Computational, and Formula Manipulative Study",
journal = j-BIT,
volume = "11",
number = "1",
pages = "107--119",
month = mar,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01935330",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:11 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=1&spage=107",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: Ackermann's function is a recursively
defined function of importance to computer science
theorists.",
}
@InProceedings{Walther:1971:UAE,
author = "J. S. Walther",
title = "A unified algorithm for elementary functions",
crossref = "AFIPS:1971:ACP",
volume = "38",
pages = "379--385",
year = "1971",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
}
@Article{Wills:1971:URR,
author = "John G. Wills",
title = "On the use of recursion relations in the numerical
evaluation of spherical {Bessel} functions and
{Coulomb} functions",
journal = j-J-COMPUT-PHYS,
volume = "8",
number = "1",
pages = "162--166",
month = aug,
year = "1971",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(71)90043-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:04 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199917190043X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{Wong:1971:SEI,
author = "R. Wong and E. Rosenbloom",
title = "Series Expansions of $ {W}_{k, m}(z) $ Involving
Parabolic Cylinder Functions",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "783--787",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bardin:1972:CFE,
author = "C. Bardin and Y. Dandeu and L. Gauthier and J.
Guillermin. T. Lena. J.-M. Pernet and H. H. Wolter and
T. Tamura",
title = "{Coulomb} Functions in Entire $ (\eta, \rho) $ Plane",
journal = j-COMP-PHYS-COMM,
volume = "3",
number = "2",
pages = "73--87",
month = mar,
year = "1972",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(72)90057-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:09:33 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Book{Bark:1972:MTF,
author = "L. S. Bark",
title = "{{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh
funktsi{\u\i}}} ($ \operatorname {sin} x $, $
\operatorname {cos} x $, $ e^x $ {\cyr i} $ e^{-x} $).
({Russian}) [Multiplace tables of the elementary
functions ($ \operatorname {sin} \ x $, $ \operatorname
{cos} \ x $, $ e^x $ and $ e^{-x} $ )]",
publisher = "Vy{\v{c}}isl. Centr Akad. Nauk SSSR",
address = "Moscow, USSR",
edition = "Second, unrevised",
pages = "134",
year = "1972",
MRclass = "65A05",
MRnumber = "50 \#6100",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Tables processed and text translated from the English
by L. S. Bark. Library of Mathematical Tables, No. 9.
1972",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Carlson:1972:ACL,
author = "B. C. Carlson",
title = "An algorithm for computing logarithms and
arctangents",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "543--549",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Iowa State Univ., Ames, IA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "acceleration; arctangents; auxiliary; Borchardt's
algorithm; convergence; fast; function approximation;
functions; inverse circular functions; inverse
hyperbolic; iterative algorithm; logarithms; numerical
methods; rational operations; recurrence relation;
square roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Chen:1972:ACE,
author = "Tien Chi Chen",
title = "Automatic Computation of Exponentials, Logarithms,
Ratios and Square Roots",
journal = j-IBM-JRD,
volume = "16",
number = "4",
pages = "380--388",
month = jul,
year = "1972",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65D20",
MRnumber = "49 \#1738",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.research.ibm.com/journal/rd/164/chen.pdf",
abstract = "It is shown how a relatively simple device can
evaluate exponentials, logarithms, ratios and square
roots for fraction arguments, employing only shifts,
adds, high-speed table lookups, and bit counting. The
scheme is based on the cotransformation of a number
pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
invariant; when $x$ is driven towards a known value $
x_w $, $y$ is driven towards the result. For an $N$-bit
fraction about $ N / 4 $ iterations are required, each
involving two or three adds; then a termination
algorithm, based on an add and an abbreviated multiply,
completes the process, for a total cost of about one
conventional multiply time. Convergence, errors and
simulation using APL are discussed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, San Jose, CA, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "adds; APL; bit counting; convergence;
cotransformation; digital arithmetic; errors;
exponentials; high speed table; iteration; logarithms;
lookups; ratios; shifts; simulation; square roots;
termination algorithm",
reviewer = "F. Gotze",
treatment = "P Practical",
}
@TechReport{Ercegovac:1972:RES,
author = "Milos D. Ercegovac",
title = "Radix 16 Evaluation of Some Elementary Functions",
number = "540",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, Illinois",
pages = "30",
year = "1972",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Frisch:1972:RAR,
author = "Michael J. Frisch",
title = "Remark on ``{Algorithms 352, 385, 392}: Remarks on
Characteristic Values and Associated Solutions of
{Mathieu}'s Differential Equation, Exponential
Integral, and Systems of Hyperbolic {P.D.E.}''",
journal = j-CACM,
volume = "15",
number = "12",
pages = "1074--??",
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:42:24 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Frisch72;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See
\cite{Clemm:1969:ACV,Paciorek:1970:AEI,Smith:1970:ASH}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Frisch72",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Frisch72",
}
@Article{Fullerton:1972:MIG,
author = "W. Fullerton",
title = "{ACM Algorithm 435}: Modified Incomplete Gamma
Function",
journal = j-CACM,
volume = "15",
number = "11",
pages = "993--995",
month = nov,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 09:47:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Schoene:1978:RMI}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Fullerton: Fortran subprogram for evaluating $ e^{x_1}
\int_{x_1}^{x_2} |y|^{a - 1} e^{-y} \, d y $ for $a$
roughly between $1$ and $2$.",
}
@Article{Hunter:1972:NEC,
author = "D. B. Hunter and T. Regan",
title = "A note on the evaluation of the complementary error
function",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "539--541",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation)",
corpsource = "Univ. Bradford, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "complementary error function; complex variable;
evaluation; integration; method of Matta and Reichel;
modification; numerical; stability",
treatment = "T Theoretical or Mathematical",
}
@Article{Kim:1972:AEH,
author = "Shoon K. Kim",
title = "The Asymptotic Expansion of a Hypergeometric Function
$_2 {F}_2 (1, \alpha; \rho_1, \rho_2; z)$",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "963--963",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Kolbig:1972:CAC,
author = "K. S. K{\"o}lbig",
title = "Certification of ``{Algorithm 363}: {Complex} error
function''",
journal = j-CACM,
volume = "15",
number = "6",
pages = "465--466",
month = jun,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:55:38 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kolbig72;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gautschi:1969:ACE}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4120 (Functional analysis); C7310 (Mathematics
computing)",
corpsource = "CERN, Geneva, Switzerland",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\erf(z)$; complex error function; function
evaluation; special functions; subroutines; Voigt
function",
oldlabel = "Kolbig72",
remark = "Fullerton: Corrections and tests of an Algol
procedure.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kolbig72",
}
@Article{Kolbig:1972:PCL,
author = "K. S. K{\"o}lbig",
title = "Programs for Computing the Logarithm of the Gamma
Function, and the Digamma Function, for Complex
Argument",
journal = j-COMP-PHYS-COMM,
volume = "4",
number = "2",
pages = "221--226",
month = nov,
year = "1972",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(72)90012-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 08:33:42 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Kolbig:1972:RCC,
author = "K. S. K{\"o}lbig",
title = "Remarks on the Computation of {Coulomb}
Wavefunctions",
journal = j-COMP-PHYS-COMM,
volume = "4",
number = "2",
pages = "214--220",
month = nov,
year = "1972",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(72)90011-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 08:35:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Kolbig:1972:ZIG,
author = "K. S. Kolbig",
title = "On the Zeros of the Incomplete Gamma Function",
journal = j-MATH-COMPUT,
volume = "26",
number = "119",
pages = "751--755",
month = jul,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "CERN, Geneva, Switzerland",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic formulae; complex w plane; function
approximation; incomplete gamma function; poles and
zeros; zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Kuki:1972:AAC,
author = "Hirondo Kuki",
title = "{ACM Algorithm 421}: Complex Gamma Function with Error
Control [{S14}]",
journal = j-CACM,
volume = "15",
number = "4",
pages = "271--272",
month = apr,
year = "1972",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/361284.361296",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "47 1249",
MRreviewer = "L. Fox",
bibdate = "Mon Jan 22 06:56:30 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; complex; complex gamma function; complex
loggamma; error control; FORTRAN; function; function
approximation; loggamma function; programme;
subroutines",
oldlabel = "Kuki72a",
remark = "Fullerton: 100-line FORTRAN routine with double
complex accuracy to $ 10^{-14} $.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}
@Article{Kuki:1972:CGF,
author = "Hirondo Kuki",
title = "Complex Gamma Function with Error Control [{S14}]",
journal = j-CACM,
volume = "15",
number = "4",
pages = "262--267",
month = apr,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "47 1249",
MRreviewer = "L. Fox",
bibdate = "Mon Jan 22 06:56:30 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; complex; complex gamma function; complex
loggamma; error control; FORTRAN; function; function
approximation; loggamma function; programme;
subroutines",
oldlabel = "Kuki72a",
remark = "Fullerton: Description of a FORTRAN routine with some
math details.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}
@Book{Lebedev:1972:SFT,
author = "N. N. (Nikolai Nikolaevich) Lebedev",
title = "Special functions and their applications",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xii + 308",
year = "1972",
ISBN = "0-486-60624-4 (paperback)",
ISBN-13 = "978-0-486-60624-8 (paperback)",
LCCN = "QA351 .L3613 1972",
bibdate = "Sat Oct 30 16:25:05 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated to English and edited by Richard A.
