# bibtab

bibtype: article
filename: elefunt.bib
label: Barnett:1976:MRC
author: A. R. Barnett
title: RCWFF --- Modification of the Real Coulomb Wavefunction Program RCWFN
journal: j-COMP-PHYS-COMM
volume: 11
number: 1
pages: 141--142
month: jan
monthnumber: 1
year: 1976
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(76)90045-X
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Fri Oct 29 21:24:02 2010
bibtimestamp: 2010.10.29 21:24:02 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. R. Barnett
rawtitle: {RCWFF} --- Modification of the Real {Coulomb} Wavefunction Program {RCWFN}
entry:
@Article{Barnett:1976:MRC,
  author =       "A. R. Barnett",
  title =        "{RCWFF} --- Modification of the Real {Coulomb}
                 Wavefunction Program {RCWFN}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "11",
  number =       "1",
  pages =        "141--142",
  month =        jan # "\slash " # feb,
  year =         "1976",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(76)90045-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Oct 29 21:24:02 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",
}


bibtype: article
filename: elefunt.bib
label: Barnett:1976:RMR
author: A. R. Barnett
title: RCWFF --- Modification of the Real Coulomb Wavefunction Program RCWFN
journal: j-COMP-PHYS-COMM
volume: 11
number: 1
pages: 141--142
month: jan
monthnumber: 1
year: 1976
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(76)90045-X
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 06:01:19 MST 2012
bibtimestamp: 2012.02.13 06:01:19 MST
URL: http://www.sciencedirect.com/science/article/pii/001046557690045X
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. R. Barnett
rawtitle: {RCWFF} --- Modification of the Real {Coulomb} Wavefunction Program {RCWFN}
entry:
@Article{Barnett:1976:RMR,
  author =       "A. R. Barnett",
  title =        "{RCWFF} --- Modification of the Real {Coulomb}
                 Wavefunction Program {RCWFN}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "11",
  number =       "1",
  pages =        "141--142",
  month =        jan # "\slash " # feb,
  year =         "1976",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(76)90045-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:19 MST 2012",
  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/001046557690045X",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  xxtitle =      "{RCWFF} --- a modification of the real {Coulomb}
                 wavefunction program {RCWFN}",
}


bibtype: article
filename: elefunt.bib
label: Blagoveshchenskii:1976:MCM
author: Yu V. Blagoveshchenskii and B. A. Popov and G. S. Tesler
title: Methods for computing mutually inverse functions
journal: j-CYBER
volume: 11
number: 2
pages: 252--256
month: mar
monthnumber: 3
year: 1976
CODEN: CYBNAW
DOI: https://doi.org/10.1007/BF01069867
ISSN: 0011-4235 (print), 2375-0189 (electronic) OR 00114235 (print), 23750189 (electronic)
ISSNL: 0011-4235 OR 00114235
bibdate: Tue Jan 24 08:29:23 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.01.24 08:29:23 ???
URL: http://www.springerlink.com/index/10.1007/BF01069867
fjournal: Cybernetics
remark: Translated from booktitle Kibernetika, No. 2, pp. 69--72, March--April, 1975.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10559
rawauthor: Yu V. Blagoveshchenskii and B. A. Popov and G. S. Tesler
rawtitle: Methods for computing mutually inverse functions
entry:
@Article{Blagoveshchenskii:1976:MCM,
  author =       "Yu V. Blagoveshchenskii and B. A. Popov and G. S.
                 Tesler",
  title =        "Methods for computing mutually inverse functions",
  journal =      j-CYBER,
  volume =       "11",
  number =       "2",
  pages =        "252--256",
  month =        mar,
  year =         "1976",
  CODEN =        "CYBNAW",
  DOI =          "https://doi.org/10.1007/BF01069867",
  ISSN =         "0011-4235 (print), 2375-0189 (electronic)",
  ISSN-L =       "0011-4235",
  bibdate =      "Tue Jan 24 08:29:23 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/index/10.1007/BF01069867",
  acknowledgement = ack-nhfb,
  fjournal =     "Cybernetics",
  journal-URL =  "http://link.springer.com/journal/10559",
  remark =       "Translated from \booktitle{Kibernetika}, No. 2, pp.
                 69--72, March--April, 1975.",
}


bibtype: article
filename: elefunt.bib
label: Blair:1976:RCA
author: J. M. Blair and C. A. Edwards and J. H. Johnson
title: Rational Chebyshev approximations for the inverse of the error function
journal: j-MATH-COMPUT
volume: 30
number: 136
pages: 827--830
month: oct
monthnumber: 10
year: 1976
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Chebyshev approximation; Chebyshev approximations; error function; inverse; rational
remark: Fullerton: With microfiche supplement.
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: Atomic Energy of Canada Ltd., Chalk River Nuclear Lab., Chalk River, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. M. Blair and C. A. Edwards and J. H. Johnson
rawtitle: Rational {Chebyshev} approximations for the inverse of the error function
entry:
@Article{Blair:1976:RCA,
  author =       "J. M. Blair and C. A. Edwards and J. H. Johnson",
  title =        "Rational {Chebyshev} approximations for the inverse of
                 the error function",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "136",
  pages =        "827--830",
  month =        oct,
  year =         "1976",
  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 of Canada Ltd., Chalk River Nuclear
                 Lab., Chalk River, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev approximation; Chebyshev approximations;
                 error function; inverse; rational",
  remark =       "Fullerton: With microfiche supplement.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Brent:1976:FMP
author: Richard P. Brent
title: Fast Multiple-Precision Evaluation of Elementary Functions
journal: j-J-ACM
volume: 23
number: 2
pages: 242--251
month: apr
monthnumber: 4
year: 1976
CODEN: JACOAH
DOI: https://doi.org/10.1145/321941.321944
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 68A20 (68A10)
MRnumber: 52 \#16111
MRreviewer: Amnon Barak
bibdate: Wed Jan 15 18:12:53 MST 1997
bibtimestamp: 1997.01.15 18:12:53 MST
fjournal: Journal of the ACM
keywords: computational complexity; computer arithmetic; computer programming
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: Richard P. Brent
rawtitle: Fast Multiple-Precision Evaluation of Elementary Functions
bibsource:
Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
Let $ f(x) $ be one of the usual elementary functions ($ exp $, $ log $, $ artan $, $ sin $, $ cosh $, etc.), and let $ M(n) $ be the number of single-precision operations required to multiply $n$-bit integers. It is shown that $ f(x) $ can be evaluated, with relative error $ O(2 - n) $, in $ O(M(n)l o g (n)) $ operations as $ n rightarrow infty $, for any floating-point number $x$ (with an $n$-bit fraction) in a suitable finite interval. From the Schonhage--Strassen bound on $ M(n) $, it follows that an $n$-bit approximation to $ f(x) $ may be evaluated in $ O(n log _(n) log log (n)) $ operations. Special cases include the evaluation of constants such as $ pi $ $e$, and $ e^pi $. The algorithms depend on the theory of elliptic integrals, using the arithmetic-geometric mean iteration and ascending Landen transformations.

rawabstract:
Let $ f(x) $ be one of the usual elementary functions ($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $, etc.), and let $ M(n) $ be the number of single-precision operations required to multiply $n$-bit integers. It is shown that $ f(x) $ can be evaluated, with relative error $ O(2 - n) $, in $ O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty $, for any floating-point number $x$ (with an $n$-bit fraction) in a suitable finite interval. From the Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows that an $n$-bit approximation to $ f(x) $ may be evaluated in $ O(n \log_(n) \log \log (n)) $ operations. Special cases include the evaluation of constants such as $ \pi $ $e$, and $ e^\pi $. The algorithms depend on the theory of elliptic integrals, using the arithmetic-geometric mean iteration and ascending Landen transformations.

entry:
@Article{Brent:1976:FMP,
  author =       "Richard P. Brent",
  title =        "Fast Multiple-Precision Evaluation of Elementary
                 Functions",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "242--251",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321941.321944",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "68A20 (68A10)",
  MRnumber =     "52 \#16111",
  MRreviewer =   "Amnon Barak",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply
                 $n$-bit integers. It is shown that $ f(x) $ can be
                 evaluated, with relative error $ O(2 - n) $, in $
                 O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
                 $, for any floating-point number $x$ (with an $n$-bit
                 fraction) in a suitable finite interval. From the
                 Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
                 that an $n$-bit approximation to $ f(x) $ may be
                 evaluated in $ O(n \log_(n) \log \log (n)) $
                 operations. Special cases include the evaluation of
                 constants such as $ \pi $ $e$, and $ e^\pi $. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic-geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "723",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  keywords =     "computational complexity; computer arithmetic;
                 computer programming",
}


bibtype: inproceedings
filename: elefunt.bib
label: Brent:1976:MPZ
author: Richard P. Brent
title: Multiple-precision zero-finding methods and the complexity of elementary function evaluation
crossref: Traub:1976:ACC
pages: 151--176
year: 1976
MRclass: 68A20
MRnumber: 54 \#11843
MRreviewer: Claus-Peter Schnorr
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Richard P. Brent
rawtitle: Multiple-precision zero-finding methods and the complexity of elementary function evaluation
entry:
@InProceedings{Brent:1976:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  crossref =     "Traub:1976:ACC",
  pages =        "151--176",
  year =         "1976",
  MRclass =      "68A20",
  MRnumber =     "54 \#11843",
  MRreviewer =   "Claus-Peter Schnorr",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Buschman:1976:IHF
author: R. G. Buschman
title: Inequalities for Hypergeometric Functions
journal: j-MATH-COMPUT
volume: 30
number: 134
pages: 303--305
month: apr
monthnumber: 4
year: 1976
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0220 (Mathematical analysis); C1120 (Mathematical analysis)
corpsource: Dept. of Math. and Statistics, Univ. of Guelph, Guelph, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: R. G. Buschman
rawtitle: Inequalities for Hypergeometric Functions
keywords:
Bessel functions; classical orthogonal polynomials; confluence; dominant diagonal matrix; function; functions; Gauss' hypergeometric; hypergeometric functions; Kummer's hypergeometric function; modified Bessel function; principle

entry:
@Article{Buschman:1976:IHF,
  author =       "R. G. Buschman",
  title =        "Inequalities for Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "134",
  pages =        "303--305",
  month =        apr,
  year =         "1976",
  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 =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Math. and Statistics, Univ. of Guelph,
                 Guelph, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; classical orthogonal polynomials;
                 confluence; dominant diagonal matrix; function;
                 functions; Gauss' hypergeometric; hypergeometric
                 functions; Kummer's hypergeometric function; modified
                 Bessel function; principle",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Davies:1976:IPS
author: M. Davies and B. Dawson
title: The incrementation parameter in square root iteration
journal: j-J-INST-MATH-APPL
volume: 17
number: 2
pages: 219--223
year: 1976
CODEN: JMTAA8
ISSN: 0020-2932 OR 00202932
MRclass: 65H05
MRnumber: 55 #9514
MRreviewer: Luciano Biasini
bibdate: Fri Apr 5 07:38:01 MST 2002
bibtimestamp: 2002.04.05 07:38:01 MST
fjournal: Journal of the Institute of Mathematics and its Applications
ZMnumber: 0319.65039
acknowledgement: ack-nhfb
journalURL: http://imamat.oxfordjournals.org/content/by/year
rawauthor: M. Davies and B. Dawson
rawtitle: The incrementation parameter in square root iteration
entry:
@Article{Davies:1976:IPS,
  author =       "M. Davies and B. Dawson",
  title =        "The incrementation parameter in square root
                 iteration",
  journal =      j-J-INST-MATH-APPL,
  volume =       "17",
  number =       "2",
  pages =        "219--223",
  year =         "1976",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  MRclass =      "65H05",
  MRnumber =     "55 #9514",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Fri Apr 5 07:38:01 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0319.65039",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
}


bibtype: article
filename: elefunt.bib
label: Deuflhard:1976:ASC
author: P. Deuflhard
title: On Algorithms for the Summation of Certain Special Functions
journal: j-COMPUTING
volume: 17
number: 1
pages: 37--48
month: mar
monthnumber: 3
year: 1976
CODEN: CMPTA2
DOI: https://doi.org/10.1007/BF02252258
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:52 MST 2001
bibtimestamp: 2001.01.02 17:40:52 MST
fjournal: Computing
acknowledgement: ack-nhfb
affiliation: Inst. fur Math., Tech. Univ. Munchen, Munchen, West Germany
journalURL: http://link.springer.com/journal/607
journalabr: Comput (Vienna/NY)
rawauthor: P. Deuflhard
rawtitle: On Algorithms for the Summation of Certain Special Functions
bibsource:
Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; INSPEC Axiom database (1968--date)

keywords:
algorithms; backward error analysis; computer programming; graph representation; mathematical techniques; special functions; stability; summation

remark:
Fullerton: An extension of Clenshaw's summation method is discussed. Spherical harmonic sums are considered as a special case.

entry:
@Article{Deuflhard:1976:ASC,
  author =       "P. Deuflhard",
  title =        "On Algorithms for the Summation of Certain Special
                 Functions",
  journal =      j-COMPUTING,
  volume =       "17",
  number =       "1",
  pages =        "37--48",
  month =        mar,
  year =         "1976",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/BF02252258",
  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/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. f{\"u}r Math., Tech. Univ. M{\"u}nchen,
                 M{\"u}nchen, West Germany",
  citedby =      "Fullerton:1980:BEM",
  classification = "723; 921; B0290B; B0290H; C4110; C4140",
  description =  "error analysis; linear algebra",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "algorithms; backward error analysis; computer
                 programming; graph representation; mathematical
                 techniques; special functions; stability; summation",
  remark =       "Fullerton: An extension of Clenshaw's summation method
                 is discussed. Spherical harmonic sums are considered as
                 a special case.",
}


bibtype: techreport
filename: elefunt.bib
label: DiDonato:1976:CIG
author: Armido R. DiDonato and R. K. Hageman
title: Computation of the incomplete gamma function ratios
type: Report
number: NSWC/DL TR-3482
institution: Naval Surface Weapons Center
address: Dahlgren, VA, USA
pages: 86
month: apr
monthnumber: 4
year: 1976
bibdate: Mon Jun 03 12:24:32 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.06.03 12:24:32 ???
URL: https://apps.dtic.mil/sti/citations/tr/ADA031812
acknowledgement: ack-nhfb
rawauthor: Armido R. DiDonato and R. K. Hageman
rawtitle: Computation of the incomplete gamma function ratios
entry:
@TechReport{DiDonato:1976:CIG,
  author =       "Armido R. DiDonato and R. K. Hageman",
  title =        "Computation of the incomplete gamma function ratios",
  type =         "Report",
  number =       "NSWC/DL TR-3482",
  institution =  "Naval Surface Weapons Center",
  address =      "Dahlgren, VA, USA",
  pages =        "86",
  month =        apr,
  year =         "1976",
  bibdate =      "Mon Jun 03 12:24:32 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://apps.dtic.mil/sti/citations/tr/ADA031812",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Eckhardt:1976:RAW
author: Ulrich Eckhardt
title: A Rational Approximation to Weierstrass' $ wp $-Function
journal: j-MATH-COMPUT
volume: 30
number: 136
pages: 818--826
month: oct
monthnumber: 10
year: 1976
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: A complex FORTRAN algorithm with accuracy down to $ 10^-18 $ is given.
acknowledgement: ack-nhfb
classcodes: A0260 (Numerical approximation and analysis); C4130 (Interpolation and function approximation)
corpsource: Nuclear Res. Center, Central Inst. for Appl. Math., Julich, West Germany
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Ulrich Eckhardt
rawtitle: A Rational Approximation to {Weierstrass}' $ \wp $-Function
keywords:
equianharmonic; function approximation; rational approximation; unit period parallelogram; Weierstrass' elliptic function; Weierstrass' p function

entry:
@Article{Eckhardt:1976:RAW,
  author =       "Ulrich Eckhardt",
  title =        "A Rational Approximation to {Weierstrass}' $ \wp
                 $-Function",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "136",
  pages =        "818--826",
  month =        oct,
  year =         "1976",
  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 =   "A0260 (Numerical approximation and analysis); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Nuclear Res. Center, Central Inst. for Appl. Math.,
                 Julich, West Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "equianharmonic; function approximation; rational
                 approximation; unit period parallelogram; Weierstrass'
                 elliptic function; Weierstrass' p function",
  remark =       "Fullerton: A complex FORTRAN algorithm with accuracy
                 down to $ 10^{-18} $ is given.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Ellacott:1976:RCA
author: S. Ellacott and Jack Williams
title: Rational Chebyshev Approximation in the Complex Plane
journal: j-SIAM-J-NUMER-ANAL
volume: 13
number: 3
pages: 310--323
month: jun
monthnumber: 6
year: 1976
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: S. Ellacott and Jack Williams
rawtitle: Rational {Chebyshev} Approximation in the Complex Plane
entry:
@Article{Ellacott:1976:RCA,
  author =       "S. Ellacott and Jack Williams",
  title =        "Rational {Chebyshev} Approximation in the Complex
                 Plane",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "13",
  number =       "3",
  pages =        "310--323",
  month =        jun,
  year =         "1976",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: article
filename: elefunt.bib
label: elLozy:1976:RAC
author: Mohamed el Lozy
title: Remark on ``Algorithm 299: Chi-Squared Integral [S15]''
journal: j-TOMS
volume: 2
number: 4
pages: 393--395
month: dec
monthnumber: 12
year: 1976
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Jul 05 16:47:38 1997
bibtimestamp: 1997.07.05 16:47:38 ???
note: See cite Hill:1967:ACS,Hill:1985:RCS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Mohamed el Lozy
rawnote: See \cite{Hill:1967:ACS,Hill:1985:RCS}.
rawtitle: Remark on {``Algorithm 299: Chi-Squared Integral [S15]''}
entry:
@Article{elLozy:1976:RAC,
  author =       "Mohamed el Lozy",
  title =        "Remark on {``Algorithm 299: Chi-Squared Integral
                 [S15]''}",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "393--395",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Jul 05 16:47:38 1997",
  bibsource =    "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:ACS,Hill:1985:RCS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1976:CR
author: Henry E. Fettis
title: Complex Roots of $ sin z = a z, cos z = a z $, and $ cosh z = a z $
journal: j-MATH-COMPUT
volume: 30
number: 135
pages: 541--545
month: jul
monthnumber: 7
year: 1976
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: complex roots; cos z=az; cosh z=az; functional equations; sin z=az
acknowledgement: ack-nhfb
classcodes: B0220 (Mathematical analysis); C1120 (Mathematical analysis)
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Henry E. Fettis
rawtitle: Complex Roots of $ \sin z = a z, \cos z = a z $, and $ \cosh z = a z $
entry:
@Article{Fettis:1976:CR,
  author =       "Henry E. Fettis",
  title =        "Complex Roots of $ \sin z = a z, \cos z = a z $, and $
                 \cosh z = a z $",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "135",
  pages =        "541--545",
  month =        jul,
  year =         "1976",
  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 =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "complex roots; cos z=az; cosh z=az; functional
                 equations; sin z=az",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Fullerton:1976:AEM
author: L. W. Fullerton and G. A. Rinker, Jr.
journal: j-PHYS-REV-A
volume: 13
number: 3
pages: 1283--1287
month: mar
monthnumber: 3
year: 1976
CODEN: PLRAAN
ISSNL: 1050-2947 OR 10502947
bibdate: Sat Oct 30 06:32:26 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 06:32:26 ???
fjournal: Physical Review A (Atomic, Molecular, and Optical Physics)
acknowledgement: ack-nhfb
journalURL: http://pra.aps.org/browse
rawauthor: L. W. Fullerton and G. A. {Rinker, Jr.}
title:
Accurate and Efficient Methods for the Evaluation of Vacuum-Polarization Potentials of Order $ Z alpha $ and $ Z alpha ^2 $

ISSN:
1050-2947 (print), 1094-1622, 1538-4446, 1538-4519 OR 10502947 (print), 10941622, 15384446, 15384519

remark:
Fullerton: Nine-figure approximations to $ K_n(x) = int _1^infty e^-x t t^n (1 / r^3 + 1 / (2 r^5)) (r^2 - 1)^1 / 2 d t $ for $ n = 0, 1, 3 $, and $5$.

rawtitle:
Accurate and Efficient Methods for the Evaluation of Vacuum-Polarization Potentials of Order {$ Z \alpha $} and {$ Z \alpha^2 $}

entry:
@Article{Fullerton:1976:AEM,
  author =       "L. W. Fullerton and G. A. {Rinker, Jr.}",
  title =        "Accurate and Efficient Methods for the Evaluation of
                 Vacuum-Polarization Potentials of Order {$ Z \alpha $}
                 and {$ Z \alpha^2 $}",
  journal =      j-PHYS-REV-A,
  volume =       "13",
  number =       "3",
  pages =        "1283--1287",
  month =        mar,
  year =         "1976",
  CODEN =        "PLRAAN",
  ISSN =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  ISSN-L =       "1050-2947",
  bibdate =      "Sat Oct 30 06:32:26 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Physical Review A (Atomic, Molecular, and Optical
                 Physics)",
  journal-URL =  "http://pra.aps.org/browse",
  remark =       "Fullerton: Nine-figure approximations to $ K_n(x) =
                 \int_1^\infty e^{-x t} t^n (1 / r^3 + 1 / (2 r^5)) (r^2
                 - 1)^{1 / 2} \, d t $ for $ n = 0, 1, 3 $, and $5$.",
}


bibtype: article
filename: elefunt.bib
label: Ikebe:1976:CZB
author: Y. Ikebe
journal: j-SIAM-REVIEW
volume: 18
number: 4
pages: 810--810
year: 1976
CODEN: SIREAD
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: Y. Ikebe
title:
Computing Zeros of Bessel and Regular Coulomb Wave Functions and of Their Derivatives by Matrix Theoretic Approach --- Practical Accuracy Criteria

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

rawtitle:
Computing Zeros of {Bessel} and Regular {Coulomb} Wave Functions and of Their Derivatives by Matrix Theoretic Approach --- Practical Accuracy Criteria

entry:
@Article{Ikebe:1976:CZB,
  author =       "Y. Ikebe",
  title =        "Computing Zeros of {Bessel} and Regular {Coulomb} Wave
                 Functions and of Their Derivatives by Matrix Theoretic
                 Approach --- Practical Accuracy Criteria",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "810--810",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "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",
}


bibtype: article
filename: elefunt.bib
label: Kerridge:1976:YAS
author: D. F. Kerridge and G. W. Cook
title: Yet Another Series for the Normal Integral
journal: j-BIOMETRIKA
volume: 63
number: 2
pages: 401--403
month: aug
monthnumber: 8
year: 1976
CODEN: BIOKAX
DOI: https://doi.org/10.2307/2335636
ISSN: 0006-3444 (print), 1464-3510 (electronic) OR 00063444 (print), 14643510 (electronic)
ISSNL: 0006-3444 OR 00063444
bibdate: Sat Jun 21 14:34:06 MDT 2014
bibtimestamp: 2014.06.21 14:34:06 MDT
URL: http://www.jstor.org/stable/2335636
fjournal: Biometrika
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00063444.html
rawauthor: D. F. Kerridge and G. W. Cook
rawtitle: Yet Another Series for the Normal Integral
bibsource:
http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315483; https://www.math.utah.edu/pub/tex/bib/biometrika1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Kerridge:1976:YAS,
  author =       "D. F. Kerridge and G. W. Cook",
  title =        "Yet Another Series for the Normal Integral",
  journal =      j-BIOMETRIKA,
  volume =       "63",
  number =       "2",
  pages =        "401--403",
  month =        aug,
  year =         "1976",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2335636",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  bibdate =      "Sat Jun 21 14:34:06 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315483;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2335636",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://www.jstor.org/journals/00063444.html",
}


bibtype: article
filename: elefunt.bib
label: Kononova:1976:CEF
author: N. F. Kononova
journal: Vycisl. Prikl. Mat. (Kiev)
volume: 29
pages: 27--39
year: 1976
ISSN: 0321-4117 OR 03214117
MRclass: 151. 65D15
MRnumber: 57 \#18026
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: N. F. Kononova
title:
The computation of elementary functions by means of polynomial approximations by the method of V. K. Dzjadik. (Russian)

rawtitle:
The computation of elementary functions by means of polynomial approximations by the method of {V. K. Dzjadik}. ({Russian})

entry:
@Article{Kononova:1976:CEF,
  author =       "N. F. Kononova",
  title =        "The computation of elementary functions by means of
                 polynomial approximations by the method of {V. K.
                 Dzjadik}. ({Russian})",
  journal =      "Vy{\v{c}}isl. Prikl. Mat. (Kiev)",
  volume =       "29",
  pages =        "27--39",
  year =         "1976",
  ISSN =         "0321-4117",
  MRclass =      "151. 65D15",
  MRnumber =     "57 \#18026",
  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",
}


bibtype: article
filename: elefunt.bib
label: Lentz:1976:GBF
author: William J. Lentz
title: Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions
journal: j-APPL-OPTICS
volume: 15
number: 3
pages: 668--671
month: mar
monthnumber: 3
year: 1976
CODEN: APOPAI
DOI: https://doi.org/10.1364/AO.15.000668
ISSN: 0003-6935 OR 00036935
bibdate: Sat Oct 30 08:41:40 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 08:41:40 ???
fjournal: Applied Optics
acknowledgement: ack-nhfb
journalURL: http://www.osapublishing.org/ao/browse.cfm
rawauthor: William J. Lentz
rawtitle: Generating {Bessel} Functions in {Mie} Scattering Calculations Using Continued Fractions
abstract:
A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The continued fraction representations for both spherical Bessel functions and ratios of Bessel functions of consecutive order are presented.

rawabstract:
A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The continued fraction representations for both spherical Bessel functions and ratios of Bessel functions of consecutive order are presented.

entry:
@Article{Lentz:1976:GBF,
  author =       "William J. Lentz",
  title =        "Generating {Bessel} Functions in {Mie} Scattering
                 Calculations Using Continued Fractions",
  journal =      j-APPL-OPTICS,
  volume =       "15",
  number =       "3",
  pages =        "668--671",
  month =        mar,
  year =         "1976",
  CODEN =        "APOPAI",
  DOI =          "https://doi.org/10.1364/AO.15.000668",
  ISSN =         "0003-6935",
  bibdate =      "Sat Oct 30 08:41:40 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A new method of generating the Bessel functions and
                 ratios of Bessel functions necessary for Mie
                 calculations is presented. Accuracy is improved while
                 eliminating the need for extended precision word
                 lengths or large storage capability. The algorithm uses
                 a new technique of evaluating continued fractions that
                 starts at the beginning rather than the tail and has a
                 built-in error check. The continued fraction
                 representations for both spherical Bessel functions and
                 ratios of Bessel functions of consecutive order are
                 presented.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Applied Optics",
  journal-URL =  "http://www.osapublishing.org/ao/browse.cfm",
}


bibtype: article
filename: elefunt.bib
label: Luke:1976:CER
author: Yudell L. Luke
title: Chebyshev expansions and rational approximations
journal: j-J-COMPUT-APPL-MATH
volume: 2
number: 2
pages: 85--93
month: jun
monthnumber: 6
year: 1976
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:14 MST 2017
bibtimestamp: 2017.02.25 11:59:14 MST
URL: http://www.sciencedirect.com/science/article/pii/0771050X76900139
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Yudell L. Luke
rawtitle: {Chebyshev} expansions and rational approximations
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib

entry:
@Article{Luke:1976:CER,
  author =       "Yudell L. Luke",
  title =        "{Chebyshev} expansions and rational approximations",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "2",
  number =       "2",
  pages =        "85--93",
  month =        jun,
  year =         "1976",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X76900139",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Morris:1976:RDF
author: Robert Morris
title: Remark on ``Algorithm 490: The Dilogarithm Function of a Real Argument [S22]''
journal: j-TOMS
volume: 2
number: 1
pages: 112--112
month: mar
monthnumber: 3
year: 1976
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355666.355680
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Aug 30 00:27:18 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.30 00:27:18 ???
note: See cite Ginsberg:1975:AAD.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Robert Morris
rawnote: See \cite{Ginsberg:1975:AAD}.
rawtitle: Remark on ``{Algorithm 490}: The Dilogarithm Function of a Real Argument [{S22}]''
entry:
@Article{Morris:1976:RDF,
  author =       "Robert Morris",
  title =        "Remark on ``{Algorithm 490}: The Dilogarithm Function
                 of a Real Argument [{S22}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "112--112",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355680",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Ginsberg:1975:AAD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Overington:1976:DSI
author: William J. G. Overington
journal: j-MATH-COMPUT-SIMUL
volume: 18
number: 1
pages: 63--64
month: jan
monthnumber: 1
year: 1976
CODEN: MCSIDR
DOI: https://doi.org/10.1016/0378-4754(76)90032-X
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Fri Aug 15 13:24:09 MDT 2025
bibtimestamp: 2025.08.15 13:24:09 MDT
URL: https://www.sciencedirect.com/science/article/pii/037847547690032X
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: William J. G. Overington
title:
A design study for an integer order Bessel function of the first kind function generator for an analogue computer

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1970.bib

rawtitle:
A design study for an integer order {Bessel} function of the first kind function generator for an analogue computer

entry:
@Article{Overington:1976:DSI,
  author =       "William J. G. Overington",
  title =        "A design study for an integer order {Bessel} function
                 of the first kind function generator for an analogue
                 computer",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "18",
  number =       "1",
  pages =        "63--64",
  month =        jan,
  year =         "1976",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(76)90032-X",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Aug 15 13:24:09 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1970.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/037847547690032X",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: article
filename: elefunt.bib
label: Paul:1976:SEF
author: George Paul and M. Wayne Wilson
title: Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?
journal: j-TOMS
volume: 2
number: 2
pages: 132--142
month: jun
monthnumber: 6
year: 1976
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355681.355684
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 27 00:30:21 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1994.08.27 00:30:21 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
ajournal: ACM Trans. Math. Softw.
journalURL: https://dl.acm.org/loi/toms
rawauthor: George Paul and M. Wayne Wilson
rawtitle: Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?
abstract:
The question whether elementary mathematical function library routines should be incorporated into a computer system as part of the machine instruction set is discussed. The prime issues affecting such a decision are accuracy, substitution, and user expectations, Support of the COMPLEX arithmetic data type is also a complicating factor. These issues are discussed and conclusions are drawn.

keywords:
computer instruction sets; elementary mathematical functions; hardware function evaluation; mathematical function libraries; programming languages

rawabstract:
The question whether elementary mathematical function library routines should be incorporated into a computer system as part of the machine instruction set is discussed. The prime issues affecting such a decision are accuracy, substitution, and user expectations, Support of the COMPLEX arithmetic data type is also a complicating factor. These issues are discussed and conclusions are drawn.

entry:
@Article{Paul:1976:SEF,
  author =       "George Paul and M. Wayne Wilson",
  title =        "Should the Elementary Function Library Be Incorporated
                 Into Computer Instruction Sets?",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "132--142",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355684",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The question whether elementary mathematical function
                 library routines should be incorporated into a computer
                 system as part of the machine instruction set is
                 discussed. The prime issues affecting such a decision
                 are accuracy, substitution, and user expectations,
                 Support of the COMPLEX arithmetic data type is also a
                 complicating factor. These issues are discussed and
                 conclusions are drawn.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computer instruction sets; elementary mathematical
                 functions; hardware function evaluation; mathematical
                 function libraries; programming languages",
}


bibtype: article
filename: elefunt.bib
label: Pike:1976:RIB
author: Malcolm C. Pike and Jennie SooHoo and N. E. Bosten
title: Remark on ``Algorithm 179: Incomplete Beta Ratio [S14]''
journal: j-TOMS
volume: 2
number: 2
pages: 207--208
month: jun
monthnumber: 6
year: 1976
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Jul 05 16:45:39 1997
bibtimestamp: 1997.07.05 16:45:39 ???
note: See remark cite Ludwig:1963:AIB,Bosten:1974:RAI.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Malcolm C. Pike and Jennie SooHoo and N. E. Bosten
rawnote: See remark \cite{Ludwig:1963:AIB,Bosten:1974:RAI}.
rawtitle: Remark on {``Algorithm 179: Incomplete Beta Ratio [S14]''}
entry:
@Article{Pike:1976:RIB,
  author =       "Malcolm C. Pike and Jennie SooHoo and N. E. Bosten",
  title =        "Remark on {``Algorithm 179: Incomplete Beta Ratio
                 [S14]''}",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "207--208",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Jul 05 16:45:39 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{Ludwig:1963:AIB,Bosten:1974:RAI}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Pomeranz:1976:REC
author: J. Pomeranz
journal: j-TOMS
volume: 2
number: 1
pages: 111--111
month: mar
monthnumber: 3
year: 1976
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:05 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:05 ???
note: See cite Pomeranz:1974:AAE.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: J. Pomeranz
rawnote: See \cite{Pomeranz:1974:AAE}.
title:
Remark on ``Algorithm 487: Exact Cumulative Distribution of the Kolmogorov--Smirnov Statistic for Small Samples [S14]''

rawtitle:
Remark on ``{Algorithm 487: Exact Cumulative Distribution of the Kolmogorov--Smirnov Statistic for Small Samples [S14]}''

entry:
@Article{Pomeranz:1976:REC,
  author =       "J. Pomeranz",
  title =        "Remark on ``{Algorithm 487: Exact Cumulative
                 Distribution of the Kolmogorov--Smirnov Statistic for
                 Small Samples [S14]}''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "111--111",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:05 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Pomeranz:1974:AAE}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Redding:1976:CPC
author: R. W. Redding and W. P. Latham
title: On the calculation of the parabolic cylinder functions. II. The function $ V(a, x) $
journal: j-J-COMPUT-PHYS
volume: 20
number: 2
pages: 256--258
month: feb
monthnumber: 2
year: 1976
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(76)90071-1
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:20 MST 2012
bibtimestamp: 2012.01.01 09:15:20 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999176900711
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. W. Redding and W. P. Latham
rawtitle: On the calculation of the parabolic cylinder functions. {II}. {The} function {$ V(a, x) $}
entry:
@Article{Redding:1976:CPC,
  author =       "R. W. Redding and W. P. Latham",
  title =        "On the calculation of the parabolic cylinder
                 functions. {II}. {The} function {$ V(a, x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "20",
  number =       "2",
  pages =        "256--258",
  month =        feb,
  year =         "1976",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(76)90071-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:20 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/0021999176900711",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Salamin:1976:CUA
author: Eugene Salamin
title: Computation of $ pi $ Using Arithmetic-Geometric Mean
journal: j-MATH-COMPUT
volume: 30
number: 135
pages: 565--570
month: jul
monthnumber: 7
year: 1976
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: A quadratically convergent algorithm.
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Charles Stark Draper Lab., Cambridge, MA, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Eugene Salamin
rawtitle: Computation of $ \pi $ Using Arithmetic-Geometric Mean
keywords:
arithmetic geometric mean; convergence; elliptic integrals; error analysis; fast Fourier transform multiplication; function evaluation; Landen's; Legendre's relation; numerical computation of pi; transformation

entry:
@Article{Salamin:1976:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic-Geometric
                 Mean",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "135",
  pages =        "565--570",
  month =        jul,
  year =         "1976",
  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 =   "Charles Stark Draper Lab., Cambridge, MA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic geometric mean; convergence; elliptic
                 integrals; error analysis; fast Fourier transform
                 multiplication; function evaluation; Landen's;
                 Legendre's relation; numerical computation of pi;
                 transformation",
  remark =       "Fullerton: A quadratically convergent algorithm.",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: incollection
filename: elefunt.bib
label: Salimov:1976:OCE
author: F. I. Salimov
booktitle: Probabilistic methods and cybernetics
title: The organization of calculations of elementary functions into tables. (Russian)
volume: 12--13
publisher: Kazan University
address: Kazan, USSR
pages: 77--90
year: 1976
MRclass: 65A05
MRnumber: 58 \#31706
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: F. I. Salimov
rawbooktitle: Probabilistic methods and cybernetics
rawtitle: The organization of calculations of elementary functions into tables. ({Russian})
entry:
@InCollection{Salimov:1976:OCE,
  author =       "F. I. Salimov",
  booktitle =    "Probabilistic methods and cybernetics",
  title =        "The organization of calculations of elementary
                 functions into tables. ({Russian})",
  volume =       "12--13",
  publisher =    "Kazan University",
  address =      "Kazan, USSR",
  pages =        "77--90",
  year =         "1976",
  MRclass =      "65A05",
  MRnumber =     "58 \#31706",
  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",
}


bibtype: article
filename: elefunt.bib
label: Schett:1976:PTS
author: Alois Schett
title: Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions
journal: j-MATH-COMPUT
volume: 30
number: 133
pages: 143--147
month: jan
monthnumber: 1
year: 1976
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: The first several coefficients are tabulated.
acknowledgement: ack-nhfb
classcodes: B0290P (Differential equations); C4170 (Differential equations)
corpsource: CENS, Gif-sur-Yvette, France
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Alois Schett
rawtitle: Properties of the {Taylor} series expansion coefficients of the {Jacobian} elliptic functions
keywords:
differential equations; Jacobian elliptic functions; randomisation distributions; series (mathematics); Taylor series expansion

entry:
@Article{Schett:1976:PTS,
  author =       "Alois Schett",
  title =        "Properties of the {Taylor} series expansion
                 coefficients of the {Jacobian} elliptic functions",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "133",
  pages =        "143--147",
  month =        jan,
  year =         "1976",
  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 =   "B0290P (Differential equations); C4170 (Differential
                 equations)",
  corpsource =   "CENS, Gif-sur-Yvette, France",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "differential equations; Jacobian elliptic functions;
                 randomisation distributions; series (mathematics);
                 Taylor series expansion",
  remark =       "Fullerton: The first several coefficients are
                 tabulated.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Schonfelder:1976:PSF
author: J. L. Schonfelder
title: The Production of Special Function Routines for a Multi-Machine Library
journal: j-SPE
volume: 6
number: 1
pages: 71--82
month: jan
monthnumber: 1
year: 1976
CODEN: SPEXBL
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Sat May 31 13:36:16 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.31 13:36:16 MDT
fjournal: Software---Practice and Experience
remark: Fullerton: The design of transportable routines for the NAG library is discussed.
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
rawauthor: J. L. Schonfelder
rawtitle: The Production of Special Function Routines for a Multi-Machine Library
entry:
@Article{Schonfelder:1976:PSF,
  author =       "J. L. Schonfelder",
  title =        "The Production of Special Function Routines for a
                 Multi-Machine Library",
  journal =      j-SPE,
  volume =       "6",
  number =       "1",
  pages =        "71--82",
  month =        jan # "\slash " # mar,
  year =         "1976",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  remark =       "Fullerton: The design of transportable routines for
                 the NAG library is discussed.",
}


bibtype: article
filename: elefunt.bib
label: Schulten:1976:REC
author: K. Schulten and R. G. Gordon
title: Recursive Evaluation of $ 3 j $ and $ 6 j $ Coefficients
journal: j-COMP-PHYS-COMM
volume: 11
number: 2
pages: 269--278
month: mar
monthnumber: 3
year: 1976
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(76)90058-8
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Oct 30 10:32:44 2010
bibtimestamp: 2010.10.30 10:32:44 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: K. Schulten and R. G. Gordon
rawtitle: Recursive Evaluation of $ 3 j $ and $ 6 j $ Coefficients
entry:
@Article{Schulten:1976:REC,
  author =       "K. Schulten and R. G. Gordon",
  title =        "Recursive Evaluation of $ 3 j $ and $ 6 j $
                 Coefficients",
  journal =      j-COMP-PHYS-COMM,
  volume =       "11",
  number =       "2",
  pages =        "269--278",
  month =        mar # "\slash " # may,
  year =         "1976",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(76)90058-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:32:44 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",
}


bibtype: article
filename: elefunt.bib
label: Shanks:1976:TER
author: D. Shanks
journal: j-MATH-COMPUT
volume: 30
number: 134
pages: 381--381
year: 1976
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1976-0386215-4
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05 (10-04 10F20)
MRnumber: 0386215 (52 \#7073)
bibdate: Wed Jan 14 13:22:34 2015
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib
bibtimestamp: 2015.01.14 13:22:34 ???
URL: http://www.ams.org/journals/mcom/1976-30-134/S0025-5718-1976-0386215-4
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: D. Shanks
title:
Table errata: ``Regular continued fractions for $ pi $ and $ gamma $'', (Math. Comp. bf 25 (1971), 403); ``Rational approximations to $ pi $'' (ibid. bf 25 (1971), 387--392) by K. Y. Choong, D. E. Daykin and C. R. Rathbone

remark:
The second paper in the title is actually a review of a report containing table of partial quotients for a simple continued fraction for $ pi $.

rawtitle:
Table errata: {``Regular continued fractions for $ \pi $ and $ \gamma $'', (Math. Comp. {\bf 25} (1971), 403); ``Rational approximations to $ \pi $'' (ibid. {\bf 25} (1971), 387--392) by K. Y. Choong, D. E. Daykin and C. R. Rathbone}

entry:
@Article{Shanks:1976:TER,
  author =       "D. Shanks",
  title =        "Table errata: {``Regular continued fractions for $ \pi
                 $ and $ \gamma $'', (Math. Comp. {\bf 25} (1971), 403);
                 ``Rational approximations to $ \pi $'' (ibid. {\bf 25}
                 (1971), 387--392) by K. Y. Choong, D. E. Daykin and C.
                 R. Rathbone}",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "134",
  pages =        "381--381",
  year =         "1976",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1976-0386215-4",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (10-04 10F20)",
  MRnumber =     "0386215 (52 \#7073)",
  bibdate =      "Wed Jan 14 13:22:34 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  URL =          "http://www.ams.org/journals/mcom/1976-30-134/S0025-5718-1976-0386215-4",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "The second paper in the title is actually a review of
                 a report containing table of partial quotients for a
                 simple continued fraction for $ \pi $.",
}


bibtype: article
filename: elefunt.bib
label: Sheorey:1976:DCE
author: V. B. Sheorey
title: Double Chebyshev Expansions for Wave Functions
journal: j-COMP-PHYS-COMM
volume: 12
number: 2
pages: 125--134
month: nov
monthnumber: 11
year: 1976
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(76)90061-8
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Oct 30 10:38:43 2010
bibtimestamp: 2010.10.30 10:38:43 ???
URL: http://www.sciencedirect.com/science/article/pii/0010465576900618
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: V. B. Sheorey
rawtitle: Double {Chebyshev} Expansions for Wave Functions
entry:
@Article{Sheorey:1976:DCE,
  author =       "V. B. Sheorey",
  title =        "Double {Chebyshev} Expansions for Wave Functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "12",
  number =       "2",
  pages =        "125--134",
  month =        nov,
  year =         "1976",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(76)90061-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:38:43 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/0010465576900618",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Siemieniuch:1976:PCR
author: J. L. Siemieniuch
title: Properties of certain rational approximations to $ e^-z $
journal: j-BIT
volume: 16
number: 2
pages: 172--191
month: jun
monthnumber: 6
year: 1976
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01931369
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:14 MST 2006
bibtimestamp: 2006.01.04 18:52:14 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=172
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: elefunt; elementary functions
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: J. L. Siemieniuch
rawtitle: Properties of certain rational approximations to $ e^{-z} $
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Siemieniuch:1976:PCR,
  author =       "J. L. Siemieniuch",
  title =        "Properties of certain rational approximations to $
                 e^{-z} $",
  journal =      j-BIT,
  volume =       "16",
  number =       "2",
  pages =        "172--191",
  month =        jun,
  year =         "1976",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01931369",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=172",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elefunt; elementary functions",
}


bibtype: article
filename: elefunt.bib
label: Stegun:1976:ACM
author: I. A. Stegun and R. Zucker
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 80B
number: 2
pages: 291--311
month: apr
monthnumber: 4
year: 1976
ISSN: 0091-0635 OR 00910635
bibdate: Sat Oct 30 11:07:19 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 11:07:19 ???
fjournal: Journal of Research of the National Bureau of Standards (1934)
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: I. A. Stegun and R. Zucker
title:
Automatic Computing Methods for Special Functions. Part III. The Sine, Cosine, Exponential Integrals, and Related Functions

remark:
Fullerton: Adjustable double precision FORTRAN. routines for $ operatorname Si $, $ operatorname Ci $, $ operatorname Ei $, $ operatorname Shi $, and $ operatorname Chi $.