Silverman.",
URL = "http://www.loc.gov/catdir/description/dover031/72086228.html",
acknowledgement = ack-nhfb,
remark = "Translation of Spe{\"e}t{\`\i}sial\S{}nye
funk{\"e}t{\`\i}sii i ikh prilozheni{\"e}i{\`\i}a.",
subject = "Functions, Special; Mathematical physics",
tableofcontents = "1 The Gamma Function \\
\\
1.1. Definition of the Gamma Function \\
1.2. Some Relations Satisfied by the Gamma Function \\
1.3. The Logarithmic Derivative of the Gamma Function
\\
1.4. Asymptotic Representation of the Gamma Function
for Large $|z|$ \\
1.5. Definite Integrals Related to the Gamma Function
\\
Problems \\
\\
2 The Probability Integral and Related Functions \\
\\
2.1. The Probability Integral and Its Basic Properties
\\
2.2. Asymptotic Representation of the Probability
Integral for Large $|z|$ \\
2.3. The Probability Integral of Imaginary Argument.
The Function $F(z)$ \\
2.4. The Probability Integral of Argument $\sqrt{i} x$.
The Fresnel Integrals, 21. \\
2.5. Application to Probability Theory \\
2.6. Application to the Theory of Heat Conduction.
Cooling of the Surface of a Heated Object \\
2.7. Application to the Theory of Vibrations.
Transverse Vibrations of an Infinite Rod under the
Action of a Suddenly Applied Concentrated Force \\
Problems \\
\\
3 The Exponential Integral and Related Functions \\
\\
3.1. The Exponential Integral and its Basic Properties
\\
3.2. Asymptotic Representation of the Exponential
Integral for Large $|z|$ \\
3.3. The Exponential Integral of Imaginary Argument.
The Sine and Cosine Integrals \\
3.4. The Logarithmic Integral \\
3.5. Application to Electromagnetic Theory, Radiation
of a Linear Half-Wave Oscillator Problems \\
\\
4 Orthogonal Polynomials \\
\\
4.1. Introductory Remarks \\
4.2. Definition and Generating Function of the Legendre
Polynomials \\
4.3. Recurrence Relations and Differential Equation for
the Legendre Polynomials \\
4.4. Integral Representations of the Legendre
Polynomials \\
4.5. Orthogonality of the Legendre Polynomials \\
4.6. Asymptotic Representation of the Legendre
Polynomials for Large $n$ \\
4.7. Expansion of Functions in Series of Legendre
Polynomials \\
4.8. Examples of Expansions in Series of Legendre
Polynomials \\
4.9. Definition and Generating Function of the Hermite
Polynomials \\
4.10. Recurrence Relations and Differential Equation
for the Hermite Polynomials \\
4.11. Integral Representations of the Hermite
Polynomials \\
4.12. Integral Equations Satisfied by the Hermite
Polynomials \\
4.13. Orthogonality of the Hermite Polynomials \\
4.14. Asymptotic Representation of the Hermite
Polynomials for Large n \\
4.15. Expansion of Functions in Series of Hermite
Polynomials \\
4.16. Examples of Expansions in Series of Hermite
Polynomials \\
4.17. Definition and Generating Function of the
Laguerre Polynomials \\
4.18. Recurrence Relations and Differential Equation
for the Laguerre Polynomials \\
4.19. An Integral Representation of the Laguerre
Polynomials. Relation between the Laguerre and Hermite
Polynomials \\
4.20. An Integral Equation Satisfied by the Laguerre
Polynomials \\
4.21. Orthogonality of the Laguerre Polynomials \\
4.22. Asymptotic Representation of the Laguerre
Polynomials for Large $n$ \\
4.23. Expansion of Functions in Series of Laguerre
Polynomials \\
4.24. Examples of Expansions in Series of Laguerre
Polynomials \\
4.25. Application to the Theory of Propagation of
Electromagnetic Waves. Reflection from the End of a
Long Transmission Line Terminated by a Lumped
Inductance \\
Problems \\
\\
5 Cylinder Functions: Theory \\
\\
5.1. Introductory Remarks \\
5.2. Bessel Functions of Nonnegative Integral Order \\
5.3. Bessel Functions of Arbitrary Order \\
5.4. General Cylinder Functions. Bessel Functions of
the Second Kind \\
5.5. Series Expansion of the Function $Y_n(z)$ \\
5.6. Bessel Functions of the Third Kind \\
5.7. Bessel Functions of Imaginary Argument \\
5.8. Cylinder Functions of Half-Integral Order \\
5.9. Wronskians of Pairs of Solutions of Bessel s
Equation \\
5.10. Integral Representations of the Cylinder
Functions \\
5.11. Asymptotic Representations of the Cylinder
Functions for Large $|z|$ \\
5.12. Addition Theorems for the Cylinder Functions,
124.Zeros of the Cylinder Functions \\
5.13. Expansions in Series and Integrals Involving
Cylinder Functions \\
5.14. Definite Integrals Involving Cylinder Functions
\\
5.15. Cylinder Functions of Nonnegative Argument and
Order \\
5.16. Airy Functions \\
Problems \\
\\
6 Cylinder Functions: Applications \\
\\
6.1. Introductory Remarks \\
6.2. Separation of Variables in Cylindrical Coordinates
\\
6.3. The Boundary Value Problems of Potential Theory.
The Dirichlet Problem for a Cylinder \\
6.4. The Dirichlet Problem for a Domain Bounded by Two
Parallel Planes \\
6.5. The Dirichlet Problem for a Wedge \\
6.6. The Field of a Point Charge near the Edge of a
Conducting Sheet \\
6.7. Cooling of a Heated Cylinder \\
6.8. Diffraction by a Cylinder \\
Problems \\
\\
7 Spherical Harmonics: Theory \\
\\
7.1. Introductory Remarks \\
7.2. The Hypergeometric Equation and Its Series
Solution \\
7.3. Legendre Functions \\
7.4. Integral Representations of the Legendre Functions
\\
7.5. Some Relations Satisfied by the Legendre Functions
\\
7.6. Series Representations of the Legendre Functions
\\
7.7. Wronskians of Pairs of Solutions of Legend-re s
Equation \\
7.8. Recurrence Relations for the Legendre Functions
\\
7.9. Legendre Functions of Nonnegative Integral Degree
and Their Relation to Legendre Polynomials \\
7.10. Legendre Functions of Half-Integral Degree \\
7.11. Asymptotic Representations of the Legendre
Functions for Large $|v|$ \\
7.12. Associated Legendre Functions \\
Problems \\
\\
8 Spherical Harmonics: Applications \\
\\
8.1. Introductory Remarks \\
8.2. Solution of Laplace s Equation in Spherical
Coordinates \\
8.3. The Dirichlet Problem for a Sphere \\
8.4. The Field of a Point Charge Inside a Hollow
Conducting Sphere \\
8.5. The Dirichlet Problem for a Cone \\
8.6. Solution of Laplace s Equation in Spheroidal
Coordinates \\
8.7. The Dirichlet Problem for a Spheroid \\
8.8. The Gravitational Attraction of a Homogeneous
Solid Spheroid \\
8.9. The Dirichlet Problem for a Hyperboloid of
Revolution \\
8.10. Solution of Laplace s Equation in Toroidal
Coordinates \\
8.11. The Dirichlet Problem for a Torus \\
8.12. The Dirichlet Problem for a Domain Bounded by Two
Intersecting Spheres \\
8.13. Solution of Laplace s Equation in Bipolar
Coordinates \\
8.14. Solution of Helmholtz s Equation in Spherical
Coordinates \\
Problems \\
\\
9 Hypergeometric Functions \\
\\
9.1. The Hypergeometric Series and Its Analytic
Continuation \\