rawtitle:
Automatic Computing Methods for Special Functions. {Part III}. {The} Sine, Cosine, Exponential Integrals, and Related Functions

entry:
@Article{Stegun:1976:ACM,
  author =       "I. A. Stegun and R. Zucker",
  title =        "Automatic Computing Methods for Special Functions.
                 {Part III}. {The} Sine, Cosine, Exponential Integrals,
                 and Related Functions",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "80B",
  number =       "2",
  pages =        "291--311",
  month =        apr,
  year =         "1976",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 11:07:19 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 $ \operatorname {Si} $, $ \operatorname
                 {Ci} $, $ \operatorname {Ei} $, $ \operatorname {Shi}
                 $, and $ \operatorname {Chi} $.",
}


bibtype: article
filename: elefunt.bib
label: Temme:1976:NEO
author: Nico M. Temme
title: On the numerical evaluation of the ordinary Bessel function of the second kind
journal: j-J-COMPUT-PHYS
volume: 21
number: 3
pages: 343--350
month: jul
monthnumber: 7
year: 1976
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(76)90032-2
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:21 MST 2012
bibtimestamp: 2012.01.01 09:15:21 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999176900322
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Nico M. Temme
rawtitle: On the numerical evaluation of the ordinary {Bessel} function of the second kind
entry:
@Article{Temme:1976:NEO,
  author =       "Nico M. Temme",
  title =        "On the numerical evaluation of the ordinary {Bessel}
                 function of the second kind",
  journal =      j-J-COMPUT-PHYS,
  volume =       "21",
  number =       "3",
  pages =        "343--350",
  month =        jul,
  year =         "1976",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(76)90032-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:21 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/0021999176900322",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Tugov:1976:MCA
author: I. I. Tugov and Yu. L. Shitkov
title: A Method of Calculating the Appell Functions $ F_a(alpha ; beta , beta '; gamma ; x, y) $
journal: j-USSR-COMP-MATH-MATH-PHYS
volume: 16
number: 6
pages: 1587--1590
year: 1976
CODEN: CMMPA9
ISSN: 0041-5553, 0502-9902 OR 00415553, 05029902
ISSNL: 0041-5553 OR 00415553
bibdate: Sat Oct 30 11:38:05 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 11:38:05 ???
fjournal: U.S.S.R. Computational Mathematics and Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00415553
rawauthor: I. I. Tugov and Yu. L. Shitkov
rawtitle: A Method of Calculating the {Appell} Functions $ {F}_a(\alpha; \beta, \beta '; \gamma; x, y) $
remark:
Fullerton: [English] translation of Russian-language Zhurnal Vychislitel'noi Matematikii Matemancheskoi Fiziki (1976).

entry:
@Article{Tugov:1976:MCA,
  author =       "I. I. Tugov and Yu. L. Shitkov",
  title =        "A Method of Calculating the {Appell} Functions $
                 {F}_a(\alpha; \beta, \beta '; \gamma; x, y) $",
  journal =      j-USSR-COMP-MATH-MATH-PHYS,
  volume =       "16",
  number =       "6",
  pages =        "1587--1590",
  year =         "1976",
  CODEN =        "CMMPA9",
  ISSN =         "0041-5553, 0502-9902",
  ISSN-L =       "0041-5553",
  bibdate =      "Sat Oct 30 11:38:05 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "U.S.S.R. Computational Mathematics and Mathematical
                 Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00415553",
  remark =       "Fullerton: [English] translation of Russian-language
                 Zhurnal Vychislitel'noi Matematikii Matemancheskoi
                 Fiziki (1976).",
}


bibtype: article
filename: elefunt.bib
label: Alexander:1977:SRR
author: V. L. Alexander
title: Square Root Routine
journal: j-IBM-TDB
volume: 20
number: 3
pages: 1222
month: aug
monthnumber: 8
year: 1977
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Thu Sep 1 10:15:41 1994
bibtimestamp: 1994.09.01 10:15:41 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nj
rawauthor: V. L. Alexander
rawtitle: Square Root Routine
entry:
@Article{Alexander:1977:SRR,
  author =       "V. L. Alexander",
  title =        "Square Root Routine",
  journal =      j-IBM-TDB,
  volume =       "20",
  number =       "3",
  pages =        "1222",
  month =        aug,
  year =         "1977",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 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,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: elefunt.bib
label: Amos:1977:ACS
author: D. E. Amos and S. L. Daniel and M. K. Weston
journal: j-TOMS
volume: 3
number: 1
pages: 93--95
month: mar
monthnumber: 3
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355719.355727
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Apr 29 15:14:12 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.04.29 15:14:12 ???
note: See erratum cite Amos:1978:ECS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: D. E. Amos and S. L. Daniel and M. K. Weston
rawnote: See erratum \cite{Amos:1978:ECS}.
title:
Algorithm 511: CDC 6600 Subroutines IBESS and JBESS for Bessel Functions $ I_nu (x) $ and $ J_nu (x) $, $ x ge 0, nu ge 0 $ [S18]

rawtitle:
{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$ I_\nu (x) $} and {$ J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $} [{S18}]

entry:
@Article{Amos:1977:ACS,
  author =       "D. E. Amos and S. L. Daniel and M. K. Weston",
  title =        "{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and
                 {JBESS} for {Bessel} Functions {$ I_\nu (x) $} and {$
                 J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $} [{S18}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "93--95",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355727",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:14:12 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Amos:1978:ECS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Amos:1977:CSI
author: D. E. Amos and S. L. Daniel and M. K. Weston
journal: j-TOMS
volume: 3
number: 1
pages: 76--92
month: mar
monthnumber: 3
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355719.355726
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20
MRnumber: 55 #6781
bibdate: Tue Sep 06 19:20:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.06 19:20:02 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
reviewer: Sven-AA ke Gustafson
rawauthor: D. E. Amos and S. L. Daniel and M. K. Weston
title:
CDC 6600 Subroutines IBESS and JBESS for Bessel Functions $ I_nu (x) $ and $ J_nu (x) $, $ x ge 0, nu ge 0 $

rawtitle:
{CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$ I_\nu (x) $} and {$ J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $}

entry:
@Article{Amos:1977:CSI,
  author =       "D. E. Amos and S. L. Daniel and M. K. Weston",
  title =        "{CDC} 6600 Subroutines {IBESS} and {JBESS} for
                 {Bessel} Functions {$ I_\nu (x) $} and {$ J_\nu (x) $},
                 {$ x \ge 0, \nu \ge 0 $}",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "76--92",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355726",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "55 #6781",
  bibdate =      "Tue Sep 06 19:20:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Sven-{\AA}ke Gustafson",
}


bibtype: article
filename: elefunt.bib
label: Ardill:1977:BFC
author: R. W. B. Ardill and K. J. M. Moriarty
title: The Bessel Functions $ J_0 $ and $ J_1 $ of Complex Argument
journal: j-COMP-PHYS-COMM
volume: 13
number: 1
pages: 17--24
month: may
monthnumber: 5
year: 1977
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(77)90023-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Fri Oct 29 21:19:09 2010
bibtimestamp: 2010.10.29 21:19:09 ???
URL: http://www.sciencedirect.com/science/article/pii/0010465577900236
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: R. W. B. Ardill and K. J. M. Moriarty
rawtitle: The {Bessel} Functions {$ J_0 $} and {$ J_1 $} of Complex Argument
entry:
@Article{Ardill:1977:BFC,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "The {Bessel} Functions {$ J_0 $} and {$ J_1 $} of
                 Complex Argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "13",
  number =       "1",
  pages =        "17--24",
  month =        may,
  year =         "1977",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(77)90023-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Oct 29 21:19:09 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/0010465577900236",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: manual
filename: elefunt.bib
label: Arnold:1977:SMF
author: Mark G. Arnold
title: SCELBAL Mathematical Functions Supplement (8008 / 8080)
organization: Scelbi Computer Consulting. Inc.
address: 1322 Rear --- Boston Post Road, Milford, CT 0646, USA
pages: 31
year: 1977
bibdate: Fri Dec 01 16:04:29 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.12.01 16:04:29 ???
URL: http://www.scelbi.com/files/docs/scelbal/SCELBAL%20Mathematical%20Functions%20Supplement.pdf
remark: Brief description of implementations of cos, sin, exp, log, and atn functions.
acknowledgement: ack-nhfb
rawauthor: Mark G. Arnold
rawtitle: {SCELBAL} Mathematical Functions Supplement (8008\slash 8080)
entry:
@Manual{Arnold:1977:SMF,
  author =       "Mark G. Arnold",
  title =        "{SCELBAL} Mathematical Functions Supplement
                 (8008\slash 8080)",
  organization = "Scelbi Computer Consulting. Inc.",
  address =      "1322 Rear --- Boston Post Road, Milford, CT 0646,
                 USA",
  pages =        "31",
  year =         "1977",
  bibdate =      "Fri Dec 01 16:04:29 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.scelbi.com/files/docs/scelbal/SCELBAL%20Mathematical%20Functions%20Supplement.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Brief description of implementations of cos, sin, exp,
                 log, and atn functions.",
}


bibtype: book
filename: elefunt.bib
label: Brezinski:1977:ACA
author: Claude Brezinski
publisher: pub-SV
address: pub-SV:adr
pages: 313
year: 1977
ISBN: 0-387-08241-7, 3-540-08241-7 OR 0387082417, 3540082417
ISBN13: 978-0-387-08241-7, 978-3-540-08241-5 OR 9780387082417, 9783540082415
bibdate: Thu Dec 1 10:17:17 MST 2011
bibsource: carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:17:17 MST
keywords: convergence acceleration
language: French
acknowledgement: ack-nhfb
rawauthor: Claude Brezinski
title:
Acceleration de la convergence en analyse numerique. (French) [Convergence acceleration in numerical analysis]

rawtitle:
Acc{\'e}l{\'e}ration de la convergence en analyse num{\'e}rique. ({French}) [{Convergence} acceleration in numerical analysis]

entry:
@Book{Brezinski:1977:ACA,
  author =       "Claude Brezinski",
  title =        "Acc{\'e}l{\'e}ration de la convergence en analyse
                 num{\'e}rique. ({French}) [{Convergence} acceleration
                 in numerical analysis]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "313",
  year =         "1977",
  ISBN =         "0-387-08241-7, 3-540-08241-7",
  ISBN-13 =      "978-0-387-08241-7, 978-3-540-08241-5",
  LCCN =         "????",
  bibdate =      "Thu Dec 1 10:17:17 MST 2011",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
  language =     "French",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1977:EIF
author: B. C. Carlson
title: Elliptic Integrals of the First Kind
journal: j-SIAM-J-MATH-ANA
volume: 8
number: 2
pages: 231--242
year: 1977
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRnumber: MR 0430341 (55:3346)
bibdate: Fri Oct 29 22:03:28 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.29 22:03:28 ???
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: B. C. Carlson
rawtitle: Elliptic Integrals of the First Kind
entry:
@Article{Carlson:1977:EIF,
  author =       "B. C. Carlson",
  title =        "Elliptic Integrals of the First Kind",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "8",
  number =       "2",
  pages =        "231--242",
  month =        "????",
  year =         "1977",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRnumber =     "MR 0430341 (55:3346)",
  bibdate =      "Fri Oct 29 22:03:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: book
filename: elefunt.bib
label: Carlson:1977:SFA
author: Bille Chandler Carlson
title: Special Functions of Applied Mathematics
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xv + 335
year: 1977
ISBN: 0-12-160150-1 OR 0121601501
ISBN13: 978-0-12-160150-8 OR 9780121601508
LCCN: QA351 .C32
bibdate: Fri Jan 22 10:33:57 MST 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.01.22 10:33:57 MST
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: Bille Chandler Carlson
rawtitle: Special Functions of Applied Mathematics
entry:
@Book{Carlson:1977:SFA,
  author =       "Bille Chandler Carlson",
  title =        "Special Functions of Applied Mathematics",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 335",
  year =         "1977",
  ISBN =         "0-12-160150-1",
  ISBN-13 =      "978-0-12-160150-8",
  LCCN =         "QA351 .C32",
  bibdate =      "Fri Jan 22 10:33:57 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special",
}


bibtype: article
filename: elefunt.bib
label: Cody:1977:CRF
author: W. J. Cody and Rose M. Motley and L. Wayne Fullerton
title: The Computation of Real Fractional Order Bessel Functions of the Second Kind
journal: j-TOMS
volume: 3
number: 3
pages: 232--239
month: sep
monthnumber: 9
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355744.355747
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Sep 20 18:24:22 1994
bibtimestamp: 1994.09.20 18:24:22 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody and Rose M. Motley and L. Wayne Fullerton
rawtitle: The Computation of Real Fractional Order {Bessel} Functions of the Second Kind
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

entry:
@Article{Cody:1977:CRF,
  author =       "W. J. Cody and Rose M. Motley and L. Wayne Fullerton",
  title =        "The Computation of Real Fractional Order {Bessel}
                 Functions of the Second Kind",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "232--239",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355747",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:22 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;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Danilcenko:1977:ETC
author: L. S. Danil'cenko
journal: Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint
volume: 18
pages: 17--21
year: 1977
MRclass: 65D15
MRnumber: 80b:65016
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: L. S. Danil'{\v{c}}enko
title:
An efficient technique for the construction of rational approximations of elementary functions. (Russian) Optimization of computations (approximation and minimization of functions)

rawtitle:
An efficient technique for the construction of rational approximations of elementary functions. ({Russian}) Optimization of computations (approximation and minimization of functions)

entry:
@Article{Danilcenko:1977:ETC,
  author =       "L. S. Danil'{\v{c}}enko",
  title =        "An efficient technique for the construction of
                 rational approximations of elementary functions.
                 ({Russian}) Optimization of computations (approximation
                 and minimization of functions)",
  journal =      "Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint",
  volume =       "18",
  pages =        "17--21",
  year =         "1977",
  MRclass =      "65D15",
  MRnumber =     "80b:65016",
  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",
}


bibtype: article
filename: elefunt.bib
label: deAPMartins:1977:DSB
author: Pedro de A.P.Martins
title: Determination of spherical Bessel functions of an order larger than the argument
journal: j-J-COMPUT-PHYS
volume: 25
number: 2
pages: 194--198
month: oct
monthnumber: 10
year: 1977
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(77)90021-3
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:26 MST 2012
bibtimestamp: 2012.01.01 09:15:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999177900213
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Pedro {de A.P.Martins}
rawtitle: Determination of spherical {Bessel} functions of an order larger than the argument
entry:
@Article{deAPMartins:1977:DSB,
  author =       "Pedro {de A.P.Martins}",
  title =        "Determination of spherical {Bessel} functions of an
                 order larger than the argument",
  journal =      j-J-COMPUT-PHYS,
  volume =       "25",
  number =       "2",
  pages =        "194--198",
  month =        oct,
  year =         "1977",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(77)90021-3",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:26 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/0021999177900213",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  xxtitle =      "Determination of spherical {Bessel}'s functions of an
                 order larger than the argument",
}


bibtype: article
filename: elefunt.bib
label: Derenzo:1977:AHC
author: Stephen E. Derenzo
title: Approximations for Hand Calculators Using Small Integer Coefficients
journal: j-MATH-COMPUT
volume: 31
number: 137
pages: 214--222
month: jan
monthnumber: 1
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Stephen E. Derenzo
rawtitle: Approximations for Hand Calculators Using Small Integer Coefficients
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/mathcomp1970.bib; JSTOR database

keywords:
approximations; function approximation; function evaluation; hand calculators; programmable calculators; small integer coefficients

classcodes:
B0290D (Functional analysis); B0290F (Interpolation and function approximation); C4120 (Functional analysis); C4130 (Interpolation and function approximation); C7310 (Mathematics computing)

entry:
@Article{Derenzo:1977:AHC,
  author =       "Stephen E. Derenzo",
  title =        "Approximations for Hand Calculators Using Small
                 Integer Coefficients",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "137",
  pages =        "214--222",
  month =        jan,
  year =         "1977",
  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;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation); C7310 (Mathematics computing)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximations; function approximation; function
                 evaluation; hand calculators; programmable calculators;
                 small integer coefficients",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: techreport
filename: elefunt.bib
label: DiDonato:1977:CPP
author: Armido R. DiDonato and R. K. Hageman
title: Computation of the percentage points of the chi-square distribution
type: Report
number: NSWC/DL TR-3569
institution: Naval Surface Weapons Center
address: Dahlgren, VA, USA
pages: 200
year: 1977
bibdate: Mon Jun 03 12:24:32 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.06.03 12:24:32 ???
URL: https://apps.dtic.mil/sti/pdfs/ADA043997.pdf
acknowledgement: ack-nhfb
rawauthor: Armido R. DiDonato and R. K. Hageman
rawtitle: Computation of the percentage points of the chi-square distribution
entry:
@TechReport{DiDonato:1977:CPP,
  author =       "Armido R. DiDonato and R. K. Hageman",
  title =        "Computation of the percentage points of the chi-square
                 distribution",
  type =         "Report",
  number =       "NSWC/DL TR-3569",
  institution =  "Naval Surface Weapons Center",
  address =      "Dahlgren, VA, USA",
  pages =        "200",
  year =         "1977",
  bibdate =      "Mon Jun 03 12:24:32 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://apps.dtic.mil/sti/pdfs/ADA043997.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dijkstra:1977:CFE
author: D. Dijkstra
title: A continued fraction expansion for a generalization of Dawson's integral
journal: j-MATH-COMPUT
volume: 31
number: 138
pages: 503--510
month: apr
monthnumber: 4
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: An expansion for $ F(p, x) = e^-x^2 int _0^x e^t^2 d t $ is given.
acknowledgement: ack-nhfb
corpsource: Dept. of Math., Tech. Univ. Twente, Enschede, Netherlands
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: D. Dijkstra
rawtitle: A continued fraction expansion for a generalization of {Dawson}'s integral
keywords:
confluent hypergeometric; continued fraction expansion; Dawson's; error analysis; function; function evaluation; generalization; integral; integration; truncation error

classcodes:
C4110 (Error analysis in numerical methods); C4120 (Functional analysis); C4160 (Numerical integration and differentiation)

entry:
@Article{Dijkstra:1977:CFE,
  author =       "D. Dijkstra",
  title =        "A continued fraction expansion for a generalization of
                 {Dawson}'s integral",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "138",
  pages =        "503--510",
  month =        apr,
  year =         "1977",
  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 =   "C4110 (Error analysis in numerical methods); C4120
                 (Functional analysis); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math., Tech. Univ. Twente, Enschede,
                 Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "confluent hypergeometric; continued fraction
                 expansion; Dawson's; error analysis; function; function
                 evaluation; generalization; integral; integration;
                 truncation error",
  remark =       "Fullerton: An expansion for $ F(p, x) = e^{-x^2}
                 \int_0^x e^{t^2} \, d t $ is given.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: elefunt.bib
label: Dzjadyk:1977:TPA
author: V. K. Dzjadyk and S. F. Karpenko
title: Tables of polynomials for the approximate solution of elementary functions. (Russian)
number: 28
institution: Akad. Nauk Ukrain. SSR Inst. Mat. Preprint
pages: 28
year: 1977
MRclass: 65A05 (65D20)
MRnumber: 58 \#19016
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: V. K. Dzjadyk and S. F. Karpenko
rawtitle: Tables of polynomials for the approximate solution of elementary functions. ({Russian})
entry:
@TechReport{Dzjadyk:1977:TPA,
  author =       "V. K. Dzjadyk and S. F. Karpenko",
  title =        "Tables of polynomials for the approximate solution of
                 elementary functions. ({Russian})",
  number =       "28",
  institution =  "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
  pages =        "28",
  year =         "1977",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "58 \#19016",
  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",
}


bibtype: techreport
filename: elefunt.bib
label: Dzyadyk:1977:OPM
author: V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko and N. F. Kononova
type: Preprint
number: IM-77-21
institution: Akad. Nauk Ukrain. SSR Inst. Mat.
address: Kiev, USSR
pages: 42
year: 1977
MRclass: 65L99
MRnumber: 57 \#11075
MRreviewer: B. D. Donevski
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko and N. F. Kononova
title:
cyr Ob effektivnom priblizhenii mnogochlenami elementarnykh funktsiui . (Russian) [Efficient approximation by polynomials of elementary functions]

rawtitle:
{{\cyr Ob {\`e}ffektivnom priblizhenii mnogochlenami {\`e}lementarnykh funktsi{\u\i}.}} ({Russian}) [Efficient approximation by polynomials of elementary functions]

entry:
@TechReport{Dzyadyk:1977:OPM,
  author =       "V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko
                 and N. F. Kononova",
  title =        "{{\cyr Ob {\`e}ffektivnom priblizhenii mnogochlenami
                 {\`e}lementarnykh funktsi{\u\i}.}} ({Russian})
                 [Efficient approximation by polynomials of elementary
                 functions]",
  type =         "Preprint",
  number =       "IM-77-21",
  institution =  "Akad. Nauk Ukrain. SSR Inst. Mat.",
  address =      "Kiev, USSR",
  pages =        "42",
  year =         "1977",
  MRclass =      "65L99",
  MRnumber =     "57 \#11075",
  MRreviewer =   "B. D. Donevski",
  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",
}


bibtype: article
filename: elefunt.bib
label: Eckhardt:1977:RAW
author: Ulrich Eckhardt
title: A rational approximation to Weierstrass' elliptic function. II. The lemniscatic case
journal: j-COMPUTING
volume: 18
number: 4
pages: 341--349
year: 1977
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:53 MST 2001
bibtimestamp: 2001.01.02 17:40:53 MST
fjournal: Computing
keywords: elliptic functions; lemniscatic case; rational approximation; Weierstrass elliptic function
remark: Fullerton: Weierstrass' function and its derivative are approximated in the complex plane to 16 S.
acknowledgement: ack-nhfb
affiliation: Zentralinst. fur Angewandte Math., Julich, West Germany
journalURL: http://link.springer.com/journal/607
rawauthor: Ulrich Eckhardt
rawtitle: A rational approximation to {Weierstrass}' elliptic function. {II}. {The} lemniscatic case
bibsource:
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)

entry:
@Article{Eckhardt:1977:RAW,
  author =       "Ulrich Eckhardt",
  title =        "A rational approximation to {Weierstrass}' elliptic
                 function. {II}. {The} lemniscatic case",
  journal =      j-COMPUTING,
  volume =       "18",
  number =       "4",
  pages =        "341--349",
  year =         "1977",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:53 MST 2001",
  bibsource =    "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 =  "Zentralinst. f{\"u}r Angewandte Math., Julich, West
                 Germany",
  citedby =      "Fullerton:1980:BEM",
  classification = "C4130",
  description =  "function approximation",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "elliptic functions; lemniscatic case; rational
                 approximation; Weierstrass elliptic function",
  remark =       "Fullerton: Weierstrass' function and its derivative
                 are approximated in the complex plane to 16 S.",
}


bibtype: article
filename: elefunt.bib
label: Egbert:1977:PCAa
author: W. E. Egbert
title: Personal calculator algorithms. I. Square roots
journal: j-HEWLETT-PACKARD-J
volume: 28
number: 9
pages: 22--23
month: may
monthnumber: 5
year: 1977
CODEN: HPJOAX
ISSN: 0018-1153 OR 00181153
bibdate: Tue Mar 25 14:12:15 MST 1997
bibtimestamp: 1997.03.25 14:12:15 MST
fjournal: Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company
keywords: electronic calculators; HP personal calculator; square root algorithm
acknowledgement: ack-nj
classcodes: C5420 (Mainframes and minicomputers); C7310 (Mathematics computing)
treatment: A Application; T Theoretical or Mathematical
rawauthor: W. E. Egbert
rawtitle: Personal calculator algorithms. {I}. Square roots
entry:
@Article{Egbert:1977:PCAa,
  author =       "W. E. Egbert",
  title =        "Personal calculator algorithms. {I}. Square roots",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "28",
  number =       "9",
  pages =        "22--23",
  month =        may,
  year =         "1977",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  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 # " and " # ack-nhfb,
  classcodes =   "C5420 (Mainframes and minicomputers); C7310
                 (Mathematics computing)",
  fjournal =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
  keywords =     "electronic calculators; HP personal calculator; square
                 root algorithm",
  treatment =    "A Application; T Theoretical or Mathematical",
  xxpages =      "22--24",
}


bibtype: article
filename: elefunt.bib
label: Ercegovac:1977:GHO
author: Milos D. Ercegovac
journal: j-IEEE-TRANS-COMPUT
volume: C-26
number: 7
pages: 667--680
month: jul
monthnumber: 7
year: 1977
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1977.1674900
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 21:56:56 MDT 2011
bibtimestamp: 2011.07.11 21:56:56 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674900
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Milo{\v{s}} D. Ercegovac
title:
A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital Computer