9.2. Elementary Properties of the Hypergeometric
Function \\
9.3. Evaluation of $F(\alpha, \beta; \gamma; z)$ for
$\Re(\gamma \alpha \beta) > 0$, 243. \\
9.4. $F(\alpha, \beta; \gamma; z)$ as a Function of its
Parameters \\
9.5. Linear Transformations of the Hypergeometric
Function \\
9.6. Quadratic Transformations of the Hypergeometric
Function \\
9.7. Formulas for Analytic Continuation of $F(\alpha,
\beta; \gamma; z)$ in Exceptional Cases \\
9.8. Representation of Various Functions in Terms of
the Hypergeometric Function \\
9.9. The Confluent Hypergeometric Function \\
9.10. The Differential Equation for the Confluent
Hypergeometric Function and Its Solution. The Confluent
Hypergeometric Function of the Second Kind \\
9.11. Integral Representations of the Confluent
Hypergeometric Functions \\
9.12. Asymptotic Representations of the Confluent
Hypergeometric Functions for Large $|z|$ \\
9.13. Representation of Various Functions in Terms of
the Confluent Hypergeometric Functions \\
9.14. Generalized Hypergeometric Functions \\
Problems \\
\\
10 Parabolic Cylinder Functions \\
\\
10.1. Separation of Variables in Laplace s Equation in
Parabolic Coordinates \\
10.2. Hermite Functions \\
10.3. Some Relations Satisfied by the Hermite Functions
\\
10.4. Recurrence Relations for the Hermite Functions
\\
10.5. Integral Representations of the Hermite Functions
\\
10.6. Asymptotic Representations of the Hermite
Functions for Large $|z|$ \\
10.7. The Dirichlet Problem for a Parabolic Cylinder
\\
10.8. Application to Quantum Mechanics \\
Problems \\
\\
Bibliography \\
\\
Index",
}
@Article{Ling:1972:EM,
author = "Chih-Bing Ling and Jung Lin",
title = "On Evaluation of Moments of $ {K}_\nu (t) / {I}_\nu
(t) $",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "529--537",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods)",
corpsource = "Virginia Politech. Inst., Blacksburg, VA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "evaluation; K/sub nu/(t)/I/sub; moments; nu/(t);
numerical methods; Watson's method",
treatment = "T Theoretical or Mathematical",
}
@Article{Linz:1972:MCB,
author = "Peter Linz",
title = "A Method for Computing {Bessel} Function Integrals",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "509--513",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4160 (Numerical integration and differentiation)",
corpsource = "Univ. California, Davis, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Abel; Bessel function integrals; Fourier integrals;
infinite integrals; integration; numerical computation;
transform",
treatment = "T Theoretical or Mathematical",
}
@Article{Luke:1972:MTB,
author = "Yudell L. Luke",
title = "Miniaturized Tables of {Bessel} Functions. {III}",
journal = j-MATH-COMPUT,
volume = "26",
number = "117",
pages = "237--240",
month = jan,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods)",
corpsource = "Univ. Missouri, Kansas City, KS, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; miniaturized tables; numerical
methods",
treatment = "T Theoretical or Mathematical",
}
@Article{MacKinnon:1972:AEH,
author = "Robert F. MacKinnon",
title = "The asymptotic expansions of {Hankel} transforms and
related integrals",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "515--527",
month = apr,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0230 (Integral transforms); C1130 (Integral
transforms)",
corpsource = "Defence Res. Establ., Pacific, Victoria, BC, Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic expansions; Bessel; functions; Hankel
transforms; integrals; transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Majithia:1972:CAE,
author = "J. C. Majithia",
title = "Cellular Array for Extraction of Squares and Square
Roots of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1023--1024",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009084",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Manos:1972:CCA,
author = "Paul Manos and L. Richard Turner",
title = "Constrained {Chebyshev} approximations to some
elementary functions suitable for evaluation with
floating-point arithmetic",
type = "{NASA} Technical Note",
number = "TN D-6698",
institution = pub-NASA,
address = pub-NASA:adr,
pages = "iii + 68",
month = mar,
year = "1972",
bibdate = "Mon May 22 11:27:24 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
acknowledgement = ack-nhfb,
}
@Article{Marino:1972:NAA,
author = "D. Marino",
title = "New Algorithms for the Approximate Evaluation in
Hardware of Binary Logarithms and Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1416--1421",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223516",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 08:05:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Morita:1972:CAG,
author = "Tohru Morita and Tsuyoshi Horiguchi",
title = "Convergence of the arithmetic-geometric mean procedure
for the complex variables and the calculation of the
complete elliptic integrals with complex modulus",
journal = j-NUM-MATH,
volume = "20",
number = "5",
pages = "425--430",
month = oct,
year = "1972",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01402565",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Thu Jan 13 10:01:46 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=20&issue=5;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=20&issue=5&spage=425",
abstract = "The convergence of the arithmetic-geometric mean
procedure is checked for complex variables. The
procedure is shown to be useful for the evaluation of
the complete elliptic integrals of the first and second
kinds with complex modulus. It is suggested that the
procedure will be useful also for the numerical
calculation of the elliptic integrals and the Jacobian
elliptic functions with complex modulus in general.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Moses:1972:TGT,
author = "Joel Moses",
title = "Toward a General Theory of Special Functions",
journal = j-CACM,
volume = "15",
number = "7",
pages = "550--554",
month = jul,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "34-02 12H05",
MRnumber = "53 3384",
MRreviewer = "K. Okugawa",
bibdate = "Mon Jan 22 07:06:21 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Moses72;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/macsyma.bib",
note = "Twenty-fifth anniversary of the Association for
Computing Machinery.",
acknowledgement = ack-nhfb,
classcodes = "C1100 (Mathematical techniques)",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "general theory; mathematics; special functions",
oldlabel = "Moses72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Moses72",
}
@Article{Olver:1972:NBR,
author = "F. W. J. Olver and D. J. Sookne",