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

abstract:
A parallel computational method, amenable for efficient hardware-level implementation, is described. It provides a simple and fast algorithm for the evaluation of polynomials, certain rational functions and arithmetic expressions, solving a class of systems of linear equations, or performing the basic arithmetic operations in a fixed-point number representation system. The time required to perform the computation is of the order of $m$ carry-free addition operations, $m$ being the number of digits in the solution. In particular, the method is suitable for fast evaluation of mathematical functions in hardware.

keywords:
Arithmetic expressions; digital computer arithmetic; E-method; evaluation of real-valued functions; fixed-point representation; hardware-level implementation; integral powers; linear systems; on-line algorithms; parallel computation; polynomials; rational functions; redundant number systems

rawabstract:
A parallel computational method, amenable for efficient hardware-level implementation, is described. It provides a simple and fast algorithm for the evaluation of polynomials, certain rational functions and arithmetic expressions, solving a class of systems of linear equations, or performing the basic arithmetic operations in a fixed-point number representation system. The time required to perform the computation is of the order of $m$ carry-free addition operations, $m$ being the number of digits in the solution. In particular, the method is suitable for fast evaluation of mathematical functions in hardware.

rawtitle:
A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital Computer

entry:
@Article{Ercegovac:1977:GHO,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "A General Hardware-Oriented Method for Evaluation of
                 Functions and Computations in a Digital Computer",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "667--680",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:56 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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674900",
  abstract =     "A parallel computational method, amenable for
                 efficient hardware-level implementation, is described.
                 It provides a simple and fast algorithm for the
                 evaluation of polynomials, certain rational functions
                 and arithmetic expressions, solving a class of systems
                 of linear equations, or performing the basic arithmetic
                 operations in a fixed-point number representation
                 system. The time required to perform the computation is
                 of the order of $m$ carry-free addition operations, $m$
                 being the number of digits in the solution. In
                 particular, the method is suitable for fast evaluation
                 of mathematical functions in hardware.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arithmetic expressions; digital computer arithmetic;
                 E-method; evaluation of real-valued functions;
                 fixed-point representation; hardware-level
                 implementation; integral powers; linear systems;
                 on-line algorithms; parallel computation; polynomials;
                 rational functions; redundant number systems",
}


bibtype: techreport
filename: elefunt.bib
label: Fox:1977:PMS
author: P. A. Fox and A. D. Hall and N. L. Schryer
title: The PORT Mathematical Subroutine Library
type: Computing Science Technical Report
number: 47
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
pages: ii + 50
day: 22
month: mar
monthnumber: 3
year: 1977
bibdate: Fri Sep 01 09:08:27 2023
bibtimestamp: 2023.09.01 09:08:27 ???
URL: http://history.siam.org/%5C/sup/Fox_bell_subroutine.pdf
remark: May 1977 revision of version of September 1976.
acknowledgement: ack-nhfb
rawauthor: P. A. Fox and A. D. Hall and N. L. Schryer
rawtitle: The {PORT} Mathematical Subroutine Library
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/unix.bib

abstract:
The development at Bell Laboratories of PORT, a library of portable Fortran programs for numerical computation, is discussed.par Portability is achieved by careful language specification, together with the key technique of specifying computer classes by means of pre-defined machine constants.par The library is built around an automatic error-handling facility and a dynamic storage allocation scheme, both of which are implemented portably. These, together with the modular structure of the library, lead to simplified calling sequences and ease of use.

TOC:
Part 1: Description Part 2: Utility program listings: Machine constants Error handling Stack allocation

rawabstract:
The development at Bell Laboratories of PORT, a library of portable Fortran programs for numerical computation, is discussed.\par Portability is achieved by careful language specification, together with the key technique of specifying computer classes by means of pre-defined machine constants.\par The library is built around an automatic error-handling facility and a dynamic storage allocation scheme, both of which are implemented portably. These, together with the modular structure of the library, lead to simplified calling sequences and ease of use.

rawTOC:
Part 1: Description \\ Part 2: Utility program listings: \\ Machine constants \\ Error handling \\ Stack allocation

entry:
@TechReport{Fox:1977:PMS,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "The {PORT} Mathematical Subroutine Library",
  type =         "Computing Science Technical Report",
  number =       "47",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "ii + 50",
  day =          "22",
  month =        mar,
  year =         "1977",
  bibdate =      "Fri Sep 01 09:08:27 2023",
  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/unix.bib",
  URL =          "http://history.siam.org/%5C/sup/Fox_bell_subroutine.pdf",
  abstract =     "The development at Bell Laboratories of PORT, a
                 library of portable Fortran programs for numerical
                 computation, is discussed.\par

                 Portability is achieved by careful language
                 specification, together with the key technique of
                 specifying computer classes by means of pre-defined
                 machine constants.\par

                 The library is built around an automatic error-handling
                 facility and a dynamic storage allocation scheme, both
                 of which are implemented portably. These, together with
                 the modular structure of the library, lead to
                 simplified calling sequences and ease of use.",
  acknowledgement = ack-nhfb,
  remark =       "May 1977 revision of version of September 1976.",
  tableofcontents = "Part 1: Description \\
                 Part 2: Utility program listings: \\
                 Machine constants \\
                 Error handling \\
                 Stack allocation",
}


bibtype: inproceedings
filename: elefunt.bib
label: Fullerton:1977:PSF
author: L. W. Fullerton
title: Portable Special Function Routines
crossref: Cowell:1977:PMS
pages: 452--483
year: 1977
bibdate: Sat Oct 30 06:40:00 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 06:40:00 ???
acknowledgement: ack-nhfb
rawauthor: L. W. Fullerton
rawtitle: Portable Special Function Routines
entry:
@InProceedings{Fullerton:1977:PSF,
  author =       "L. W. Fullerton",
  title =        "Portable Special Function Routines",
  crossref =     "Cowell:1977:PMS",
  pages =        "452--483",
  year =         "1977",
  bibdate =      "Sat Oct 30 06:40:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1977:ACC
author: Walter Gautschi
title: Anomalous convergence of a continued fraction for ratios of Kummer functions
journal: j-MATH-COMPUT
volume: 31
number: 140
pages: 994--999
month: oct
monthnumber: 10
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C1120 (Mathematical analysis); C4170 (Differential equations)
corpsource: Dept. of Computer Sci., Purdue Univ., Lafayette, IN, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Walter Gautschi
rawtitle: Anomalous convergence of a continued fraction for ratios of {Kummer} functions
keywords:
apparent; Bessel functions; continued fraction; convergence; differential equations; gamma functions; Kummer functions; wrong limit

entry:
@Article{Gautschi:1977:ACC,
  author =       "Walter Gautschi",
  title =        "Anomalous convergence of a continued fraction for
                 ratios of {Kummer} functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "140",
  pages =        "994--999",
  month =        oct,
  year =         "1977",
  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 =   "C1120 (Mathematical analysis); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "apparent; Bessel functions; continued fraction;
                 convergence; differential equations; gamma functions;
                 Kummer functions; wrong limit",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1977:ERI
author: Walter Gautschi
title: Evaluation of Repeated Integrals of the Coerror Function
journal: j-TOMS
volume: 3
number: 3
pages: 240--252
month: sep
monthnumber: 9
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355744.355748
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 27 22:26:34 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.27 22:26:34 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
remark: Fullerton: An arbitrary-accuracy method for evaluating $ i^n erfc (x) $ is given.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Walter Gautschi
rawtitle: Evaluation of Repeated Integrals of the Coerror Function
entry:
@Article{Gautschi:1977:ERI,
  author =       "Walter Gautschi",
  title =        "Evaluation of Repeated Integrals of the Coerror
                 Function",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "240--252",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355748",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: An arbitrary-accuracy method for evaluating
                 $ i^n \erfc (x) $ is given.",
}


bibtype: article
filename: elefunt.bib
label: Harris:1977:CAT
author: F. E. Harris
journal: j-J-MATH-PHYS
volume: 18
number: 12
pages: 2377--2381
month: dec
monthnumber: 12
year: 1977
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Jan 2 14:59:17 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.01.02 14:59:17 MST
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
corpsource: Dept. of Chem., Univ. of Hawaii, Honolulu, HI, USA
journalURL: http://jmp.aip.org/
treatment: T Theoretical or Mathematical
rawauthor: F. E. Harris
title:
Convergence acceleration technique for lattice sums arising in electronic-structure studies of crystalline solids

keywords:
convergence acceleration; convergence of numerical methods; crystalline solids; electronic structure; Laplace transform; Laplace transforms; lattice energy; lattice sums; Poisson's summation formula

rawtitle:
Convergence acceleration technique for lattice sums arising in electronic-structure studies of crystalline solids

entry:
@Article{Harris:1977:CAT,
  author =       "F. E. Harris",
  title =        "Convergence acceleration technique for lattice sums
                 arising in electronic-structure studies of crystalline
                 solids",
  journal =      j-J-MATH-PHYS,
  volume =       "18",
  number =       "12",
  pages =        "2377--2381",
  month =        dec,
  year =         "1977",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Jan 2 14:59:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "A0260 (Numerical approximation and analysis); A6150L
                 (Crystal binding)",
  corpsource =   "Dept. of Chem., Univ. of Hawaii, Honolulu, HI, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "convergence acceleration; convergence of numerical
                 methods; crystalline solids; electronic structure;
                 Laplace transform; Laplace transforms; lattice energy;
                 lattice sums; Poisson's summation formula",
  pubcountry =   "USA",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: elefunt.bib
label: Henrici:1977:ACC
author: Peter Henrici
publisher: pub-WILEY
address: pub-WILEY:adr
pages: ix + 662
year: 1977
ISBN: 0-471-01525-3 OR 0471015253
ISBN13: 978-0-471-01525-3 OR 9780471015253
LCCN: QA331 .H453 1974
MRclass: 30-02 (33-02 44A10)
MRnumber: 0453984
MRreviewer: A. E. Heins
bibdate: Mon Jan 28 07:08:10 2019
bibtimestamp: 2019.01.28 07:08:10 ???
acknowledgement: ack-nhfb
authordates: Peter Karl Henrici (13 September 1923--13 March 1987)
rawauthor: Peter Henrici
title:
Applied and Computational Complex Analysis. Volume 2: Special Functions, Integral Transforms, Asymptotics, Continued Fractions

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

TOC:
8: Infinite Products / 1--74 9: Ordinary Differential Equations / 75--194 10: Integral Transforms / 195--350 11: Asymptotic Methods / 351--472 12: Continued Fractions / 473--641 Bibliography / 642--649 Appendix [Some additional problems for Volume 1] / 650--651 Index / 653--662

rawtitle:
Applied and Computational Complex Analysis. Volume 2: Special Functions, Integral Transforms, Asymptotics, Continued Fractions

rawTOC:
8: Infinite Products / 1--74 \\ 9: Ordinary Differential Equations / 75--194 \\ 10: Integral Transforms / 195--350 \\ 11: Asymptotic Methods / 351--472 \\ 12: Continued Fractions / 473--641 \\ Bibliography / 642--649 \\ Appendix [Some additional problems for Volume 1] / 650--651 \\ Index / 653--662

entry:
@Book{Henrici:1977:ACC,
  author =       "Peter Henrici",
  title =        "Applied and Computational Complex Analysis. Volume 2:
                 Special Functions, Integral Transforms, Asymptotics,
                 Continued Fractions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "ix + 662",
  year =         "1977",
  ISBN =         "0-471-01525-3",
  ISBN-13 =      "978-0-471-01525-3",
  LCCN =         "QA331 .H453 1974",
  MRclass =      "30-02 (33-02 44A10)",
  MRnumber =     "0453984",
  MRreviewer =   "A. E. Heins",
  bibdate =      "Mon Jan 28 07:08:10 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Peter Karl Henrici (13 September 1923--13 March
                 1987)",
  tableofcontents = "8: Infinite Products / 1--74 \\
                 9: Ordinary Differential Equations / 75--194 \\
                 10: Integral Transforms / 195--350 \\
                 11: Asymptotic Methods / 351--472 \\
                 12: Continued Fractions / 473--641 \\
                 Bibliography / 642--649 \\
                 Appendix [Some additional problems for Volume 1] /
                 650--651 \\
                 Index / 653--662",
}


bibtype: book
filename: elefunt.bib
label: Henrici:1977:ART
author: Peter Henrici
publisher: Oldenbourg
address: Munchen, West Germany
pages: 280
year: 1977
ISBN: 0-471-02938-6 OR 0471029386
ISBN13: 978-0-471-02938-0 OR 9780471029380
bibdate: Mon Jan 28 08:25:06 MST 2019
bibtimestamp: 2019.01.28 08:25:06 MST
language: German
subject: Numerische Mathematik; Programmierung <EDV>; Kleinrechner
acknowledgement: ack-nhfb
authordates: 1923--1987
rawauthor: Peter Henrici
title:
Analytische Rechenverfahren fur den Taschenrechner HP-25. (German) [Analytical Calculations for the HP-25 Calculator]

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

TOC:
Einleitung / 9 Teil I: Zahlentheorie / 13 Primfaktorzerlegung / 14 Euklidscher Algorithmus / 18 Rationale Binomialkoeffizienten / 22 Kettenbruchdarstellungen reeller Zahlen / 28 Genaue Kettenbruchdarstellungen von quadratischen Irrationalitaten / 33 Teil II: Iteration / 39 Iteration / 40 Iteration mit Aitken-Beschleunigung / 45 Aitken--Steffensen-Iteration / 50 Newton-Iteration fur Wurzeln komplexer Zahlen / 55 Teil III: Polynome / 61 Der Horner-Algorithmus 6 / 2 Das Newton-Verfahren bei Polynomen / 66 Bernoulli-Verfahren: Eine reelle dominante Nullstelle / 71 Bernoulli-Verfahren: Zwei konjugiert komplexe dominante Nullstellen / 76 Der Quotienten--Differenzen-Algorithmus / 82 Der Routh-Algorithmus / 87 Der Schur--Cohn-Algorithmus I / 92 Der Schur--Cohn-Algorithmus II / 97 Teil IV: Potenzreihen / 101 Reziproke Potenzreihe / 102 Potenz einer Potenzreihe / 111 Exponentiation einer Potenzreihe / 118 Teil V: Integration / 123 Numerische Integration mit Schrittverfeinerung / 124 Der Romberg-Algorithmus / 129 Die Planasche Summationsformel / 136 Eine Differentialgleichung erster Ordnung: Trapezregel / 143 Autonome Differentialgleichung zweiter Ordnung ohne erste Ableitung / 150 Lineare Differentialgleichung zweiter Ordnung / 155 Teil VI: Spezielle Konstanten und Funktionen / 161 Log-Arcsinus-Algorithmus / 162 Die Gamma-Funktion / 167 Unvollstandige Gamma-Funktion / 174 Die Fehlerfunktion / 181 Vollstandige elliptische Integrale / 187 Besselfunktionen ganzzahliger Ordnung / 191 Besselfunktionen beliebiger Ordnung / 196 Besselfunktionen: Asymptotische Reihe / 201 Die Riemannsche Zetafunktion auf der kritischen Geraden / 207 Stichwortverzeichnis / 213

rawtitle:
{Analytische Rechenverfahren f{\"u}r den Taschenrechner HP-25}. ({German}) [{Analytical} Calculations for the {HP-25} Calculator]

rawTOC:
Einleitung / 9 \\ Teil I: Zahlentheorie / 13 \\ Primfaktorzerlegung / 14 \\ Euklidscher Algorithmus / 18 \\ Rationale Binomialkoeffizienten / 22 \\ Kettenbruchdarstellungen reeller Zahlen / 28 \\ Genaue Kettenbruchdarstellungen von quadratischen Irrationalit{\"a}ten / 33 \\ Teil II: Iteration / 39 \\ Iteration / 40 \\ Iteration mit Aitken-Beschleunigung / 45 \\ Aitken--Steffensen-Iteration / 50 \\ Newton-Iteration f{\"u}r Wurzeln komplexer Zahlen / 55 \\ Teil III: Polynome / 61 \\ Der Horner-Algorithmus 6 / 2 \\ Das Newton-Verfahren bei Polynomen / 66 \\ Bernoulli-Verfahren: Eine reelle dominante Nullstelle / 71 \\ Bernoulli-Verfahren: Zwei konjugiert komplexe dominante Nullstellen / 76 \\ Der Quotienten--Differenzen-Algorithmus / 82 \\ Der Routh-Algorithmus / 87 \\ Der Schur--Cohn-Algorithmus I / 92 \\ Der Schur--Cohn-Algorithmus II / 97 \\ Teil IV: Potenzreihen / 101 \\ Reziproke Potenzreihe / 102 \\ Potenz einer Potenzreihe / 111 \\ Exponentiation einer Potenzreihe / 118 \\ Teil V: Integration / 123 \\ Numerische Integration mit Schrittverfeinerung / 124 \\ Der Romberg-Algorithmus / 129 \\ Die Planasche Summationsformel / 136 \\ Eine Differentialgleichung erster Ordnung: Trapezregel / 143 \\ Autonome Differentialgleichung zweiter Ordnung ohne erste Ableitung / 150 \\ Lineare Differentialgleichung zweiter Ordnung / 155 \\ Teil VI: Spezielle Konstanten und Funktionen / 161 \\ Log-Arcsinus-Algorithmus / 162 \\ Die Gamma-Funktion / 167 \\ Unvollst{\"a}ndige Gamma-Funktion / 174 \\ Die Fehlerfunktion / 181 \\ Vollst{\"a}ndige elliptische Integrale / 187 \\ Besselfunktionen ganzzahliger Ordnung / 191 \\ Besselfunktionen beliebiger Ordnung / 196 \\ Besselfunktionen: Asymptotische Reihe / 201 \\ Die Riemannsche Zetafunktion auf der kritischen Geraden / 207 \\ Stichwortverzeichnis / 213

entry:
@Book{Henrici:1977:ART,
  author =       "Peter Henrici",
  title =        "{Analytische Rechenverfahren f{\"u}r den
                 Taschenrechner HP-25}. ({German}) [{Analytical}
                 Calculations for the {HP-25} Calculator]",
  publisher =    "Oldenbourg",
  address =      "M{\"u}nchen, West Germany",
  pages =        "280",
  year =         "1977",
  ISBN =         "0-471-02938-6",
  ISBN-13 =      "978-0-471-02938-0",
  LCCN =         "????",
  bibdate =      "Mon Jan 28 08:25:06 MST 2019",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1923--1987",
  language =     "German",
  subject =      "Numerische Mathematik; Programmierung <EDV>;
                 Kleinrechner",
  tableofcontents = "Einleitung / 9 \\
                 Teil I: Zahlentheorie / 13 \\
                 Primfaktorzerlegung / 14 \\
                 Euklidscher Algorithmus / 18 \\
                 Rationale Binomialkoeffizienten / 22 \\
                 Kettenbruchdarstellungen reeller Zahlen / 28 \\
                 Genaue Kettenbruchdarstellungen von quadratischen
                 Irrationalit{\"a}ten / 33 \\
                 Teil II: Iteration / 39 \\
                 Iteration / 40 \\
                 Iteration mit Aitken-Beschleunigung / 45 \\
                 Aitken--Steffensen-Iteration / 50 \\
                 Newton-Iteration f{\"u}r Wurzeln komplexer Zahlen / 55
                 \\
                 Teil III: Polynome / 61 \\
                 Der Horner-Algorithmus 6 / 2 \\
                 Das Newton-Verfahren bei Polynomen / 66 \\
                 Bernoulli-Verfahren: Eine reelle dominante Nullstelle /
                 71 \\
                 Bernoulli-Verfahren: Zwei konjugiert komplexe dominante
                 Nullstellen / 76 \\
                 Der Quotienten--Differenzen-Algorithmus / 82 \\
                 Der Routh-Algorithmus / 87 \\
                 Der Schur--Cohn-Algorithmus I / 92 \\
                 Der Schur--Cohn-Algorithmus II / 97 \\
                 Teil IV: Potenzreihen / 101 \\
                 Reziproke Potenzreihe / 102 \\
                 Potenz einer Potenzreihe / 111 \\
                 Exponentiation einer Potenzreihe / 118 \\
                 Teil V: Integration / 123 \\
                 Numerische Integration mit Schrittverfeinerung / 124
                 \\
                 Der Romberg-Algorithmus / 129 \\
                 Die Planasche Summationsformel / 136 \\
                 Eine Differentialgleichung erster Ordnung: Trapezregel
                 / 143 \\
                 Autonome Differentialgleichung zweiter Ordnung ohne
                 erste Ableitung / 150 \\
                 Lineare Differentialgleichung zweiter Ordnung / 155 \\
                 Teil VI: Spezielle Konstanten und Funktionen / 161 \\
                 Log-Arcsinus-Algorithmus / 162 \\
                 Die Gamma-Funktion / 167 \\
                 Unvollst{\"a}ndige Gamma-Funktion / 174 \\
                 Die Fehlerfunktion / 181 \\
                 Vollst{\"a}ndige elliptische Integrale / 187 \\
                 Besselfunktionen ganzzahliger Ordnung / 191 \\
                 Besselfunktionen beliebiger Ordnung / 196 \\
                 Besselfunktionen: Asymptotische Reihe / 201 \\
                 Die Riemannsche Zetafunktion auf der kritischen Geraden
                 / 207 \\
                 Stichwortverzeichnis / 213",
}


bibtype: book
filename: elefunt.bib
label: Higgins:1977:CBP
author: John Rowland Higgins
title: Completeness and basis properties of sets of special functions
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: x + 134
year: 1977
bibdate: Sat Oct 30 16:52:55 MDT 2010
bibsource: carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 16:52:55 MDT
acknowledgement: ack-nhfb
rawauthor: John Rowland Higgins
rawtitle: Completeness and basis properties of sets of special functions
ISBN:
0-521-21376-2 (hardcover), 0-521-60488-5 (paperback) OR 0521213762 (hardcover), 0521604885 (paperback)

ISBN13:
978-0-521-21376-9 (hardcover), 978-0-521-60488-8 (paperback) OR 9780521213769 (hardcover), 9780521604888 (paperback)

entry:
@Book{Higgins:1977:CBP,
  author =       "John Rowland Higgins",
  title =        "Completeness and basis properties of sets of special
                 functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 134",
  year =         "1977",
  ISBN =         "0-521-21376-2 (hardcover), 0-521-60488-5 (paperback)",
  ISBN-13 =      "978-0-521-21376-9 (hardcover), 978-0-521-60488-8
                 (paperback)",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 16:52:55 MDT 2010",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Hill:1977:AIB
author: G. W. Hill
title: Algorithm 518: Incomplete Bessel Function $ I_0 $. The von Mises Distribution [S14]
journal: j-TOMS
volume: 3
number: 3
pages: 279--284
month: sep
monthnumber: 9
year: 1977
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355744.355753
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Oct 24 15:46:06 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.10.24 15:46:06 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
remark: Fullerton: Adjustable-accuracy 50-statement FORTRAN subprogram.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: G. W. Hill
rawtitle: {Algorithm 518}: Incomplete {Bessel} Function {$ I_0 $}. {The von Mises} Distribution [{S14}]
entry:
@Article{Hill:1977:AIB,
  author =       "G. W. Hill",
  title =        "{Algorithm 518}: Incomplete {Bessel} Function {$ I_0
                 $}. {The von Mises} Distribution [{S14}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "279--284",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355753",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 24 15:46:06 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: Adjustable-accuracy 50-statement FORTRAN
                 subprogram.",
}


bibtype: article
filename: elefunt.bib
label: Hinden:1977:PAR
author: Harvey J. Hinden
journal: j-FIB-QUART
volume: 15
number: 2
pages: 112, 152
month: apr
monthnumber: 4
year: 1977
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 17:59:17 MDT 2011
bibtimestamp: 2011.10.20 17:59:17 MDT
URL: http://www.fq.math.ca/Scanned/15-2/hinden-a.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Harvey J. Hinden
title:
Phi Again: a Relationship Between the Golden Ratio and the Limit of a Ratio of Modified Bessel Functions

bibsource:
http://www.fq.math.ca/15-2.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib

rawtitle:
Phi Again: a Relationship Between the Golden Ratio and the Limit of a Ratio of Modified {Bessel} Functions

entry:
@Article{Hinden:1977:PAR,
  author =       "Harvey J. Hinden",
  title =        "Phi Again: a Relationship Between the Golden Ratio and
                 the Limit of a Ratio of Modified {Bessel} Functions",
  journal =      j-FIB-QUART,
  volume =       "15",
  number =       "2",
  pages =        "112, 152",
  month =        apr,
  year =         "1977",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:17 MDT 2011",
  bibsource =    "http://www.fq.math.ca/15-2.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/15-2/hinden-a.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: elefunt.bib
label: Ismail:1977:IRC
author: Mourad E. H. Ismail
title: Integral representations and complete monotonicity of various quotients of Bessel functions
journal: j-CAN-J-MATH
volume: 29
pages: 1198--1207
year: 1977
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1977-119-5
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
bibdate: Sat Sep 10 15:38:50 MDT 2011
bibtimestamp: 2011.09.10 15:38:50 MDT
fjournal: Canadian Journal of Mathematics = Journal canadien de mathematiques
acknowledgement: ack-nhfb
journalURL: http://cms.math.ca/cjm/
rawauthor: Mourad E. H. Ismail
rawtitle: Integral representations and complete monotonicity of various quotients of {Bessel} functions
bibsource:
http://cms.math.ca/cjm/v29/; https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Ismail:1977:IRC,
  author =       "Mourad E. H. Ismail",
  title =        "Integral representations and complete monotonicity of
                 various quotients of {Bessel} functions",
  journal =      j-CAN-J-MATH,
  volume =       "29",
  number =       "??",
  pages =        "1198--1207",
  month =        "????",
  year =         "1977",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1977-119-5",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:38:50 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v29/;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
}


bibtype: article
filename: elefunt.bib
label: Jansen:1977:RLF
author: J. K. M. Jansen
title: Remark on ``Algorithm 259: Legendre Functions for Arguments Larger than One''
journal: j-TOMS
volume: 3
number: 2
pages: 204--250
month: jun
monthnumber: 6
year: 1977
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:08 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:08 ???
note: See cite Gautschi:1965:ALF.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: J. K. M. Jansen
rawnote: See \cite{Gautschi:1965:ALF}.
rawtitle: Remark on ``{Algorithm 259: Legendre Functions for Arguments Larger than One}''
entry:
@Article{Jansen:1977:RLF,
  author =       "J. K. M. Jansen",
  title =        "Remark on ``{Algorithm 259: Legendre Functions for
                 Arguments Larger than One}''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "204--250",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:08 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1965:ALF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: book
filename: elefunt.bib
label: Luke:1977:ACM
author: Yudell L. Luke
title: Algorithms for the Computation of Mathematical Functions
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xiii + 284
year: 1977
ISBN: 0-12-459940-0 OR 0124599400
ISBN13: 978-0-12-459940-6 OR 9780124599406
LCCN: QA351 .L7961
bibdate: Wed Dec 15 10:38:19 1993
bibtimestamp: 1993.12.15 10:38:19 ???
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawtitle: Algorithms for the Computation of Mathematical Functions
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/master.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib

TOC:
Preface / xi 1: Basic Formulas / 1 1.1 Introduction / 1 1.2 The Generalized Hypergeometric Function and the $G$-Function / 1 1.3 Expansion of $_pF_q(z)$ and $G^q - r, 1_p + 1, q(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev Polynomials of the First Kind / 4 1.4 Efficient Evaluation of Series of Chebyshev Polynomials / 17 1.5 Rational Approximations for Generalized Hypergeometric Functions / 20 1.6 The Pade Table / 27 1.7 Computations of and Checks on Coefficients and Tables / 29 1.8 Tables of the Functions $e^-zeta $, and $e^-xi $ / 35 2: Identification of Functions / 41 2.1 Introduction / 41 2.2 The Generalized Hypergeometric Function $_pF_q(z)$ / 41 2.3 The G-Function / 47 2.4 Miscellaneous Functions / 48 3: General Remarks on the Algorithms and Programs / 49 3.1 Introduction / 49 3.2 Precision and Complex Arithmetic / 49 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 5: Coefficients for the Expansion of the Confluent Hypergeometric Function $_1F_1(a;c;z)$ in Ascending Series of Chebyshev Polynomials / 70 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$ in Ascending Series of Chebyshev Polynomials / 82 8: Coefficients for the Expansion of the Confluent Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$ in Descending Series of Chebyshev Polynomials / 88 9: Coefficients for the Expansion of the Functions $G^m,1_1,3(z^2/4|^1_a,b,c)$, $m = 3$ or $m = 2$, in Descending Series of Chebyshev Polynomials / 101 10: Differential and Integral Properties of Expansions in Series of Chebyshev Polynomials of the First Kind / 116 11: Expansion of Exponential Type Integrals in Series of Chebyshev Polynomials of the First Kind / 126 11.1 Introduction / 126 11.2 The Representation for $g(x)$ / 127 11.3 The Representation for $G(x)$ / 129 11.4 Exponential Type Integrals Involving Logarithms / 133 11.5 Numerical Examples / 135 11.6 Errata / 139 12: Conversion of a Power Series into a Series of Chebyshev Polynomials of the First Kind / 154 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159 14: Pade Approximations for $_2F_1(1,b;c;-z)$ / 174 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182 16: Pade Approximations for $_1F_1(1;c;-z)$ / 192 17: Rational Approximations for Bessel Functions of the First Kind / 203 18: Pade Approximations for $I_nu + 1(z)/I_nu (z)$ / 220 19: Evaluation of Bessel Functions of the First Kind by Use of the Backward Recurrence Formula 19.1 Introduction / 230 19.2 Backward Recurrence Schemata for $I_nu (z)$ and $J_nu (z)$ / 230 19.3 Numerical Examples / 240 19.4 Mathematical Description of Programs / 243 19.4.1 Evaluation of Functions Related to $I_m + nu (z)$ and $J_m + nu (z)$ / 243 19.4.2 Evaluation of Functions Related to $e^-lI_m + nu (z)$ / 245 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ / 252 21: Pade Approximations for $z U(1;2-b;z)$ / 265 Appendices Bibliography / 280 Notation Index / 281 Subject Index / 283

rawTOC:
Preface / xi \\ 1: Basic Formulas / 1 \\ 1.1 Introduction / 1 \\ 1.2 The Generalized Hypergeometric Function and the $G$-Function / 1 \\ 1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1, q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev Polynomials of the First Kind / 4 \\ 1.4 Efficient Evaluation of Series of Chebyshev Polynomials / 17 \\ 1.5 Rational Approximations for Generalized Hypergeometric Functions / 20 \\ 1.6 The Pad{\'e} Table / 27 \\ 1.7 Computations of and Checks on Coefficients and Tables / 29 \\ 1.8 Tables of the Functions $e^{-\zeta}$, and $e^{-\xi}$ / 35 \\ 2: Identification of Functions / 41 \\ 2.1 Introduction / 41 \\ 2.2 The Generalized Hypergeometric Function $_pF_q(z)$ / 41 \\ 2.3 The G-Function / 47 \\ 2.4 Miscellaneous Functions / 48 \\ 3: General Remarks on the Algorithms and Programs / 49 \\ 3.1 Introduction / 49 \\ 3.2 Precision and Complex Arithmetic / 49 \\ 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\ 5: Coefficients for the Expansion of the Confluent Hypergeometric Function $_1F_1(a;c;z)$ in Ascending Series of Chebyshev Polynomials / 70 \\ 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\ 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$ in Ascending Series of Chebyshev Polynomials / 82 \\ 8: Coefficients for the Expansion of the Confluent Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$ in Descending Series of Chebyshev Polynomials / 88 \\ 9: Coefficients for the Expansion of the Functions $G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$, in Descending Series of Chebyshev Polynomials / 101 \\ 10: Differential and Integral Properties of Expansions in Series of Chebyshev Polynomials of the First Kind / 116 \\ 11: Expansion of Exponential Type Integrals in Series of Chebyshev Polynomials of the First Kind / 126 \\ 11.1 Introduction / 126 \\ 11.2 The Representation for $g(x)$ / 127 \\ 11.3 The Representation for $G(x)$ / 129 \\ 11.4 Exponential Type Integrals Involving Logarithms / 133 \\ 11.5 Numerical Examples / 135 \\ 11.6 Errata / 139 \\ 12: Conversion of a Power Series into a Series of Chebyshev Polynomials of the First Kind / 154 \\ 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159 \\ 14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174 \\ 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182 \\ 16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192 \\ 17: Rational Approximations for Bessel Functions of the First Kind / 203 \\ 18: Pad{\'e} Approximations for $I_{\nu + 1}(z)/I_\nu(z)$ / 220 \\ 19: Evaluation of Bessel Functions of the First Kind by Use of the Backward Recurrence Formula \\ 19.1 Introduction / 230 \\ 19.2 Backward Recurrence Schemata for $I_\nu(z)$ and $J_\nu(z)$ / 230 \\ 19.3 Numerical Examples / 240 \\ 19.4 Mathematical Description of Programs / 243 \\ 19.4.1 Evaluation of Functions Related to $I_{m + \nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\ 19.4.2 Evaluation of Functions Related to $e^{-l}I_{m + \nu}(z)$ / 245 \\ 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ / 252 \\ 21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265 \\ Appendices \\ Bibliography / 280 \\ Notation Index / 281 \\ Subject Index / 283

entry:
@Book{Luke:1977:ACM,
  author =       "Yudell L. Luke",
  title =        "Algorithms for the Computation of Mathematical
                 Functions",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiii + 284",
  year =         "1977",
  ISBN =         "0-12-459940-0",
  ISBN-13 =      "978-0-12-459940-6",
  LCCN =         "QA351 .L7961",
  bibdate =      "Wed Dec 15 10:38:19 1993",
  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/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / xi \\
                 1: Basic Formulas / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 The Generalized Hypergeometric Function and the
                 $G$-Function / 1 \\
                 1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1,
                 q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev
                 Polynomials of the First Kind / 4 \\
                 1.4 Efficient Evaluation of Series of Chebyshev
                 Polynomials / 17 \\
                 1.5 Rational Approximations for Generalized
                 Hypergeometric Functions / 20 \\
                 1.6 The Pad{\'e} Table / 27 \\
                 1.7 Computations of and Checks on Coefficients and
                 Tables / 29 \\
                 1.8 Tables of the Functions $e^{-\zeta}$, and
                 $e^{-\xi}$ / 35 \\
                 2: Identification of Functions / 41 \\
                 2.1 Introduction / 41 \\
                 2.2 The Generalized Hypergeometric Function $_pF_q(z)$
                 / 41 \\
                 2.3 The G-Function / 47 \\
                 2.4 Miscellaneous Functions / 48 \\
                 3: General Remarks on the Algorithms and Programs / 49
                 \\
                 3.1 Introduction / 49 \\
                 3.2 Precision and Complex Arithmetic / 49 \\
                 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\
                 5: Coefficients for the Expansion of the Confluent
                 Hypergeometric Function $_1F_1(a;c;z)$ in Ascending
                 Series of Chebyshev Polynomials / 70 \\
                 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\
                 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$
                 in Ascending Series of Chebyshev Polynomials / 82 \\
                 8: Coefficients for the Expansion of the Confluent
                 Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$
                 in Descending Series of Chebyshev Polynomials / 88 \\
                 9: Coefficients for the Expansion of the Functions
                 $G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$,
                 in Descending Series of Chebyshev Polynomials / 101 \\
                 10: Differential and Integral Properties of Expansions
                 in Series of Chebyshev Polynomials of the First Kind /
                 116 \\
                 11: Expansion of Exponential Type Integrals in Series
                 of Chebyshev Polynomials of the First Kind / 126 \\
                 11.1 Introduction / 126 \\
                 11.2 The Representation for $g(x)$ / 127 \\
                 11.3 The Representation for $G(x)$ / 129 \\
                 11.4 Exponential Type Integrals Involving Logarithms /
                 133 \\
                 11.5 Numerical Examples / 135 \\
                 11.6 Errata / 139 \\
                 12: Conversion of a Power Series into a Series of
                 Chebyshev Polynomials of the First Kind / 154 \\
                 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159
                 \\
                 14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174
                 \\
                 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182
                 \\
                 16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192
                 \\
                 17: Rational Approximations for Bessel Functions of the
                 First Kind / 203 \\
                 18: Pad{\'e} Approximations for $I_{\nu +
                 1}(z)/I_\nu(z)$ / 220 \\
                 19: Evaluation of Bessel Functions of the First Kind by
                 Use of the Backward Recurrence Formula \\
                 19.1 Introduction / 230 \\
                 19.2 Backward Recurrence Schemata for $I_\nu(z)$ and
                 $J_\nu(z)$ / 230 \\
                 19.3 Numerical Examples / 240 \\
                 19.4 Mathematical Description of Programs / 243 \\
                 19.4.1 Evaluation of Functions Related to $I_{m +
                 \nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\
                 19.4.2 Evaluation of Functions Related to $e^{-l}I_{m +
                 \nu}(z)$ / 245 \\
                 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ /
                 252 \\
                 21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265
                 \\
                 Appendices \\
                 Bibliography / 280 \\
                 Notation Index / 281 \\
                 Subject Index / 283",
  wrongisbn =    "0-12-459940-6",
}


bibtype: article
filename: elefunt.bib
label: Marsaglia:1977:SMG
author: George Marsaglia
title: The squeeze method for generating gamma variates
journal: j-COMPUT-MATH-APPL
volume: 3
number: 4
pages: 321--325
year: 1977
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(77)90089-X
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 65C10
MRnumber: 58 \#13613
bibdate: Mon Oct 24 11:37:20 2011
bibtimestamp: 2011.10.24 11:37:20 ???
fjournal: Computers and Mathematics with Applications
ZMnumber: 0384.65005
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
ZMclass: *65C10 Random number generation 60E05 General theory of probability distributions
rawauthor: George Marsaglia
rawtitle: The squeeze method for generating gamma variates
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database

abstract:
This paper describes an exact method for computer generation of random variables with a gamma distribution. The method is based on the Wilson--Hilferty transformation and an improvement on the rejection technique. The idea is to ``squeeze'' a target density between two functions, the top one easy to sample from, the bottom one easy to evaluate.

rawabstract:
This paper describes an exact method for computer generation of random variables with a gamma distribution. The method is based on the Wilson--Hilferty transformation and an improvement on the rejection technique. The idea is to ``squeeze'' a target density between two functions, the top one easy to sample from, the bottom one easy to evaluate.

entry:
@Article{Marsaglia:1977:SMG,
  author =       "George Marsaglia",
  title =        "The squeeze method for generating gamma variates",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "4",
  pages =        "321--325",
  year =         "1977",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(77)90089-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65C10",
  MRnumber =     "58 \#13613",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  ZMnumber =     "0384.65005",
  abstract =     "This paper describes an exact method for computer
                 generation of random variables with a gamma
                 distribution. The method is based on the
                 Wilson--Hilferty transformation and an improvement on
                 the rejection technique. The idea is to ``squeeze'' a
                 target density between two functions, the top one easy
                 to sample from, the bottom one easy to evaluate.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  ZMclass =      "*65C10 Random number generation 60E05 General theory
                 of probability distributions",
}


bibtype: article
filename: elefunt.bib
label: McCarthy:1977:OAE
author: D. P. McCarthy
title: The optimal algorithm to evaluate $ x^n $ using elementary multiplication methods
journal: j-MATH-COMPUT
volume: 31
number: 137
pages: 251--256
month: jan
monthnumber: 1
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4120 (Functional analysis); C4240 (Programming and algorithm theory)
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: D. P. McCarthy
rawtitle: The optimal algorithm to evaluate $ x^n $ using elementary multiplication methods
keywords:
computational complexity; function evaluation; optimal multiplication chains; symbolic algebraic manipulation

entry:
@Article{McCarthy:1977:OAE,
  author =       "D. P. McCarthy",
  title =        "The optimal algorithm to evaluate $ x^n $ using
                 elementary multiplication methods",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "137",
  pages =        "251--256",
  month =        jan,
  year =         "1977",
  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 =   "C4120 (Functional analysis); C4240 (Programming and
                 algorithm theory)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; function evaluation; optimal
                 multiplication chains; symbolic algebraic
                 manipulation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Ng:1977:CAL
author: E. W. Ng
title: Computations and Applications of Linear Hypergeometric Transformations
journal: j-COMPUT-MATH-APPL
volume: 3
number: 1
pages: 65--70
year: 1977
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(77)90115-8
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sat Oct 30 09:27:55 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 09:27:55 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: E. W. Ng
rawtitle: Computations and Applications of Linear Hypergeometric Transformations
abstract:
Linear transformations are well-known in the theory of hypergeometric functions. In this note, it is indicated, both by analyses and by supporting numerical experiments, how these transformations can be applied to the computation of Legendre's functions, the incomplete Beta function, and the variance-ratio probability distribution function. It is shown that a simple transformation can in many cases cause dramatic improvement in computation.