title = "Note on Backward Recurrence Algorithms",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "941--947",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290Z (Other numerical methods); C4190 (Other
numerical methods)",
corpsource = "Univ. Maryland, College Park, MD, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "backward recurrence algorithms; Bessel; Bessel
functions; difference equations; functions; recessive
solution; second order linear difference equation",
treatment = "T Theoretical or Mathematical",
}
@Article{Parnes:1972:CZM,
author = "R. Parnes",
title = "Complex zeros of the modified {Bessel} function {$
K_n(Z) $}",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "949--953",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "City Univ., New York, NY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "and zeros; Bessel functions; complex zeros;
interpolation; interpolation scheme; iterative;
iterative methods; modified Bessel function; poles",
treatment = "T Theoretical or Mathematical",
}
@Article{Rabin:1972:FEP,
author = "Michael O. Rabin and Shmuel Winograd",
title = "Fast evaluation of polynomials by rational
preparation",
journal = j-COMM-PURE-APPL-MATH,
volume = "25",
number = "4",
pages = "433--458",
month = jul,
year = "1972",
CODEN = "CPAMAT, CPMAMV",
DOI = "https://doi.org/10.1002/cpa.3160250405",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
bibdate = "Fri Oct 20 09:03:28 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
ajournal = "Comm. Pure Appl. Math.",
fjournal = "Communications on Pure and Applied Mathematics (New
York)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
keywords = "number of multiplications to evaluate a polynomial",
}
@Article{Ramamoorthy:1972:SPI,
author = "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
title = "Some Properties of Iterative Square-Rooting Methods
Using High-Speed Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "837--847",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:45 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Samet:1972:CDL,
author = "P. A. Samet and D. W. Honey",
title = "Calculation of a Double-Length Square Root from
Double-Length Number using Single Precision
Techniques",
journal = j-COMP-J,
volume = "15",
number = "2",
pages = "116--116",
month = may,
year = "1972",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/15.2.116",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:49 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/15/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Coll., London, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; double length; precision
techniques; single; square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Strecok:1972:HPE,
author = "A. J. Strecok and J. A. Gregory",
title = "High Precision Evaluation of the Irregular {Coulomb}
Wave Functions",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "955--961 + s1--s10",
month = oct,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "A0365G (Solutions of wave equations: bound state in
quantum theory); B0290F (Interpolation and function
approximation); C4130 (Interpolation and function
approximation)",
corpsource = "Argonne Nat. Lab., IL, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "function approximation; high precision evaluation;
irregular Coulomb wave functions; numerical methods;
wave functions",
treatment = "T Theoretical or Mathematical",
}
@Article{Turunov:1972:EFD,
author = "M. Turunov",
title = "Elementary functions of a discrete real and complex
argument. ({Russian})",
journal = "Ta{\v{s}}kent. Gos. Univ. Nau{\v{c}}n. Trudy",
volume = "418 Voprosy Mat.",
pages = "263--271, 386",
year = "1972",
MRclass = "30A95",
MRnumber = "50 \#13556",
MRreviewer = "G. Berzsenyi",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Wimp:1972:CPE,
author = "Jet Wimp",
title = "Corrigendum: {{\booktitle{Polynomial expansions of
Bessel functions and some associated functions}} (Math.
Comp. {\bf 16} (1962), 446--458)}",
journal = j-MATH-COMPUT,
volume = "26",
number = "117",
pages = "309--309",
month = jan,
year = "1972",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sat Dec 22 06:54:10 MST 2018",
bibsource = "http://www.ams.org/mcom/1972-26-117;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
note = "See \cite{Wimp:1962:PEB}.",
URL = "http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X;
http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X/S0025-5718-1972-0400659-X.pdf;
https://www.ams.org/mathscinet-getitem?mr=400659;
https://www.ams.org/mathscinet/search/authors.html?authorName=Wimp%2C%20Jet",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wynn:1972:CAM,
author = "Peter Wynn",
title = "Convergence Acceleration by a Method of
Intercalation",
journal = j-COMPUTING,
volume = "9",
number = "4",
pages = "267--273",
year = "1972",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "Louisiana State Univ., New Orleans, LA, USA",
classification = "B0290Z; C4190",
description = "convergence; series (mathematics)",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "convergence acceleration; method of intercalation;
series of real terms",
}
@Article{Amos:1973:BIC,
author = "D. E. Amos",
title = "Bounds on Iterated Coerror Functions and Their
Ratios",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "413--427",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Baker:1973:PAS,
author = "P. W. Baker",
title = "Predictive algorithms for some elementary functions in
radix $2$",
journal = j-ELECT-LETTERS,
volume = "9",
pages = "493--494",
year = "1973",
CODEN = "ELLEAK",
ISBN = "0013-5194",
ISBN-13 = "0013-5194",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
MRclass = "68A10",
MRnumber = "57 \#18203",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Besslich:1973:MDS,
author = "P. W. Besslich and S. Raman",
title = "Multiplication, Division and Square Root Extraction
Methods for Electronic Desk Calculators",
journal = "Journal of the Institution of Telecommunication
Engineers (India)",
volume = "19",
number = "4",
month = apr,
year = "1973",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Braithwaite:1973:ALP,
author = "W. J. Braithwaite",
title = "Associated {Legendre} Polynomials, Ordinary and
Modified Spherical Harmonics",
journal = j-COMP-PHYS-COMM,
volume = "5",
number = "5",
pages = "390--394",
month = may,
year = "1973",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(73)90065-9",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Oct 29 21:45:41 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Cody:1973:CAP,
author = "W. J. Cody and Anthony J. Strecok and Henry C.