rawabstract:
Linear transformations are well-known in the theory of hypergeometric functions. In this note, it is indicated, both by analyses and by supporting numerical experiments, how these transformations can be applied to the computation of Legendre's functions, the incomplete Beta function, and the variance-ratio probability distribution function. It is shown that a simple transformation can in many cases cause dramatic improvement in computation.

entry:
@Article{Ng:1977:CAL,
  author =       "E. W. Ng",
  title =        "Computations and Applications of Linear Hypergeometric
                 Transformations",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "1",
  pages =        "65--70",
  year =         "1977",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(77)90115-8",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sat Oct 30 09:27:55 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Linear transformations are well-known in the theory of
                 hypergeometric functions. In this note, it is
                 indicated, both by analyses and by supporting numerical
                 experiments, how these transformations can be applied
                 to the computation of Legendre's functions, the
                 incomplete Beta function, and the variance-ratio
                 probability distribution function. It is shown that a
                 simple transformation can in many cases cause dramatic
                 improvement in computation.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Page:1977:MAC
author: E. Page
journal: j-APPL-STAT
volume: 26
number: 1
pages: 75--76
year: 1977
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
bibdate: Sat Apr 21 10:21:55 MDT 2001
bibtimestamp: 2001.04.21 10:21:55 MDT
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: E. Page
title:
Miscellanea: Approximations to the Cumulative Normal Function and its Inverse for Use on a Pocket Calculator

bibsource:
https://www.math.utah.edu/pub/tex/bib/as1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

rawtitle:
Miscellanea: Approximations to the Cumulative Normal Function and its Inverse for Use on a Pocket Calculator

entry:
@Article{Page:1977:MAC,
  author =       "E. Page",
  title =        "Miscellanea: Approximations to the Cumulative Normal
                 Function and its Inverse for Use on a Pocket
                 Calculator",
  journal =      j-APPL-STAT,
  volume =       "26",
  number =       "1",
  pages =        "75--76",
  year =         "1977",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:21:55 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",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: article
filename: elefunt.bib
label: Pexton:1977:RTTa
author: Robert L. Pexton and Arno D. Steiger
title: Roots of two transcendental equations involving spherical Bessel functions
journal: j-MATH-COMPUT
volume: 31
number: 139
pages: 752--753
month: jul
monthnumber: 7
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; root; spherical Bessel functions; transcendental equations
acknowledgement: ack-nhfb
classcodes: C1110 (Algebra)
corpsource: Univ. of California, Livermore, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Robert L. Pexton and Arno D. Steiger
rawtitle: Roots of two transcendental equations involving spherical {Bessel} functions
entry:
@Article{Pexton:1977:RTTa,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Roots of two transcendental equations involving
                 spherical {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "139",
  pages =        "752--753",
  month =        jul,
  year =         "1977",
  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 =   "C1110 (Algebra)",
  corpsource =   "Univ. of California, Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; root; spherical Bessel functions;
                 transcendental equations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Randazzo:1977:DFE
author: D. J. Randazzo
booktitle: Numerical analysis (Proceedings of the Colloquium, Lausanne, 1976)
title: Data fits with exponential functions
volume: 37
publisher: pub-BIRKHAUSER
address: pub-BIRKHAUSER:adr
pages: 77--94
year: 1977
ISBN: 3-7643-0939-3 OR 3764309393
ISBN13: 978-3-7643-0939-8 OR 9783764309398
MRclass: 65D15
MRnumber: 468111
MRreviewer: C. W. Clenshaw
bibdate: Mon Nov 13 08:14:42 2023
bibtimestamp: 2023.11.13 08:14:42 ???
series: Internat. Ser. Numer. Math.
acknowledgement: ack-nhfb
rawauthor: D. J. Randazzo
rawbooktitle: Numerical analysis ({Proceedings of the Colloquium, Lausanne, 1976})
rawtitle: Data fits with exponential functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Randazzo:1977:DFE,
  author =       "D. J. Randazzo",
  booktitle =    "Numerical analysis ({Proceedings of the Colloquium,
                 Lausanne, 1976})",
  title =        "Data fits with exponential functions",
  volume =       "37",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "77--94",
  year =         "1977",
  ISBN =         "3-7643-0939-3",
  ISBN-13 =      "978-3-7643-0939-8",
  MRclass =      "65D15",
  MRnumber =     "468111",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Mon Nov 13 08:14:42 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 =       "Internat. Ser. Numer. Math.",
  acknowledgement = ack-nhfb,
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
}


bibtype: article
filename: elefunt.bib
label: Schett:1977:RFT
author: Alois Schett
title: Recurrence formula of the Taylor series expansion coefficients of the Jacobian elliptic functions
journal: j-MATH-COMPUT
volume: 31
number: 140
pages: 1003--1005
month: oct
monthnumber: 10
year: 1977
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C1110 (Algebra)
corpsource: CENS, Gif-sur-Yvette, France
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Alois Schett
keywords:
elliptic functions; functions; Jacobian elliptic; peak; recurrence formula; run up; Taylor series expansion coefficients

rawtitle:
Recurrence formula of the {Taylor} series expansion coefficients of the {Jacobian} elliptic functions

entry:
@Article{Schett:1977:RFT,
  author =       "Alois Schett",
  title =        "Recurrence formula of the {Taylor} series expansion
                 coefficients of the {Jacobian} elliptic functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "140",
  pages =        "1003--1005",
  month =        oct,
  year =         "1977",
  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 =   "C1110 (Algebra)",
  corpsource =   "CENS, Gif-sur-Yvette, France",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "elliptic functions; functions; Jacobian elliptic;
                 peak; recurrence formula; run up; Taylor series
                 expansion coefficients",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Schindler:1977:CCS
author: Susan Schindler and R. Mirman
title: The Clebsch--Gordan coefficients of $ S_n $
journal: j-J-MATH-PHYS
volume: 18
number: 8
pages: 1697--1704
month: aug
monthnumber: 8
year: 1977
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.523470
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Jan 2 14:59:17 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.01.02 14:59:17 MST
fjournal: Journal of Mathematical Physics
keywords: $S_n$ group; Clebsch Gordan coefficients; Clebsch--Gordan coefficients; working triplets
acknowledgement: ack-nhfb
corpsource: Baruch Coll., City Univ. of New York, NY, USA
journalURL: http://jmp.aip.org/
treatment: T Theoretical or Mathematical
rawauthor: Susan Schindler and R. Mirman
rawtitle: The {Clebsch--Gordan} coefficients of {$ S_n $}
abstract:
Ordering schemes for the frames and tableaux of $ S_n $ are presented, and some results, expressible in terms of these, are developed. A formula is derived for the sign function on tableaux. A table of the nonzero Clebsch--Gordon coefficients for the ''working triplets'' is given. Methods are described, and a needed table supplied, for finding the other coefficients from the tabulated ones. The values are for $ n = 2, ldots , 6 $, with the coefficients for $ n = 6 $ relegated to PAPS.

rawabstract:
Ordering schemes for the frames and tableaux of $ S_n $ are presented, and some results, expressible in terms of these, are developed. A formula is derived for the sign function on tableaux. A table of the nonzero Clebsch--Gordon coefficients for the ''working triplets'' is given. Methods are described, and a needed table supplied, for finding the other coefficients from the tabulated ones. The values are for $ n = 2, \ldots {}, 6 $, with the coefficients for $ n = 6 $ relegated to PAPS.

entry:
@Article{Schindler:1977:CCS,
  author =       "Susan Schindler and R. Mirman",
  title =        "The {Clebsch--Gordan} coefficients of {$ S_n $}",
  journal =      j-J-MATH-PHYS,
  volume =       "18",
  number =       "8",
  pages =        "1697--1704",
  month =        aug,
  year =         "1977",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.523470",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Jan 2 14:59:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Ordering schemes for the frames and tableaux of $ S_n
                 $ are presented, and some results, expressible in terms
                 of these, are developed. A formula is derived for the
                 sign function on tableaux. A table of the nonzero
                 Clebsch--Gordon coefficients for the ''working
                 triplets'' is given. Methods are described, and a
                 needed table supplied, for finding the other
                 coefficients from the tabulated ones. The values are
                 for $ n = 2, \ldots {}, 6 $, with the coefficients for
                 $ n = 6 $ relegated to PAPS.",
  acknowledgement = ack-nhfb,
  classification = "A0365F (Algebraic methods in quantum theory); A1130L
                 (Other internal and higher symmetries in particle
                 physics)",
  corpsource =   "Baruch Coll., City Univ. of New York, NY, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "$S_n$ group; Clebsch Gordan coefficients;
                 Clebsch--Gordan coefficients; working triplets",
  pubcountry =   "USA",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schonfelder:1977:PTS
author: J. L. Schonfelder
title: The Production and Testing of Special Function Software in the NAG Library
crossref: Cowell:1977:PMS
pages: 425--451
year: 1977
bibdate: Sat Oct 30 10:24:29 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:24:29 ???
acknowledgement: ack-nhfb
rawauthor: J. L. Schonfelder
rawtitle: The Production and Testing of Special Function Software in the {NAG} Library
entry:
@InProceedings{Schonfelder:1977:PTS,
  author =       "J. L. Schonfelder",
  title =        "The Production and Testing of Special Function
                 Software in the {NAG} Library",
  crossref =     "Cowell:1977:PMS",
  pages =        "425--451",
  year =         "1977",
  bibdate =      "Sat Oct 30 10:24:29 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Sharma:1977:GMA
author: R. R. Sharma and Bahman Zohuri
title: A general method for an accurate evaluation of exponential integrals $ E_1 (x), x > 0 $
journal: j-J-COMPUT-PHYS
volume: 25
number: 2
pages: 199--204
month: oct
monthnumber: 10
year: 1977
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(77)90022-5
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:26 MST 2012
bibtimestamp: 2012.01.01 09:15:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999177900225
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. R. Sharma and Bahman Zohuri
rawtitle: A general method for an accurate evaluation of exponential integrals {$ E_1 (x), x > 0 $}
entry:
@Article{Sharma:1977:GMA,
  author =       "R. R. Sharma and Bahman Zohuri",
  title =        "A general method for an accurate evaluation of
                 exponential integrals {$ E_1 (x), x > 0 $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "25",
  number =       "2",
  pages =        "199--204",
  month =        oct,
  year =         "1977",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(77)90022-5",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:26 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/0021999177900225",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Verma:1977:CSF
author: Arun Verma
title: Certain summation formulae for basic hypergeometric series
journal: j-CAN-MATH-BULL
volume: 20
pages: 369--376
year: 1977
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-1977-055-8
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
bibdate: Thu Sep 8 10:04:41 MDT 2011
bibtimestamp: 2011.09.08 10:04:41 MDT
fjournal: Canadian mathematical bulletin = Bulletin canadien de mathematiques
acknowledgement: ack-nhfb
journalURL: http://cms.math.ca/cmb/
rawauthor: Arun Verma
rawtitle: Certain summation formulae for basic hypergeometric series
bibsource:
http://cms.math.ca/cmb/v20/; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Verma:1977:CSF,
  author =       "Arun Verma",
  title =        "Certain summation formulae for basic hypergeometric
                 series",
  journal =      j-CAN-MATH-BULL,
  volume =       "20",
  number =       "??",
  pages =        "369--376",
  month =        "????",
  year =         "1977",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1977-055-8",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  bibdate =      "Thu Sep 8 10:04:41 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v20/;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
}


bibtype: article
filename: elefunt.bib
label: Amos:1978:ECS
author: Donald E. Amos
journal: j-TOMS
volume: 4
number: 4
pages: 411--411
month: dec
monthnumber: 12
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/356502.356501
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Aug 30 00:28:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.30 00:28:02 ???
note: See cite Amos:1977:ACS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Donald E. Amos
rawnote: See \cite{Amos:1977:ACS}.
title:
Erratum: ``Algorithm 511: CDC 6600 Subroutines IBESS and JBESS for Bessel Functions $ I_nu (x) $ and $ J_nu (x) $, $ x ge 0, nu ge 0 $ [S18]''

rawtitle:
Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$ I_\nu (x) $} and {$ J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $} [{S18}]''

entry:
@Article{Amos:1978:ECS,
  author =       "Donald E. Amos",
  title =        "Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines
                 {IBESS} and {JBESS} for {Bessel} Functions {$ I_\nu (x)
                 $} and {$ J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $}
                 [{S18}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "411--411",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356501",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Amos:1977:ACS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Andrews:1978:EFM
author: M. Andrews and S. F. McCormick and G. D. Taylor
title: Evaluation of Functions on Microcomputers: Square Root
journal: j-COMPUT-MATH-APPL
volume: 4
number: 4
pages: 359--367
year: 1978
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Thu Sep 15 18:40:29 1994
bibtimestamp: 1994.09.15 18:40:29 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: M. Andrews and S. F. McCormick and G. D. Taylor
rawtitle: Evaluation of Functions on Microcomputers: Square Root
entry:
@Article{Andrews:1978:EFM,
  author =       "M. Andrews and S. F. McCormick and G. D. Taylor",
  title =        "Evaluation of Functions on Microcomputers: Square
                 Root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "4",
  number =       "4",
  pages =        "359--367",
  year =         "1978",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:40:29 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 =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}


bibtype: article
filename: elefunt.bib
label: Andrews:1978:UEF
author: M. Andrews and T. Mraz
title: Unified elementary function generator
journal: j-MICROPROC-MICROSYS
volume: 2
number: 5
pages: 270--273
month: oct
monthnumber: 10
year: 1978
CODEN: MIMID5
ISSN: 0141-9331 (print), 1872-9436 (electronic) OR 01419331 (print), 18729436 (electronic)
ISSNL: 0141-9331 OR 01419331
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
bibtimestamp: 1994.09.01 10:15:39 ???
fjournal: Microprocessors and Microsystems
acknowledgement: ack-nj
rawauthor: M. Andrews and T. Mraz
rawtitle: Unified elementary function generator
entry:
@Article{Andrews:1978:UEF,
  author =       "M. Andrews and T. Mraz",
  title =        "Unified elementary function generator",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "5",
  pages =        "270--273",
  month =        oct,
  year =         "1978",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  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,
  fjournal =     "Microprocessors and Microsystems",
}


bibtype: article
filename: elefunt.bib
label: Ardill:1978:SBF
author: R. W. B. Ardill and K. J. M. Moriarty
title: Spherical Bessel functions $ j_n $ and $ y_n $ of integer order and real argument
journal: j-COMP-PHYS-COMM
volume: 14
number: 3--4
pages: 261--265
month: may
monthnumber: 5
year: 1978
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(78)90019-X
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Apr 24 10:35:27 2008
bibtimestamp: 2008.04.24 10:35:27 ???
URL: http://www.sciencedirect.com/science/article/pii/001046557890019X
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: R. W. B. Ardill and K. J. M. Moriarty
rawtitle: Spherical {Bessel} functions $ j_n $ and $ y_n $ of integer order and real argument
entry:
@Article{Ardill:1978:SBF,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "Spherical {Bessel} functions $ j_n $ and $ y_n $ of
                 integer order and real argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "14",
  number =       "3--4",
  pages =        "261--265",
  month =        may # "\slash " # jun,
  year =         "1978",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(78)90019-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  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/001046557890019X",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Benton:1978:CZT
author: T. C. Benton and H. D. Knoble
title: Common Zeros of Two Bessel Functions
journal: j-MATH-COMPUT
volume: 32
number: 142
pages: 533--535
month: apr
monthnumber: 4
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; common zeros; poles and zeros; positive zeros; zeros
acknowledgement: ack-nhfb
classcodes: C1110 (Algebra)
corpsource: Pennsylvania State Univ., University Park, PA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: T. C. Benton and H. D. Knoble
rawtitle: Common Zeros of Two {Bessel} Functions
entry:
@Article{Benton:1978:CZT,
  author =       "T. C. Benton and H. D. Knoble",
  title =        "Common Zeros of Two {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "142",
  pages =        "533--535",
  month =        apr,
  year =         "1978",
  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 =   "C1110 (Algebra)",
  corpsource =   "Pennsylvania State Univ., University Park, PA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; common zeros; poles and zeros;
                 positive zeros; zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Blair:1978:RCA
author: J. M. Blair and C. A. Edwards and J. H. Johnson
title: Rational Chebyshev approximations for the Bickley functions $ K i_n(x) $
journal: j-MATH-COMPUT
volume: 32
number: 143
pages: 876--886
month: jul
monthnumber: 7
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Atomic Energy of Canada Ltd., Chalk River, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. M. Blair and C. A. Edwards and J. H. Johnson
rawtitle: Rational {Chebyshev} approximations for the {Bickley} functions {$ K i_n(x) $}
keywords:
approximation; Bessel functions; Bickley functions; Chebyshev approximation; Chebyshev approximations; function; recurrence; relation

remark:
Fullerton: Approximations accurate to 23 digits of repeated integrals of the Bessel function $ K_0 (x) $ for $ n = 1, 2, ldots , 10 $.

entry:
@Article{Blair:1978:RCA,
  author =       "J. M. Blair and C. A. Edwards and J. H. Johnson",
  title =        "Rational {Chebyshev} approximations for the {Bickley}
                 functions {$ K i_n(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "143",
  pages =        "876--886",
  month =        jul,
  year =         "1978",
  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 =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy of Canada Ltd., Chalk River, Ont.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximation; Bessel functions; Bickley functions;
                 Chebyshev approximation; Chebyshev approximations;
                 function; recurrence; relation",
  remark =       "Fullerton: Approximations accurate to 23 digits of
                 repeated integrals of the Bessel function $ K_0 (x) $
                 for $ n = 1, 2, \ldots {}, 10 $.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Bowman:1978:ASS
author: K. O. Bowman and L. R. Shenton
title: Asymptotic series and Stieltjes continued fractions for a gamma function ratio
journal: j-J-COMPUT-APPL-MATH
volume: 4
number: 2
pages: 105--111
month: jun
monthnumber: 6
year: 1978
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:17 MST 2017
bibtimestamp: 2017.02.25 11:59:17 MST
URL: http://www.sciencedirect.com/science/article/pii/0771050X78900347
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: K. O. Bowman and L. R. Shenton
rawtitle: Asymptotic series and {Stieltjes} continued fractions for a gamma function ratio
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib

entry:
@Article{Bowman:1978:ASS,
  author =       "K. O. Bowman and L. R. Shenton",
  title =        "Asymptotic series and {Stieltjes} continued fractions
                 for a gamma function ratio",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "4",
  number =       "2",
  pages =        "105--111",
  month =        jun,
  year =         "1978",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:17 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X78900347",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Brezinski:1978:AAC
author: Claude Brezinski
publisher: Editions Technip
address: Paris, France
pages: xi + 392
year: 1978
ISBN: 2-7108-0341-0 (paperback) OR 2710803410 (paperback)
ISBN13: 978-2-7108-0341-6 (paperback) OR 9782710803416 (paperback)
bibdate: Thu Dec 1 10:20:23 MST 2011
bibsource: carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:20:23 MST
keywords: convergence acceleration
language: French
acknowledgement: ack-nhfb
rawauthor: Claude Brezinski
title:
Algorithmes d'acceleration de la convergence: etude numerique. (French) [Algorithms for convergence acceleration: numerical study]

rawtitle:
Algorithmes d'acc{\'e}l{\'e}ration de la convergence: {\'e}tude num{\'e}rique. ({French}) [Algorithms for convergence acceleration: numerical study]

entry:
@Book{Brezinski:1978:AAC,
  author =       "Claude Brezinski",
  title =        "Algorithmes d'acc{\'e}l{\'e}ration de la convergence:
                 {\'e}tude num{\'e}rique. ({French}) [Algorithms for
                 convergence acceleration: numerical study]",
  publisher =    "{\'E}ditions Technip",
  address =      "Paris, France",
  pages =        "xi + 392",
  year =         "1978",
  ISBN =         "2-7108-0341-0 (paperback)",
  ISBN-13 =      "978-2-7108-0341-6 (paperback)",
  LCCN =         "????",
  bibdate =      "Thu Dec 1 10:20:23 MST 2011",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
  language =     "French",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:1978:CAS
author: C. Brezinski
title: Convergence acceleration of some sequences by the $ epsilon $-algorithm
journal: j-NUM-MATH
volume: 29
number: 2
pages: 173--177
month: jan
monthnumber: 1
year: 1978
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon May 26 11:49:34 MDT 1997
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: UER d'IEEA-Informatique, Univ. de Lille I, Villeneuve d'Ascq, France
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: C. Brezinski
rawtitle: Convergence acceleration of some sequences by the $ \epsilon $-algorithm
keywords:
acceleration; converge; convergence acceleration; convergence of numerical methods; epsilon-algorithm; sequences

entry:
@Article{Brezinski:1978:CAS,
  author =       "C. Brezinski",
  title =        "Convergence acceleration of some sequences by the $
                 \epsilon $-algorithm",
  journal =      j-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "173--177",
  month =        jan,
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra)",
  corpsource =   "UER d'IEEA-Informatique, Univ. de Lille I, Villeneuve
                 d'Ascq, France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "acceleration; converge; convergence acceleration;
                 convergence of numerical methods; epsilon-algorithm;
                 sequences",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:1978:SCA
author: C. Brezinski
title: Survey on convergence acceleration methods in numerical analysis
journal: j-MATH-STUDENT
volume: 46
number: 1
pages: 28--41 (1979)
year: 1978
CODEN: MTHSBH
ISSN: 0025-5742 OR 00255742
MRclass: 65B99
MRnumber: 698176 (84d:65003)
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: The Mathematics Student
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: C. Brezinski
rawtitle: Survey on convergence acceleration methods in numerical analysis
entry:
@Article{Brezinski:1978:SCA,
  author =       "C. Brezinski",
  title =        "Survey on convergence acceleration methods in
                 numerical analysis",
  journal =      j-MATH-STUDENT,
  volume =       "46",
  number =       "1",
  pages =        "28--41 (1979)",
  year =         "1978",
  CODEN =        "MTHSBH",
  ISSN =         "0025-5742",
  MRclass =      "65B99",
  MRnumber =     "698176 (84d:65003)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Student",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Chin:1978:DAD
author: R. C. Y. Chin and G. W. Hedstrom
title: A dispersion analysis for difference schemes: tables of generalized Airy functions
journal: j-MATH-COMPUT
volume: 32
number: 144
pages: 1163--1170
month: oct
monthnumber: 10
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation); C4170 (Differential equations)
corpsource: Univ. of California, Lawrence Livermore Lab., Livermore, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: R. C. Y. Chin and G. W. Hedstrom
rawtitle: A dispersion analysis for difference schemes: tables of generalized {Airy} functions
keywords:
artificial viscosity; difference schemes; dispersion analysis; function approximation; functions; generalized Airy; linear hyperbolic equation

entry:
@Article{Chin:1978:DAD,
  author =       "R. C. Y. Chin and G. W. Hedstrom",
  title =        "A dispersion analysis for difference schemes: tables
                 of generalized {Airy} functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "144",
  pages =        "1163--1170",
  month =        oct,
  year =         "1978",
  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);
                 C4170 (Differential equations)",
  corpsource =   "Univ. of California, Lawrence Livermore Lab.,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "artificial viscosity; difference schemes; dispersion
                 analysis; function approximation; functions;
                 generalized Airy; linear hyperbolic equation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Coleman:1978:RSN
author: John P. Coleman
title: Remark on ``Algorithm 49: Spherical Neumann Function''
journal: j-TOMS
volume: 4
number: 3
pages: 295--295
month: sep
monthnumber: 9
year: 1978
CODEN: ACMSCU
ISSN: 0098-3500 OR 00983500
bibdate: Sat Jul 05 16:48:40 1997
bibtimestamp: 1997.07.05 16:48:40 ???
note: See cite Herndon:1961:ASN.
keywords: Neumann functions; special functions
acknowledgement: ack-nhfb
rawauthor: John P. Coleman
rawnote: See \cite{Herndon:1961:ASN}.
rawtitle: Remark on {``Algorithm 49: Spherical Neumann Function''}
entry:
@Article{Coleman:1978:RSN,
  author =       "John P. Coleman",
  title =        "Remark on {``Algorithm 49: Spherical Neumann
                 Function''}",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "295--295",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Sat Jul 05 16:48:40 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Herndon:1961:ASN}.",
  acknowledgement = ack-nhfb,
  keywords =     "Neumann functions; special functions",
}


bibtype: article
filename: elefunt.bib
label: DiDonato:1978:AR
author: A. R. DiDonato
title: An Approximation for $ int ^infty _x e^-t^2 / 2 t^p d t, x > 0, p $ Real
journal: j-MATH-COMPUT
volume: 32
number: 141
pages: 271--275
month: jan
monthnumber: 1
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: integral approximation; integration; numerical analysis
remark: Fullerton: Closely related to the complementary incomplete gamma function.
acknowledgement: ack-nhfb
classcodes: C4160 (Numerical integration and differentiation)
corpsource: Naval Surface Weapons Center, Dahlgren, VA, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; N New Development; T Theoretical or Mathematical
rawauthor: A. R. DiDonato
rawtitle: An Approximation for $ \int^\infty_x e^{-t^2 / 2} t^p d t, x > 0, p $ Real
entry:
@Article{DiDonato:1978:AR,
  author =       "A. R. DiDonato",
  title =        "An Approximation for $ \int^\infty_x e^{-t^2 / 2} t^p
                 d t, x > 0, p $ Real",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "271--275",
  month =        jan,
  year =         "1978",
  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 =   "Naval Surface Weapons Center, Dahlgren, VA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "integral approximation; integration; numerical
                 analysis",
  remark =       "Fullerton: Closely related to the complementary
                 incomplete gamma function.",
  treatment =    "A Application; N New Development; T Theoretical or
                 Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Drezner:1978:CBN
author: Z. Drezner
title: Computation of the Bivariate Normal Integral
journal: j-MATH-COMPUT
volume: 32
number: 141
pages: 277--279
month: jan
monthnumber: 1
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: bivariate normal integral; computation; Gauss quadrature method; integration; numerical analysis
acknowledgement: ack-nhfb
corpsource: Faculty of Business, McMaster Univ., Hamilton, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Z. Drezner
rawtitle: Computation of the Bivariate Normal Integral
classcodes:
B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)

entry:
@Article{Drezner:1978:CBN,
  author =       "Z. Drezner",
  title =        "Computation of the Bivariate Normal Integral",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "277--279",
  month =        jan,
  year =         "1978",
  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 =   "Faculty of Business, McMaster Univ., Hamilton, Ont.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "bivariate normal integral; computation; Gauss
                 quadrature method; integration; numerical analysis",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Dzjadyk:1978:CRP
author: V. K. Dzjadyk and L. I. Filozof
title: The convergence rate of Pade approximants for some elementary functions. (Russian)
journal: Mat. Sb. (N.S.)
volume: 107(149)
number: 3
pages: 347--363, 463
year: 1978
ISSN: 0368-8666 OR 03688666
MRclass: 41A21 (30E10 41A25)
MRnumber: 81b:41043
MRreviewer: B. D. Donevski
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: V. K. Dzjadyk and L. {\=I}. F{\'\i}lozof
rawtitle: The convergence rate of {Pad{\'e}} approximants for some elementary functions. ({Russian})
entry:
@Article{Dzjadyk:1978:CRP,
  author =       "V. K. Dzjadyk and L. {\=I}. F{\'\i}lozof",
  title =        "The convergence rate of {Pad{\'e}} approximants for
                 some elementary functions. ({Russian})",
  journal =      "Mat. Sb. (N.S.)",
  volume =       "107(149)",
  number =       "3",
  pages =        "347--363, 463",
  year =         "1978",
  ISSN =         "0368-8666",
  MRclass =      "41A21 (30E10 41A25)",
  MRnumber =     "81b:41043",
  MRreviewer =   "B. D. Donevski",
  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",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ercegovac:1978:LSR
author: Milos D. Ercegovac
title: An On-Line Square Rooting Algorithm
crossref: IEEE:1978:PSC
pages: 183--189
year: 1978
bibdate: Thu Nov 15 10:49:40 2007
bibtimestamp: 2007.11.15 10:49:40 ???
URL: http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf
keywords: ARITH-4
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac
rawtitle: An On-Line Square Rooting Algorithm
abstract:
An on-line algorithm for computing square roots in a radix 2, normalized floating-point number system with the redundant digit set $ - 1, 0, 1 $ is described. The algorithm has on-line delay of one and it is amenable for modular implementation. A systematic approach, used in deriving this algorithm, is presented in detail.

rawabstract:
An on-line algorithm for computing square roots in a radix 2, normalized floating-point number system with the redundant digit set $ \{ - 1, 0, 1 \} $ is described. The algorithm has on-line delay of one and it is amenable for modular implementation. A systematic approach, used in deriving this algorithm, is presented in detail.

entry:
@InProceedings{Ercegovac:1978:LSR,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "An On-Line Square Rooting Algorithm",
  crossref =     "IEEE:1978:PSC",
  pages =        "183--189",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
  abstract =     "An on-line algorithm for computing square roots in a
                 radix 2, normalized floating-point number system with
                 the redundant digit set $ \{ - 1, 0, 1 \} $ is
                 described. The algorithm has on-line delay of one and
                 it is amenable for modular implementation. A systematic
                 approach, used in deriving this algorithm, is presented
                 in detail.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}


bibtype: book
filename: elefunt.bib
label: Feinsilver:1978:SFP
author: Philip J. (Philip Joel) Feinsilver
title: Special functions, probability semigroups, and Hamiltonian flows
volume: 696
publisher: pub-SV
address: pub-SV:adr
pages: vi + 112
year: 1978
ISBN: 0-387-09100-9 OR 0387091009
ISBN13: 978-0-387-09100-6 OR 9780387091006
LCCN: QA3 .L28 no. 696; QA273
bibdate: Sat Oct 30 19:22:05 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 19:22:05 MDT
series: Lecture notes in mathematics
subject: probabilities; semigroups; functions, special; Hamiltonian systems
acknowledgement: ack-nhfb
rawauthor: Philip J. (Philip Joel) Feinsilver
rawtitle: Special functions, probability semigroups, and {Hamiltonian} flows
entry:
@Book{Feinsilver:1978:SFP,
  author =       "Philip J. (Philip Joel) Feinsilver",
  title =        "Special functions, probability semigroups, and
                 {Hamiltonian} flows",
  volume =       "696",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vi + 112",
  year =         "1978",
  ISBN =         "0-387-09100-9",
  ISBN-13 =      "978-0-387-09100-6",
  LCCN =         "QA3 .L28 no. 696; QA273",
  bibdate =      "Sat Oct 30 19:22:05 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Lecture notes in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "probabilities; semigroups; functions, special;
                 Hamiltonian systems",
}


bibtype: inproceedings
filename: elefunt.bib
label: Frankowski:1978:RME
author: Krzysztof S. Frankowski
title: A Realistic Model for Error Estimates in the Evaluation of Elementary Functions
crossref: IEEE:1978:PSC
pages: 70--74
year: 1978
MRclass: 65G05 (65D20)
MRnumber: 80g:65050
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
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Krzysztof S. Frankowski
rawtitle: A Realistic Model for Error Estimates in the Evaluation of Elementary Functions
entry:
@InProceedings{Frankowski:1978:RME,
  author =       "Krzysztof S. Frankowski",
  title =        "A Realistic Model for Error Estimates in the
                 Evaluation of Elementary Functions",
  crossref =     "IEEE:1978:PSC",
  pages =        "70--74",
  year =         "1978",
  MRclass =      "65G05 (65D20)",
  MRnumber =     "80g:65050",
  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",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1978:CMB
author: Walter Gautschi and Josef Slavik
title: On the computation of modified Bessel function ratios
journal: j-MATH-COMPUT
volume: 32
number: 143
pages: 865--875
month: jul
monthnumber: 7
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C1120 (Mathematical analysis); C4130 (Interpolation and function approximation)
corpsource: Dept. of Computer Sci., Purdue Univ., Lafayette, IN, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Walter Gautschi and Josef Slavik
rawtitle: On the computation of modified {Bessel} function ratios
keywords:
Bessel; Bessel functions; continued fraction; fraction; function approximation; functions; Gauss' continued; modified Bessel function ratios; Perron's continued fraction

entry:
@Article{Gautschi:1978:CMB,
  author =       "Walter Gautschi and Josef Slavik",
  title =        "On the computation of modified {Bessel} function
                 ratios",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "143",
  pages =        "865--875",
  month =        jul,
  year =         "1978",
  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 =   "C1120 (Mathematical analysis); C4130 (Interpolation
                 and function approximation)",
  corpsource =   "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel; Bessel functions; continued fraction;
                 fraction; function approximation; functions; Gauss'
                 continued; modified Bessel function ratios; Perron's
                 continued fraction",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Gustafson:1978:ATC
author: S.-AA . Gustafson
title: Algorithm $ 38 $. Two computer codes for convergence acceleration
journal: j-COMPUTING
volume: 21
number: 1
pages: 87--91
year: 1978
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65B10
MRnumber: 83a:65005
bibdate: Tue Jan 2 17:40:53 MST 2001
bibtimestamp: 2001.01.02 17:40:53 MST
fjournal: Computing
keywords: codes, symbolic; convergence acceleration; power series sum
acknowledgement: ack-nhfb
affiliation: Australian Nat. Univ., Canberra, ACT, Australia
journalURL: http://link.springer.com/journal/607
journalabr: Computing (Vienna/New York)
rawauthor: S.-{\AA}. Gustafson
rawtitle: Algorithm $ 38 $. {Two} computer codes for convergence acceleration
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); MathSciNet database

entry:
@Article{Gustafson:1978:ATC,
  author =       "S.-{\AA}. Gustafson",
  title =        "Algorithm $ 38 $. {Two} computer codes for convergence
                 acceleration",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "1",
  pages =        "87--91",
  year =         "1978",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65B10",
  MRnumber =     "83a:65005",
  bibdate =      "Tue Jan 2 17:40:53 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); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "Australian Nat. Univ., Canberra, ACT, Australia",
  classification = "723; C4140",
  description =  "convergence of numerical methods",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "codes, symbolic; convergence acceleration; power
                 series sum",
}


bibtype: article
filename: elefunt.bib
label: Gustafson:1978:CAG
author: S.-AA . Gustafson
title: Convergence acceleration on a general class of power series
journal: j-COMPUTING
volume: 21
number: 1
pages: 53--69
year: 1978
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65B10 (40A05)
MRnumber: 83m:65005
MRreviewer: A. M. Cohen
bibdate: Tue Jan 2 17:40:53 MST 2001
bibtimestamp: 2001.01.02 17:40:53 MST
fjournal: Computing
keywords: algorithms; convergence acceleration; power series
acknowledgement: ack-nhfb
affiliation: Australian Nat. Univ., Canberra, ACT, Australia
journalURL: http://link.springer.com/journal/607
rawauthor: S.-{\AA}. Gustafson
rawtitle: Convergence acceleration on a general class of power series
bibsource:
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); MathSciNet database

entry:
@Article{Gustafson:1978:CAG,
  author =       "S.-{\AA}. Gustafson",
  title =        "Convergence acceleration on a general class of power
                 series",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "1",
  pages =        "53--69",
  year =         "1978",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65B10 (40A05)",
  MRnumber =     "83m:65005",
  MRreviewer =   "A. M. Cohen",
  bibdate =      "Tue Jan 2 17:40:53 MST 2001",
  bibsource =    "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); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "Australian Nat. Univ., Canberra, ACT, Australia",
  classification = "C4120",
  description =  "convergence of numerical methods; function
                 evaluation",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "algorithms; convergence acceleration; power series",
}


bibtype: article
filename: elefunt.bib
label: Hamaker:1978:MAC
author: Hugo C. Hamaker
title: Miscellanea: Approximating the Cumulative Normal Distribution and its Inverse
journal: j-APPL-STAT
volume: 27
number: 1
pages: 76--77
month: jan
monthnumber: 1
year: 1978
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
bibdate: Sat Apr 21 10:22:12 MDT 2001
bibtimestamp: 2001.04.21 10:22:12 MDT
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: Hugo C. Hamaker
rawtitle: Miscellanea: Approximating the Cumulative Normal Distribution and its Inverse
bibsource:
https://www.math.utah.edu/pub/tex/bib/as1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

entry:
@Article{Hamaker:1978:MAC,
  author =       "Hugo C. Hamaker",
  title =        "Miscellanea: Approximating the Cumulative Normal
                 Distribution and its Inverse",
  journal =      j-APPL-STAT,
  volume =       "27",
  number =       "1",
  pages =        "76--77",
  month =        jan,
  year =         "1978",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:22:12 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",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hull:1978:DFP
author: T. E. Hull
title: Desirable Floating-Point Arithmetic and Elementary Functions for Numerical Computation
crossref: IEEE:1978:PSC
pages: 63--69
year: 1978
bibdate: Thu Sep 01 12:14:34 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 12:14:34 ???
acknowledgement: ack-nj
rawauthor: T. E. Hull
rawtitle: Desirable Floating-Point Arithmetic and Elementary Functions for Numerical Computation
entry:
@InProceedings{Hull:1978:DFP,
  author =       "T. E. Hull",
  title =        "Desirable Floating-Point Arithmetic and Elementary
                 Functions for Numerical Computation",
  crossref =     "IEEE:1978:PSC",
  pages =        "63--69",
  year =         "1978",
  bibdate =      "Thu Sep 01 12:14:34 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Katholi:1978:CVP
author: Charles R. Katholi
title: On the computation of values of the psi function from rapidly converging power series expansions
journal: j-J-STAT-COMPUT-SIMUL
volume: 8
number: 1
pages: 25--42
year: 1978
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949657808810245
ISSNL: 0094-9655 OR 00949655
bibdate: Tue Apr 22 09:10:43 MDT 2014
bibtimestamp: 2014.04.22 09:10:43 MDT
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
rawauthor: Charles R. Katholi
rawtitle: On the computation of values of the psi function from rapidly converging power series expansions
ISSN:
0094-9655 (print), 1026-7778 (electronic), 1563-5163 OR 00949655 (print), 10267778 (electronic), 15635163

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib

entry:
@Article{Katholi:1978:CVP,
  author =       "Charles R. Katholi",
  title =        "On the computation of values of the psi function from
                 rapidly converging power series expansions",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "8",
  number =       "1",
  pages =        "25--42",
  year =         "1978",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657808810245",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:10:43 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",
}


bibtype: article
filename: elefunt.bib
label: Kobayashi:1978:FPA
author: Yasuhiro Kobayashi and Masaaki Ohkita and Michio Inoue
title: Fractional power approximations of elliptic integrals and Bessel functions
journal: j-MATH-COMPUT-SIMUL
volume: 20
number: 4
pages: 285--290
month: dec
monthnumber: 12
year: 1978
CODEN: MCSIDR
DOI: https://doi.org/10.1016/0378-4754(78)90020-4
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Fri Aug 15 13:24:17 MDT 2025
bibtimestamp: 2025.08.15 13:24:17 MDT
URL: https://www.sciencedirect.com/science/article/pii/0378475478900204
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: Yasuhiro Kobayashi and Masaaki Ohkita and Michio Inoue
rawtitle: Fractional power approximations of elliptic integrals and {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1970.bib

entry:
@Article{Kobayashi:1978:FPA,
  author =       "Yasuhiro Kobayashi and Masaaki Ohkita and Michio
                 Inoue",
  title =        "Fractional power approximations of elliptic integrals
                 and {Bessel} functions",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "20",
  number =       "4",
  pages =        "285--290",
  month =        dec,
  year =         "1978",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(78)90020-4",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Aug 15 13:24:17 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1970.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0378475478900204",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: article
filename: elefunt.bib
label: Ling:1978:EWZ
author: Chin-Bing Ling
title: Evaluation of Weierstrass Zeta Functions
journal: j-SIAM-REVIEW
volume: 20
number: 1
pages: 183--183
year: 1978
CODEN: SIREAD
DOI: https://doi.org/10.1137/1020017
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Sat Mar 29 09:52:48 MDT 2014
bibtimestamp: 2014.03.29 09:52:48 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1978
rawauthor: Chin-Bing Ling
rawtitle: Evaluation of {Weierstrass} Zeta Functions
bibsource:
http://epubs.siam.org/toc/siread/20/1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Ling:1978:EWZ,
  author =       "Chin-Bing Ling",
  title =        "Evaluation of {Weierstrass} Zeta Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "20",
  number =       "1",
  pages =        "183--183",
  month =        "????",
  year =         "1978",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1020017",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:52:48 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/20/1;
                 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 1978",
}


bibtype: article
filename: elefunt.bib
label: Morita:1978:CCE
author: T. Morita
title: Calculation of the complete elliptic integrals with complex modulus
journal: j-NUM-MATH
volume: 29
number: 2
pages: 233--236
month: jan
monthnumber: 1
year: 1978
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
keywords: complete elliptic integrals; complex modulus; integration
remark: Fullerton: Addendum to a paper by Morita and Horiguchi.
acknowledgement: ack-nhfb
corpsource: Dept. of Appl. Sci., Faculty of Engng., Tohoku Univ., Sendai, Japan
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: T. Morita
rawtitle: Calculation of the complete elliptic integrals with complex modulus
entry:
@Article{Morita:1978:CCE,
  author =       "T. Morita",
  title =        "Calculation of the complete elliptic integrals with
                 complex modulus",
  journal =      j-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "233--236",
  month =        jan,
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classification = "C4160 (Numerical integration and differentiation)",
  corpsource =   "Dept. of Appl. Sci., Faculty of Engng., Tohoku Univ.,
                 Sendai, Japan",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "complete elliptic integrals; complex modulus;
                 integration",
  remark =       "Fullerton: Addendum to a paper by Morita and
                 Horiguchi.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Pexton:1978:RTT
author: Robert L. Pexton and Arno D. Steiger
title: Roots of two transcendental equations as functions of a continuous real parameter
journal: j-MATH-COMPUT
volume: 32
number: 142
pages: 511--518
month: apr
monthnumber: 4
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: continuous real parameter; equations; roots; spherical Bessel functions; transcendental equations
acknowledgement: ack-nhfb
classcodes: C1110 (Algebra)
corpsource: Lawrence Livermore Lab., Univ. of California, Livermore, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Robert L. Pexton and Arno D. Steiger
rawtitle: Roots of two transcendental equations as functions of a continuous real parameter
entry:
@Article{Pexton:1978:RTT,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Roots of two transcendental equations as functions of
                 a continuous real parameter",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "142",
  pages =        "511--518",
  month =        apr,
  year =         "1978",
  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 =   "C1110 (Algebra)",
  corpsource =   "Lawrence Livermore Lab., Univ. of California,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "continuous real parameter; equations; roots; spherical
                 Bessel functions; transcendental equations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Preston:1978:NAT
author: F. S. Preston
title: A New Algorithm for the Tangent
journal: j-IEEE-TRANS-COMPUT
volume: C-27
number: 2
pages: 167--167
month: feb
monthnumber: 2
year: 1978
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1978.1675052
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Mon Jul 11 08:13:26 MDT 2011
bibtimestamp: 2011.07.11 08:13:26 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675052
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: F. S. Preston
rawtitle: A New Algorithm for the Tangent
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

abstract:
A new mathematical algorithm has been developed for the tangent. The form of the equation guarantees that the error is zero at $ 0^circ $, $ 45^circ $, and $ 90^circ $ corresponding to tangents of $0$, $1$, and infinity. With only one constant the error is brought to zero at two more points and the maximum error is less than one part in $ 3000 $. By adding a second constant, the error is reduced to less than one in $ 720 000 $. Further terms improve the accuracy geometrically.

rawabstract:
A new mathematical algorithm has been developed for the tangent. The form of the equation guarantees that the error is zero at $ 0^\circ $, $ 45^\circ $, and $ 90^\circ $ corresponding to tangents of $0$, $1$, and infinity. With only one constant the error is brought to zero at two more points and the maximum error is less than one part in $ 3000 $. By adding a second constant, the error is reduced to less than one in $ 720 \, 000 $. Further terms improve the accuracy geometrically.