{Thacher, Jr.}",
title = "{Chebyshev} Approximations for the Psi Function",
journal = j-MATH-COMPUT,
volume = "27",
number = "121",
pages = "123--127",
month = jan,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65-06 (68-06)",
MRnumber = "50 6095",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Argonne Nat. Lab., IL, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Chebyshev approximation; Chebyshev approximations;
digamma function; psi function",
remark = "Fullerton: Relative errors down to $ 10^{-20} $",
treatment = "T Theoretical or Mathematical",
}
@Book{Dingle:1973:AET,
author = "Robert B. Dingle",
title = "Asymptotic expansions: their derivation and
interpretation",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 521",
year = "1973",
ISBN = "0-12-216550-0",
ISBN-13 = "978-0-12-216550-4",
LCCN = "QA295 .D45",
bibdate = "Sat Feb 18 14:52:17 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Asymptotic expansions; Power series",
}
@Article{Ercegovac:1973:REC,
author = "M. D. Ercegovac",
title = "Radix-16 Evaluation of Certain Elementary Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "561--566",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009107",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fettis:1973:CZE,
author = "Henry E. Fettis and James C. Caslin and Kenneth R.
Cramer",
title = "Complex zeros of the error function and of the
complementary error function",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "401--407",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Wright-Patterson Air Force Base, OH, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic formula; complementary error function;
complex zeros; error function; errors; first one
hundred zeros; function evaluation; poles and zeros",
treatment = "T Theoretical or Mathematical",
}
@Article{Fettis:1973:SPC,
author = "Henry E. Fettis and James C. Caslin and Kenneth R.
Cramer",
title = "Saddle Points of the Complementary Error Function",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "409--412",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Sandia Labs., Albuquerque, NM, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "asymptotic; complementary error function; errors;
formula; function evaluation; poles and zeros; saddle
points",
treatment = "T Theoretical or Mathematical",
}
@Article{Fisher:1973:NEI,
author = "N. I. Fisher",
title = "A note on the evaluation of the incomplete gamma
function",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "2",
number = "4",
pages = "325--332",
year = "1973",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657308810058",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:10:34 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Gautschi:1973:AAE,
author = "Walter Gautschi",
title = "{ACM Algorithm 471}: Exponential Integrals [{S13}]",
journal = j-CACM,
volume = "16",
number = "12",
pages = "761--763",
month = dec,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:43:23 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Gautschi73;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation);
C7310 (Mathematics computing)",
corpsource = "Purdue Univ., Lafayette, IN, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "ALGOL; computation; continued fractions; exponential
integrals; integration; recurrence relations;
recursive; subroutine; subroutines",
oldlabel = "Gautschi73",
remark = "Fullerton: Algol-language routine for $ E_n(x) =
\int_1^\infty e^{-x t} t^n \, d t, x > 0 $.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gautschi73",
}
@TechReport{Hemker:1973:SDL,
author = "P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen}
and H. L. Oudshoorn and D. T. Winter",
title = "Single- and double-length computation of elementary
functions",
number = "NW 7",
institution = "Mathematical Centre",
address = "Amsterdam",
year = "1973",
bibdate = "Mon May 19 13:30:58 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1973:AAN,
author = "G. W. Hill and A. W. Davis",
title = "{ACM Algorithm 442}: Normal Deviate [{S14}]",
journal = j-CACM,
volume = "16",
number = "1",
pages = "51--52",
month = jan,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:49:54 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1973.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#HillD73;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, Australia",
country = "USA",
descriptors = "RVG",
enum = "7393",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "ALGOL; normal deviate; normal distribution inverse;
probit; statistics; subroutines; Taylor series
approximation; transform",
oldlabel = "HillD73",
references = "0",
remark = "Fullerton: Short Algol-language procedure with
accuracy to 24 digits.",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/HillD73",
}
@Article{Hill:1973:AAS,
author = "G. W. Hill",
title = "{ACM Algorithm 465}: {Student}'s $t$ Frequency
[{S14}]",
journal = j-CACM,
volume = "16",
number = "11",
pages = "690--690",
month = nov,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:49:52 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Hill73a;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "CSIRO, Glen Osmond, SA, Australia",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "ALGOL; approximation; density function; series;
statistics; student's t statistic; subroutine;
subroutines",
oldlabel = "Hill73a",
remark = "Fullerton: Algol-language routine for $ f(t | n) =
\frac {\Gamma (n / 2 + 1 / 2)}{(\pi n)^{1 / 2} \Gamma
(n / 2)} (1 + t^2 / n)^{n / 2 + 1 / 2} $.",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Hill73a",
}
@Article{Hill:1973:SAA,
author = "I. D. Hill",
title = "Statistical Algorithms: {Algorithm AS 66}: The Normal
Integral",
journal = j-APPL-STAT,
volume = "22",
number = "3",
pages = "424--427",
month = sep,
year = "1973",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:20:49 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
URL = "http://lib.stat.cmu.edu/apstat/66",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@Article{Hwang:1973:RRS,
author = "W. G. Hwang and John Todd",
title = "A recurrence relation for the square root",
journal = j-J-APPROX-THEORY,
volume = "9",
pages = "299--306",
year = "1973",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(73)90075-0",
ISSN = "0021-9045,1096-0430",
ISSN-L = "0021-9045",
MRclass = "65H05",
MRnumber = "373270",
MRreviewer = "L. Fox",
bibdate = "Sat Oct 21 14:25:01 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0271.65032",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
received = "19 April 1971",
ZBmath = "3426800",
}
@Article{Laurenzi:1973:DWF,
author = "Bernard J. Laurenzi",
title = "Derivatives of {Whittaker} Functions $ {W}_{k, 1 / 2}
$ and $ {M}_{k, 1 / 2} $ with Respect to Order $ {K}
$",
journal = j-MATH-COMPUT,
volume = "27",
number = "121",
pages = "129--132",
month = jan,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Levin:1973:DNL,
author = "D. Levin",
title = "Development of non-linear transformations for
improving convergence of sequences",
journal = j-INT-J-COMPUT-MATH,
volume = "3",
number = "1--4",
pages = "371--388",
month = "????",
year = "1973",
CODEN = "IJCMAT",
DOI = "https://doi.org/10.1080/00207167308803075",
ISSN = "0020-7160",
ISSN-L = "0020-7160",
bibdate = "Thu Dec 01 10:27:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
ZMnumber = "0274.65004",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Computer Mathematics",
journal-URL = "http://www.tandfonline.com/loi/gcom20",
keywords = "convergence acceleration",
}
@Article{Linz:1973:NCI,
author = "Peter Linz and T. E. Kropp",
title = "A note on the computation of integrals involving
products of trigonometric and {Bessel} functions",
journal = j-MATH-COMPUT,
volume = "27",
number = "124",
pages = "871--872",
month = oct,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Univ. California, Davies, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; computation; integration; numerical;
numerical methods; products; trigonometric",
treatment = "T Theoretical or Mathematical",
}
@Article{Lozier:1973:BCP,
author = "D. W. Lozier and L. C. Maximon and W. L. Sadowski",
title = "A bit comparison program for algorithm testing",
journal = j-COMP-J,
volume = "16",
number = "2",
pages = "111--117",
month = may,
year = "1973",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:11 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif",
acknowledgement = ack-nhfb,
classcodes = "C6150G (Diagnostic, testing, debugging and evaluating
systems)",
corpsource = "Nat. Bur. Stand., Washington, DC, USA",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "accuracy; algorithm testing; bit comparison program;
computer algorithms; program debugging",
treatment = "P Practical",
}
@Article{McNolty:1973:SPD,
author = "Frank McNolty",
title = "Some probability density functions and their
characteristic functions",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "495--504",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0240 (Probability and statistics); C1140 (Probability
and statistics)",
corpsource = "Lockheed Palo Alto Res. Lab., CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel function; characteristic functions; functions;
hypergeometric function; probability; probability
density functions",
treatment = "T Theoretical or Mathematical",
}
@Article{Rice:1973:EEI,
author = "S. O. Rice",
title = "Efficient Evaluation of Integrals of Analytic
Functions by the Trapezoidal Rule",
journal = j-BELL-SYST-TECH-J,
volume = "52",
number = "5",
pages = "707--722",
month = may # "--" # jun,
year = "1973",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1973/BSTJ.1973.5205.html;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol52/bstj52-5-707.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Schmid:1973:BLVa,
author = "H. Schmid",
title = "{BCD} logic {V}: {BCD} square root",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "17",
pages = "62--69",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
keywords = "decimal fixed-point arithmetic",
}
@Article{Sookne:1973:BFC,
author = "D. J. Sookne",
title = "{Bessel} Functions {$I$} and {$J$} of Complex Argument
and Integer Order",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "77B",
number = "3--4",
pages = "111--114",
month = jul,
year = "1973",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:49:13 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: A program is described but not published.",
}
@Article{Sookne:1973:BFR,
author = "D. J. Sookne",
title = "{Bessel} Functions of Real Argument and Integer
Order",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "77A",
number = "3--4",
pages = "125--132",
month = jul,
year = "1973",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:51:18 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Sequences of $ I_n(x) $ and $ J_n(x) $ are
computed with a FORTRAN routine.",
}
@Article{Sookne:1973:CABa,
author = "D. J. Sookne",
title = "Certification of an Algorithm for {Bessel} Functions
of Real Argument",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "77B",
number = "3--4",
pages = "115--124",
month = jul,
year = "1973",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:55:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: An algorithm is shown to lose at most about
3 bits of precision.",
}
@Article{Sookne:1973:CABb,
author = "D. J. Sookne",
title = "Certification of an Algorithm for {Bessel} Functions
of Complex Argument",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "77B",
number = "3",
pages = "133--136",
month = jul,
year = "1973",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 10:53:39 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: The algorithm is shown to lose at most
about 3 bits of precision.",
}
@Article{Vos:1973:RAC,
author = "H. Vos",
title = "Remark on ``{Algorithm 300}: {Coulomb} Wave
Functions''",
journal = j-CACM,
volume = "16",
number = "5",
pages = "308--309",
month = may,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:27:34 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Vos73;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Gunn:1967:ACW}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
corpsource = "Vrije Univ., Amsterdam, Netherlands",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Coulomb wave functions; function evaluation;
mathematics; wave functions",
oldlabel = "Vos73",
remark = "Fullerton: Algol-language accuracy monitor for
Algorithm 300, which is generally accurate only to 3
digits.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Vos73",
}
@Article{Wong:1973:AEL,
author = "R. Wong",
title = "An Asymptotic Expansion of {$ W_{k, m}(z) $} with
Large Variable and Parameters",
journal = j-MATH-COMPUT,
volume = "27",
number = "122",
pages = "429--436",
month = apr,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wong:1973:UAE,
author = "R. Wong",
title = "On uniform asymptotic expansion of definite
integrals",
journal = j-J-APPROX-THEORY,
volume = "7",
number = "1",
pages = "76--86",
month = jan,
year = "1973",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(73)90055-5",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A60",
MRnumber = "0340910",
MRreviewer = "L. Berg",
bibdate = "Sat Feb 18 15:20:40 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021904573900555",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
keywords = "incomplete gamma functions",
}
@Article{Wrench:1973:ECT,
author = "John W. Wrench",
title = "Erratum: {Concerning Two Series for the Gamma
Function}",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "681--682",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Fullerton: Minor last-digit rounding errors are
reported.",
}
@Article{Wrigge:1973:EII,
author = "H. S. Wrigge",
title = "An Elliptic Integral Identity",
journal = j-MATH-COMPUT,
volume = "27",
number = "124",
pages = "839--840",
month = oct,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Yohe:1973:IBS,
author = "J. M. Yohe",
title = "Interval Bounds for Square Roots and Cube Roots",
journal = j-COMPUTING,
volume = "11",
number = "1",
pages = "51--57",
month = mar,
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-jr # " and " # ack-nhfb,
affiliation = "Univ. Wisconsin, Madison, WI, USA",
classification = "C5230",
description = "digital arithmetic; error analysis",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "binary computers; cube roots; error analysis; interval
bounds; machine representable number; optimal upward
directed rounding; smallest machine representable
interval; square roots",
}
@Article{Acton:1974:RRF,
author = "Forman S. Acton",
title = "Recurrence relations for the {Fresnel} integral $
\int_0^{\infty } \exp ( - c t) \, d t / \sqrt {t (1 +
t^2)} $ and similar integrals",
journal = j-CACM,
volume = "17",
number = "8",
pages = "480--481",
month = aug,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20 (33A70)",
MRnumber = "49 6554",
bibdate = "Mon Jan 22 06:20:27 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Acton74;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "The class of functions defined by $ \int_0^\infty
[\exp ( - c X)d t / (1 + Y)(t^{1 / 2})^k] $ where $X$
and $Y$ are either $t$ or $ t^2 $ and $k$ is $ - 1 $,
$0$, or $1$ can be evaluated by recurrences for all but
small values of the parameter $c$. These recurrences,
given here, are more efficient than the usual
asymptotic series.",
acknowledgement = ack-nhfb,
classification = "921",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "exponential integral; Fresnel integral; mathematical
techniques; recurrence relations",
oldlabel = "Acton74",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Acton74",
}
@Article{Amos:1974:CMB,
author = "D. E. Amos",
title = "Computation of modified {Bessel} functions and their
ratios",
journal = j-MATH-COMPUT,
volume = "28",
number = "125",
pages = "239--251",
month = jan,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Sandia Labs., Albuquerque, NM, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; computation; low order Bessel
functions; modified Bessel functions; monotonicity;
properties; ratios; recursion; relation",
remark = "Fullerton: Ratios $ I_{\nu + 1}(x) / I_\nu (x) $ are
considered.",
treatment = "T Theoretical or Mathematical",
}
@Book{Anonymous:1974:TCH,
editor = "Anonymous",
title = "Tables of Complex Hyperbolic and Circular Functions",
volume = "23",
publisher = "Corona Pub. Co.",
address = "Tokyo, Japan",
pages = "621",
year = "1974",
LCCN = "QA55 .T172",
bibdate = "Sat Apr 1 14:49:41 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Advanced series of mathematical and engineering
tables",
acknowledgement = ack-nhfb,
remark = "Title and introduction also in Japanese: Fukuso
s{\aa}okyokusen kans{\aa}u hy{\aa}o.",
subject = "Mathematics; Tables; Exponential functions;
Trigonometrical functions",
}
@Article{Barlow:1974:CCF,
author = "R. H. Barlow",
title = "Convergent Continued Fraction Approximants to
Generalised Polylogarithms",
journal = j-BIT,
volume = "14",
number = "1",
pages = "112--116",
month = mar,
year = "1974",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933124",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:13 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=14&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=1&spage=112",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
remark = "Fullerton: Nielsen's generalization $ S_{n, p}(z) =
\frac {( - 1)^{n + p - 1}(n - 1)! p!} \int_0^1 \ln^{n -
1}(t) \ln^p(1 - z t) / t \, d t $ is evaluated in the
complex plane.",
}
@Article{Barnett:1974:CWF,
author = "A. R. Barnett and D. H. Feng and J. W. Steed and L. J.
B. Goldfarb",
title = "{Coulomb} wave functions for all real $ \eta $ and $
\rho $",
journal = j-COMP-PHYS-COMM,
volume = "8",
number = "5",
pages = "377--395",
month = dec,
year = "1974",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(74)90013-7",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Jul 14 09:47:42 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
remark = "This paper may contain the first presentation of
Steed's algorithm for computing continued fractions.",
}
@Article{Blair:1974:RCA,
author = "J. M. Blair",
title = "Rational {Chebyshev} approximations for the modified
{Bessel} functions {$ I_0 (x) $} and {$ I_1 (x) $}",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "581--583",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Atomic Energy Canada Ltd., Chalk River, Ont., Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Chebyshev approximation; functions; modified Bessel;
nearly best rational approximations; rational Chebyshev
approximations; series (mathematics)",
remark = "Fullerton: With microfiche supplement. Relative errors
down to $ 10^{-23} $.",
treatment = "T Theoretical or Mathematical",
}
@Article{Bosten:1974:RAI,
author = "Nancy E. Bosten and E. L. Battiste",
title = "Remark on ``{Algorithm 179}: {Incomplete} Beta
Ratio''",
journal = j-CACM,
volume = "17",
number = "3",
pages = "156--157",
month = mar,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:27:36 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#BostenB74;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Ludwig:1963:AIB,Pike:1976:RIB}.",
acknowledgement = ack-nhfb,
bdate = "Mon Jan 22 06:27:36 MST 2001",
citedby = "Fullerton:1980:BEM",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C7310
(Mathematics computing)",
corpsource = "IMSL, Houston, TX, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Algorithm 179; computer aided analysis; function
approximation; incomplete beta ratio; subroutines",
oldlabel = "BostenB74",
remark = "Fullerton: FORTRAN routine with accuracy about $
10^{-6} $. See M. C. Pike (1976) for a Remark.",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/BostenB74",
}
@Article{Brent:1974:AAG,
author = "Richard P. Brent",
title = "{ACM Algorithm 488}: a {Gaussian} pseudo-random number
generator [{G5}]",
journal = j-CACM,
volume = "17",
number = "12",
pages = "704--706",
month = dec,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:05 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Brent74;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7890 (Other special applications of computing)",
corpsource = "Australian Nat. Univ., Canberra, Australia",
country = "USA",
descriptors = "RVG",
enum = "7061",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "distribution; FORTRAN; Gaussian; generator; GRAND;
normal distribution; pseudo random numbers; random
number generation; random numbers; subroutines",
location = "SEL: Wi",
oldlabel = "Brent74",
references = "0",
remark = "Fullerton: A FORTRAN routine that returns normally
distributed numbers with zero mean and unit standard
deviation.",
revision = "16/01/94",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Brent74",
}
@Article{Burrell:1974:AAE,
author = "Keith H. Burrell",
title = "{ACM Algorithm 484}: Evaluation of the Modified
{Bessel} Functions {$ K_0 (z) $} and {$ K_1 (z) $} for
Complex Arguments [{S17}]",
journal = j-CACM,
volume = "17",
number = "9",
pages = "524--526",
month = sep,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:58 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Burrell74;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis); C7310 (Mathematics computing)",
corpsource = "California Inst. Technol., Pasadena, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; applications of computers; Bessel
functions; complex arguments; function evaluation;
Gauss-Hermite quadrature; Hankel functions; modified
Bessel functions; natural sciences; subroutines",
oldlabel = "Burrell74",
remark = "Fullerton: 10-digit accuracy FORTRAN program.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Burrell74",
}
@Article{Buschman:1974:FSR,
author = "R. G. Buschman",
title = "Finite sum representations for partial derivatives of
special functions with respect to parameters",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "817--824",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Univ. Wyoming, Laramie, WY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; differentiation; finite sum
representations; finite sums; functions; G function;
Gegenbauer functions; hypergeometric; Legendre; Mellin
transformation; partial derivatives; special functions;
Whittaker functions",
remark = "Fullerton: Whittaker and Bessel functions are
considered.",
treatment = "T Theoretical or Mathematical",
}
@Article{Carta:1974:HLR,
author = "David G. Carta",
title = "Help!!: {The} Lost Reference: ({A} Modified {Newton}
Method for Square Roots)",
journal = j-SIGNUM,
volume = "9",
number = "4",
pages = "9--9",
month = oct,
year = "1974",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1206085.1206086",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Jun 17 18:47:00 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
abstract = "Around 1970 I saw a journal article describing a
modified Newton iteration for square roots. It involved
changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
(x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
0.5 $, thereby increasing the asymptotic rate of
convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
1} = 0.25 e_n^2 $.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Fettis:1974:SAC,
author = "Henry E. Fettis",
title = "A stable algorithm for computing the inverse error
function in the `tail-end' region",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "585--587",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Wright-Patterson Air Force Base, OH, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "function evaluation; inverse error function; iterative
algorithm; stability; stable algorithm; tail end
region",
treatment = "T Theoretical or Mathematical",
}
@Article{Glasser:1974:SDI,
author = "M. L. Glasser",
title = "Some definite integrals of the product of two {Bessel}
functions of the second kind: (order zero)",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "613--615",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Battelle Memorial Inst., Columbus, OH, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; definite integrals; evaluate;
function evaluation; integral representation; order;
second kind; zero",
treatment = "T Theoretical or Mathematical",
}
@Article{Hitotumatu:1974:NMC,
author = "Sin Hitotumatu",
title = "A new method for the computation of square root,
exponential and logarithmic functions through
hyperbolic {CORDIC}",
journal = "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
l'Approximation",
volume = "3",
number = "2",
pages = "173--180",
year = "1974",
ISSN = "1010-3376 (print), 2457-8118 (electronic)",
ISSN-L = "1010-3376",
MRclass = "65D20",
MRnumber = "381249",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://ictp.acad.ro/jnaat/journal/article/view/1974-vol3-no2-art7",
acknowledgement = ack-nhfb,
ajournal = "Rev. Anal. Num{\'e}r. Th{\'e}orie Approximation",
fjournal = "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
l'Approximation",
journal-URL = "https://ictp.acad.ro/jnaat/journal",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Koppelaar:1974:CRA,
author = "Henk Koppelaar",
title = "Certification and Remark on ``{Algorithm 191}:
Hypergeometric''",
journal = j-CACM,
volume = "17",
number = "10",
pages = "589--590",
month = oct,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:55:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Kopelaar74;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See \cite{Relph:1963:AH}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "Utrecht State Univ., Netherlands",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; hypergeometric; improvements; inefficiency;
natural sciences applications of computers;
subroutines",
oldlabel = "Kopelaar74",
remark = "Fullerton: Algol-language modifications for Algorithm
191, which does not appear to be accurate far from the
origin.",
treatment = "G General Review; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kopelaar74",
}
@Article{Kyriakopoulos:1974:GFH,
author = "E. Kyriakopoulos",
title = "Generating functions of the hypergeometric functions",
journal = j-J-MATH-PHYS,
volume = "15",
number = "6",
pages = "753--759",
month = jun,
year = "1974",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1666724",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 28 16:40:13 MDT 2011",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
URL = "http://jmp.aip.org/resource/1/jmapaq/v15/i6/p753_s1",
acknowledgement = ack-nhfb,
classification = "A0210 (Algebra, set theory, and graph theory); A0220
(Group theory); A0230 (Function theory, analysis)",
corpsource = "Nuclear Res. Center 'Democritos', Athens, Greece",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "functions; generating functions; hypergeometric
functions; Lie groups; Lie theory; multiplier
representation theory; Weisner's technique",
onlinedate = "4 November 2003",
pagecount = "7",
treatment = "T Theoretical or Mathematical",
}
@Article{Latham:1974:CPC,
author = "W. P. Latham and Rogers W. Redding",
title = "On the calculation of the parabolic cylinder
functions",
journal = j-J-COMPUT-PHYS,
volume = "16",
number = "1",
pages = "66--75",
month = sep,
year = "1974",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(74)90104-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:15 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999174901041",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@Article{McCabe:1974:CFE,
author = "J. H. McCabe",
title = "A continued fraction expansion, with a truncation
error estimate, for {Dawson}'s integral",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "811--816",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "B0290B (Error analysis in numerical methods); B0290F
(Interpolation and function approximation); C4110
(Error analysis in numerical methods); C4130
(Interpolation and function approximation)",
corpsource = "Univ. St. Andrews, Fife, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "continued fraction expansion; convergents; Dawson's
integral; error analysis; function approximation;
rational approximations; truncation error estimate",
treatment = "T Theoretical or Mathematical",
}
@Article{Nasell:1974:IMB,
author = "Ingemar Nasell",
title = "Inequalities for Modified {Bessel} Functions",
journal = j-MATH-COMPUT,
volume = "28",
number = "125",
pages = "253--256",
month = jan,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Bell Labs., Holmdel, NJ, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Bessel functions; inequalities; modified Bessel
functions; sharp versions",
treatment = "T Theoretical or Mathematical",
}
@Book{Olver:1974:ASF,
author = "F. W. J. Olver",
title = "Asymptotics and Special Functions",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvi + 572",
year = "1974",
ISBN = "0-12-525850-X",
ISBN-13 = "978-0-12-525850-0",
LCCN = "QA351 .O481 1974",
bibdate = "Wed Dec 15 10:40:06 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pisarskii:1974:QCD,
author = "A. V. Pisarski{\u\i} and A. F. Kurgaev and A. V.
Palagin",
title = "On the question of the convergence of the {``digit by
digit''} methods of computing the elementary
functions",
journal = "Kibernetika (Kiev)",
volume = "4",
pages = "147--149",
year = "1974",
CODEN = "KBRNA5",
ISSN = "0023-1274",
MRclass = "65D20",
MRnumber = "53 \#1915",
MRreviewer = "V. V. Ivanov",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
}
@Article{Pomeranz:1974:AAE,
author = "John Pomeranz",
title = "{ACM Algorithm 487}: Exact Cumulative Distribution of
the {Kolmogorov--Smirnov} Statistic for Small Samples",
journal = j-CACM,
volume = "17",
number = "12",
pages = "703--704",
month = dec,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:12:56 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Pomeranz74;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "See also \cite{Pomeranz:1976:REC}.",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C7310 (Mathematics computing)",
corpsource = "Purdue Univ., West Lafayette, IN, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; exact cumulative distribution; FORTRAN;
Kolmogorov Smirnov test; natural sciences applications
of computers; small samples; statistic; statistics;
subroutines",
oldlabel = "Pomeranz74",
remark = "Fullerton: FORTRAN routine accurate apparently to 5
digits.",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Pomeranz74",
}
@Article{Shaw:1974:NME,
author = "Mary Shaw and J. F. Traub",
title = "On the Number of Multiplications for the Evaluation of
a Polynomial and Some of Its Derivatives",
journal = j-J-ACM,
volume = "21",
number = "1",
pages = "161--167",
month = jan,
year = "1974",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321796.321810",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "A family of new algorithms is given for evaluating the
first $m$ derivatives of a polynomial. In particular,
it is shown that all derivatives may be evaluated in $
3 n - 2 $ multiplications. The best previous result
required $ (1 / 2) n (n + 1) $ multiplications. Some
optimality results are presented.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
classification = "921",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "https://dl.acm.org/loi/jacm",
keywords = "mathematical techniques; number of multiplications to
evaluate a polynomial",
}
@Article{Sheorey:1974:CEW,
author = "V. B. Sheorey",
title = "{Chebyshev} Expansions for Wavefunctions",
journal = j-COMP-PHYS-COMM,
volume = "7",
number = "1",
pages = "1--12",
month = jan,
year = "1974",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(74)90053-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Oct 30 10:36:29 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Stegun:1974:ACM,
author = "I. A. Stegun and R. Zucker",
title = "Automatic Computing Methods for Special Functions.
{Part II}. {The} Exponential Integral {$ E_n(x) $}",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "78B",
number = "4",
pages = "199--216",
month = oct,
year = "1974",
ISSN = "0091-0635",
bibdate = "Sat Oct 30 11:00:40 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Fullerton: Adjustable double precision FORTRAN
routines for $ E_n(x) $ and $ e^x E_n(x) $.",
}
@Article{Wang:1974:UEZ,
author = "Paul S. Wang",
title = "The Undecidability of the Existence of Zeros of Real
Elementary Functions",
journal = j-J-ACM,
volume = "21",
number = "4",
pages = "586--589",
month = oct,
year = "1974",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
abstract = "From Richardson's undecidability results, it is shown
that the predicate ``there exists a real number such
that G(r) equals 0'' is recursively undecidable for
G(x) in a class of functions which involves polynomials
and the sine function. The deduction follows that the
convergence of a class of improper integrals is
recursively undecidable.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
classification = "921",
fjournal = "Journal of the ACM",
journal-URL = "https://dl.acm.org/loi/jacm",
keywords = "mathematical techniques",
}
@Article{Wimp:1974:CTP,
author = "J. Wimp",
title = "On the computation of {Tricomi}'s {Psi} function",
journal = j-COMPUTING,
volume = "13",
number = "3--4",
pages = "195--203",
year = "1974",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:52 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nhfb,
affiliation = "Drexel Univ., Philadelphia, PA, USA",
citedby = "Fullerton:1980:BEM",
classification = "723; 921; B0290D; C4120",
description = "convergence of numerical methods; function
evaluation",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "computation; computer programming --- Subroutines;
confluent hypergeometric function; convergence;
mathematical techniques; recur