entry:
@Article{Preston:1978:NAT,
  author =       "F. S. Preston",
  title =        "A New Algorithm for the Tangent",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "2",
  pages =        "167--167",
  month =        feb,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675052",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:26 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 =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675052",
  abstract =     "A new mathematical algorithm has been developed for
                 the tangent. The form of the equation guarantees that
                 the error is zero at $ 0^\circ $, $ 45^\circ $, and $
                 90^\circ $ corresponding to tangents of $0$, $1$, and
                 infinity. With only one constant the error is brought
                 to zero at two more points and the maximum error is
                 less than one part in $ 3000 $. By adding a second
                 constant, the error is reduced to less than one in $
                 720 \, 000 $. Further terms improve the accuracy
                 geometrically.",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Schindler:1978:GCG
author: Susan Schindler and R. Mirman
title: Generation of the Clebsch-Gordan coefficients for $ S_n $
journal: j-COMP-PHYS-COMM
volume: 15
number: 1--2
pages: 131--145
month: sep
monthnumber: 9
year: 1978
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(78)90087-5
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sun Oct 31 09:20:58 2010
bibtimestamp: 2010.10.31 09:20:58 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Susan Schindler and R. Mirman
rawtitle: Generation of the {Clebsch-Gordan} coefficients for {$ S_n $}
entry:
@Article{Schindler:1978:GCG,
  author =       "Susan Schindler and R. Mirman",
  title =        "Generation of the {Clebsch-Gordan} coefficients for {$
                 S_n $}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "15",
  number =       "1--2",
  pages =        "131--145",
  month =        sep,
  year =         "1978",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(78)90087-5",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sun Oct 31 09:20:58 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",
}


bibtype: article
filename: elefunt.bib
label: Schmidt:1978:EI
author: Paul W. Schmidt
journal: j-MATH-COMPUT
volume: 32
number: 141
pages: 265--269
month: jan
monthnumber: 1
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Phys. Dept., Univ. of Missouri, Columbia, MO, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Paul W. Schmidt
title:
Evaluation of the Integral $ int ^infty _0 frac t^2 alpha - 1 J_nu (x sqrt 1 + t^2)(1 + t^2)^alpha + beta - 1 d t $

keywords:
cylinder diameter distribution; first kind Bessel function; integral evaluation; integration; long circular; neutron scattering data; numerical analysis; power series expansions; recurrence; relations

rawtitle:
Evaluation of the Integral $ \int^\infty_0 \frac {t^{2 \alpha - 1} J_\nu (x \sqrt {1 + t^2})(1 + t^2)^{\alpha + \beta - 1}} d t $

entry:
@Article{Schmidt:1978:EI,
  author =       "Paul W. Schmidt",
  title =        "Evaluation of the Integral $ \int^\infty_0 \frac {t^{2
                 \alpha - 1} J_\nu (x \sqrt {1 + t^2})(1 + t^2)^{\alpha
                 + \beta - 1}} d t $",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "265--269",
  month =        jan,
  year =         "1978",
  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 =   "Phys. Dept., Univ. of Missouri, Columbia, MO, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "cylinder diameter distribution; first kind Bessel
                 function; integral evaluation; integration; long
                 circular; neutron scattering data; numerical analysis;
                 power series expansions; recurrence; relations",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Schoene:1978:RMI
author: Andrew Y. Schoene
title: Remark on ``Algorithm 435: Modified Incomplete Gamma Function [S14]''
journal: j-TOMS
volume: 4
number: 3
pages: 296--304
month: sep
monthnumber: 9
year: 1978
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355791.355803
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Aug 30 00:28:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.30 00:28:02 ???
note: See cite Fullerton:1972:MIG.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Andrew Y. Schoene
rawnote: See \cite{Fullerton:1972:MIG}.
rawtitle: Remark on ``{Algorithm 435}: Modified Incomplete Gamma Function [{S14}]''
entry:
@Article{Schoene:1978:RMI,
  author =       "Andrew Y. Schoene",
  title =        "Remark on ``{Algorithm 435}: Modified Incomplete Gamma
                 Function [{S14}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "296--304",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355803",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Fullerton:1972:MIG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Schonfelder:1978:CEE
author: J. L. Schonfelder
title: Chebyshev expansions for the error and related functions
journal: j-MATH-COMPUT
volume: 32
number: 144
pages: 1232--1240
month: oct
monthnumber: 10
year: 1978
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4110 (Error analysis in numerical methods); C4130 (Interpolation and function approximation)
corpsource: Computer Centre, Univ. of Birmingham, Birmingham, UK
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. L. Schonfelder
rawtitle: {Chebyshev} expansions for the error and related functions
keywords:
approximations; Chebyshev approximation; Chebyshev expansions; error analysis; error function; mappings; NAG library

remark:
Fullerton: Approximations for $ erf (x) $, $ erfc (x) $, and probability functions $ P(x) $, $ Q(x) $ with accuracy down to $ 10^-30 $.

entry:
@Article{Schonfelder:1978:CEE,
  author =       "J. L. Schonfelder",
  title =        "{Chebyshev} expansions for the error and related
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "144",
  pages =        "1232--1240",
  month =        oct,
  year =         "1978",
  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 =   "C4110 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Computer Centre, Univ. of Birmingham, Birmingham, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximations; Chebyshev approximation; Chebyshev
                 expansions; error analysis; error function; mappings;
                 NAG library",
  remark =       "Fullerton: Approximations for $ \erf (x) $, $ \erfc
                 (x) $, and probability functions $ P(x) $, $ Q(x) $
                 with accuracy down to $ 10^{-30} $.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Skovgaard:1978:RCE
author: Ove Skovgaard
title: Remark on ``Algorithm 149: Complete Elliptic Integral [S21]''
journal: j-TOMS
volume: 4
number: 1
pages: 95--95
month: mar
monthnumber: 3
year: 1978
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:13 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:13 ???
note: See cite Merner:1962:AAC.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ove Skovgaard
rawnote: See \cite{Merner:1962:AAC}.
rawtitle: Remark on ``{Algorithm 149: Complete Elliptic Integral [S21]}''
entry:
@Article{Skovgaard:1978:RCE,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 149: Complete Elliptic Integral
                 [S21]}''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "95--95",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:13 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Merner:1962:AAC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Slepian:1978:PSW
author: D. Slepian
title: Prolate Spheroidal Wave Functions, Fourier Analysis, and Uncertainty --- V: The Discrete Case
journal: j-BELL-SYST-TECH-J
volume: 57
number: 5
pages: 1371--1430
month: may
monthnumber: 5
year: 1978
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:56 MST 2010
bibtimestamp: 2010.11.09 11:15:56 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol57/bstj57-5-1371.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: D. Slepian
rawtitle: Prolate Spheroidal Wave Functions, {Fourier} Analysis, and Uncertainty --- {V}: The Discrete Case
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1978/BSTJ.1978.5705.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Slepian:1978:PSW,
  author =       "D. Slepian",
  title =        "Prolate Spheroidal Wave Functions, {Fourier} Analysis,
                 and Uncertainty --- {V}: The Discrete Case",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "57",
  number =       "5",
  pages =        "1371--1430",
  month =        may # "--" # jun,
  year =         "1978",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:56 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1978/BSTJ.1978.5705.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol57/bstj57-5-1371.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: elefunt.bib
label: Temme:1978:UAE
author: N. M. Temme
title: Uniform asymptotic expansions of confluent hypergeometric functions
journal: j-J-INST-MATH-APPL
volume: 22
number: 2
pages: 215--223
year: 1978
CODEN: JMTAA8
ISSN: 0020-2932 OR 00202932
MRclass: 33A30
MRnumber: 80a:33004
MRreviewer: F. W. J. Olver
bibdate: Fri Apr 5 05:48:27 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database
bibtimestamp: 2002.04.05 05:48:27 MST
fjournal: Journal of the Institute of Mathematics and its Applications
acknowledgement: ack-nhfb
journalURL: http://imamat.oxfordjournals.org/content/by/year
rawauthor: N. M. Temme
rawtitle: Uniform asymptotic expansions of confluent hypergeometric functions
entry:
@Article{Temme:1978:UAE,
  author =       "N. M. Temme",
  title =        "Uniform asymptotic expansions of confluent
                 hypergeometric functions",
  journal =      j-J-INST-MATH-APPL,
  volume =       "22",
  number =       "2",
  pages =        "215--223",
  year =         "1978",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  MRclass =      "33A30",
  MRnumber =     "80a:33004",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Fri Apr 5 05:48:27 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
}


bibtype: article
filename: elefunt.bib
label: Wang:1978:EPF
author: J. Y. Wang
title: The Evaluation of Periodic Functions with Large Input Arguments
journal: j-SIGNUM
volume: 13
number: 4
pages: 7--8
month: dec
monthnumber: 12
year: 1978
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1053412.1053413
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:05 MDT 2005
bibtimestamp: 2005.04.12 07:50:05 MDT
acknowledgement: ack-nhfb
classcodes: C4120 (Functional analysis); C4240 (Programming and algorithm theory)
corpsource: Appl. Math. Div., Argonne Nat. Lab., Argonne, IL, USA
journalURL: https://dl.acm.org/loi/signum
treatment: T Theoretical or Mathematical
rawauthor: J. Y. Wang
rawtitle: The Evaluation of Periodic Functions with Large Input Arguments
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/signum.bib

abstract:
The argument reduction scheme plays an important role in the evaluation of periodic functions. In this report we discuss the criteria for determining the domain of computer routines that evaluate periodic functions, and apply the results to the widely used sine and cosine functions.

keywords:
argument; computational complexity; computer routines; cosine functions; FORTRAN IV; function evaluation; large input arguments; periodic functions; reduction scheme

rawabstract:
The argument reduction scheme plays an important role in the evaluation of periodic functions. In this report we discuss the criteria for determining the domain of computer routines that evaluate periodic functions, and apply the results to the widely used sine and cosine functions.

entry:
@Article{Wang:1978:EPF,
  author =       "J. Y. Wang",
  title =        "The Evaluation of Periodic Functions with Large Input
                 Arguments",
  journal =      j-SIGNUM,
  volume =       "13",
  number =       "4",
  pages =        "7--8",
  month =        dec,
  year =         "1978",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1053412.1053413",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:05 MDT 2005",
  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/signum.bib",
  abstract =     "The argument reduction scheme plays an important role
                 in the evaluation of periodic functions. In this report
                 we discuss the criteria for determining the domain of
                 computer routines that evaluate periodic functions, and
                 apply the results to the widely used sine and cosine
                 functions.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C4120 (Functional analysis); C4240 (Programming and
                 algorithm theory)",
  corpsource =   "Appl. Math. Div., Argonne Nat. Lab., Argonne, IL,
                 USA",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "argument; computational complexity; computer routines;
                 cosine functions; FORTRAN IV; function evaluation;
                 large input arguments; periodic functions; reduction
                 scheme",
  remark-1 =     "From page 7: ``In this report, we will examine bounds
                 on the domain that guarantees that the computed
                 function values retain half of the significant
                 digits.''",
  remark-2 =     "From page 8: ``Improvement: \ldots{} this can he
                 accomplished by storing PI/4 in two words, i.e., PI/4 =
                 C1 + C2.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: elefunt.bib
label: Wang:1978:SMR
author: J. Y. Wang and J. Boyer
type: Report
number: AMD-TM 304
institution: Applied Mathematics Division, Argonne National Laboratory
address: Argonne, IL, USA
pages: 7--8
month: jan
monthnumber: 1
year: 1978
bibdate: Fri Sep 20 14:26:48 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.09.20 14:26:48 ???
note: Cited in cite [Reference 8]Agarwal:1986:NSV in elefunt.bib and fparith.bib.
acknowledgement: ack-nhfb
rawauthor: J. Y. Wang and J. Boyer
rawnote: Cited in \cite[Reference 8]{Agarwal:1986:NSV} in elefunt.bib and fparith.bib.
title:
A Studv of the Mathematical Routines in the IBM System/360 FORTRAN IV and FORTRAN IV (Mod II) Libraries

rawtitle:
A Studv of the Mathematical Routines in the {IBM System/360 FORTRAN IV} and {FORTRAN IV (Mod II)} Libraries

entry:
@TechReport{Wang:1978:SMR,
  author =       "J. Y. Wang and J. Boyer",
  title =        "A Studv of the Mathematical Routines in the {IBM
                 System/360 FORTRAN IV} and {FORTRAN IV (Mod II)}
                 Libraries",
  type =         "Report",
  number =       "AMD-TM 304",
  institution =  "Applied Mathematics Division, Argonne National
                 Laboratory",
  address =      "Argonne, IL, USA",
  month =        jan,
  year =         "1978",
  bibdate =      "Fri Sep 20 14:26:48 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Cited in \cite[Reference 8]{Agarwal:1986:NSV} in
                 elefunt.bib and fparith.bib.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Alt:1979:SRD
author: H. Alt
title: Square Rooting Is as Difficult as Multiplication
journal: j-COMPUTING
volume: 21
number: 3
pages: 221--232
month: sep
monthnumber: 9
year: 1979
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 68C25
MRnumber: 82m:68081
bibdate: Tue Jan 2 17:40:54 MST 2001
bibtimestamp: 2001.01.02 17:40:54 MST
fjournal: Computing
keywords: algorithm; computer programming; square rooting
acknowledgement: ack-nj
affiliation: Math. & Information, Univ. of Saarlandes, Saarbrucken, West Germany
journalURL: http://link.springer.com/journal/607
journalabr: Computing (Vienna/New York)
rawauthor: H. Alt
rawtitle: Square Rooting Is as Difficult as Multiplication
bibsource:
Compendex database; 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); MathSciNet database

entry:
@Article{Alt:1979:SRD,
  author =       "H. Alt",
  title =        "Square Rooting Is as Difficult as Multiplication",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  month =        sep,
  year =         "1979",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68C25",
  MRnumber =     "82m:68081",
  bibdate =      "Tue Jan 2 17:40:54 MST 2001",
  bibsource =    "Compendex database;
                 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); MathSciNet
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Math. \& Information, Univ. of Saarlandes,
                 Saarbrucken, West Germany",
  classification = "723; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "algorithm; computer programming; square rooting",
}


bibtype: article
filename: elefunt.bib
label: Ardill:1979:ABF
author: R. W. B. Ardill and K. J. M. Moriarty
journal: j-COMP-PHYS-COMM
volume: 17
number: 3
pages: 321--336
month: jun
monthnumber: 6
year: 1979
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(79)90060-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Apr 24 10:35:27 2008
bibtimestamp: 2008.04.24 10:35:27 ???
fjournal: Computer Physics Communications
remark: Fullerton: Description of a program with accuracy about $ 10^-10 $.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: R. W. B. Ardill and K. J. M. Moriarty
title:
Accurate Bessel functions $ J_n(z) $, $ Y_n(z) $, $ H_n^(1)(z) $ and $ H_n^(2)(z) $ of integer order and complex argument

rawtitle:
Accurate {Bessel} functions {$ J_n(z) $}, {$ Y_n(z) $}, {$ H_n^{(1)}(z) $} and {$ H_n^{(2)}(z) $} of integer order and complex argument

entry:
@Article{Ardill:1979:ABF,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "Accurate {Bessel} functions {$ J_n(z) $}, {$ Y_n(z)
                 $}, {$ H_n^{(1)}(z) $} and {$ H_n^{(2)}(z) $} of
                 integer order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "17",
  number =       "3",
  pages =        "321--336",
  month =        jun,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90060-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 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 =       "Fullerton: Description of a program with accuracy
                 about $ 10^{-10} $.",
}


bibtype: article
filename: elefunt.bib
label: Atkins:1979:FSC
author: D. E. Atkins
title: Fourth Symposium on Computer Arithmetic: crunching with quality and LSI
journal: j-COMPUTER
volume: 12
number: 4
pages: 94--97
month: apr
monthnumber: 4
year: 1979
CODEN: CPTRB4
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Thu Dec 12 07:20:54 MST 1996
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.12.12 07:20:54 MST
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
journalabr: Computer
rawauthor: D. E. Atkins
rawtitle: {Fourth Symposium on Computer Arithmetic}: crunching with quality and {LSI}
abstract:
Computer arithmetic problems --- faster computation rates and more efficient representations of real numbers --- are considered in the paper. Floating-point arithmetic standardization, novel implementation of basic arithmetic operators, evaluation of elementary functions --- these are the main considerations of the conference review.

keywords:
computer arithmetic; computer systems, digital; data processing --- data description; mathematical techniques --- digital arithmetic

rawabstract:
Computer arithmetic problems --- faster computation rates and more efficient representations of real numbers --- are considered in the paper. Floating-point arithmetic standardization, novel implementation of basic arithmetic operators, evaluation of elementary functions --- these are the main considerations of the conference review.

entry:
@Article{Atkins:1979:FSC,
  author =       "D. E. Atkins",
  title =        "{Fourth Symposium on Computer Arithmetic}: crunching
                 with quality and {LSI}",
  journal =      j-COMPUTER,
  volume =       "12",
  number =       "4",
  pages =        "94--97",
  month =        apr,
  year =         "1979",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Dec 12 07:20:54 MST 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Computer arithmetic problems --- faster computation
                 rates and more efficient representations of real
                 numbers --- are considered in the paper. Floating-point
                 arithmetic standardization, novel implementation of
                 basic arithmetic operators, evaluation of elementary
                 functions --- these are the main considerations of the
                 conference review.",
  acknowledgement = ack-nhfb,
  classification = "722; 723",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabr =   "Computer",
  keywords =     "computer arithmetic; computer systems, digital; data
                 processing --- data description; mathematical
                 techniques --- digital arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Babb:1979:OEC
author: Stanley E. Babb, Jr. and James W. Cafky
title: Operational evaluation of certain infinite Bessel function integrals
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1033--1039
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 44A99
MRnumber: 80e:44002
MRreviewer: L. Arteaga
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4180 (Integral equations)
corpsource: Dept. of Phys. and Astron., Univ. of Oklahoma, Norman, OK, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Stanley E. {Babb, Jr.} and James W. Cafky
rawtitle: Operational evaluation of certain infinite {Bessel} function integrals
keywords:
Bessel function integral; integration; numerical methods; Schafheitlin method; trigonometric function; Weber

entry:
@Article{Babb:1979:OEC,
  author =       "Stanley E. {Babb, Jr.} and James W. Cafky",
  title =        "Operational evaluation of certain infinite {Bessel}
                 function integrals",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1033--1039",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "44A99",
  MRnumber =     "80e:44002",
  MRreviewer =   "L. Arteaga",
  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 =   "C4180 (Integral equations)",
  corpsource =   "Dept. of Phys. and Astron., Univ. of Oklahoma, Norman,
                 OK, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function integral; integration; numerical
                 methods; Schafheitlin method; trigonometric function;
                 Weber",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Borjesson:1979:SAE
author: P. Borjesson and C.-E. Sundberg
title: Simple Approximations of the Error Function $ Q(x) $ for Communications Applications
journal: j-IEEE-TRANS-COMM
volume: 27
number: 3
pages: 639--643
month: mar
monthnumber: 3
year: 1979
CODEN: IECMBT
DOI: https://doi.org/10.1109/tcom.1979.1094433
ISSN: 0090-6778 (print), 1558-0857 (electronic) OR 00906778 (print), 15580857 (electronic)
ISSNL: 0090-6778 OR 00906778
bibdate: Sat Dec 16 15:29:00 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 15:29:00 ???
fjournal: IEEE Transactions on Communications
acknowledgement: ack-nhfb
rawauthor: P. B{\"o}rjesson and C.-E. Sundberg
rawtitle: Simple Approximations of the Error Function {$ Q(x) $} for Communications Applications
entry:
@Article{Borjesson:1979:SAE,
  author =       "P. B{\"o}rjesson and C.-E. Sundberg",
  title =        "Simple Approximations of the Error Function {$ Q(x) $}
                 for Communications Applications",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "27",
  number =       "3",
  pages =        "639--643",
  month =        mar,
  year =         "1979",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcom.1979.1094433",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Sat Dec 16 15:29:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
}


bibtype: article
filename: elefunt.bib
label: Campbell:1979:BFR
author: J. B. Campbell
title: Bessel functions $ J_nu (x) $ and $ Y_nu (x) $ of real order and real argument
journal: j-COMP-PHYS-COMM
volume: 18
number: 1
pages: 133--142
month: sep
monthnumber: 9
year: 1979
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(79)90030-4
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 06:01:26 MST 2012
bibtimestamp: 2012.02.13 06:01:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465579900304
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. B. Campbell
rawtitle: {Bessel} functions {$ J_\nu (x) $} and {$ Y_\nu (x) $} of real order and real argument
entry:
@Article{Campbell:1979:BFR,
  author =       "J. B. Campbell",
  title =        "{Bessel} functions {$ J_\nu (x) $} and {$ Y_\nu (x) $}
                 of real order and real argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "18",
  number =       "1",
  pages =        "133--142",
  month =        sep,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90030-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:26 MST 2012",
  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/0010465579900304",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1979:CEI
author: B. C. Carlson
title: Computing elliptic integrals by duplication
journal: j-NUM-MATH
volume: 33
number: 1
pages: 1--16
month: mar
monthnumber: 3
year: 1979
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65D20
MRnumber: 80h:65008
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Dept. of Math. and Phys., Iowa Univ., Ames, IA, USA
journalURL: http://link.springer.com/journal/211
treatment: A Application; T Theoretical or Mathematical
rawauthor: B. C. Carlson
rawtitle: Computing elliptic integrals by duplication
abstract:
Logarithms, arctangents, and elliptic integrals of all three kinds (including complete integrals) are evaluated numerically by successive applications of the duplication theorem. When the convergence is improved by including a fixed number of terms of Taylor's series, the error ultimately decreases by a factor of 4096 in each cycle of iteration. Except for Cauchy principal values there is no separation of cases according to the values of the variables, and no serious cancellations occur if the variables are real and nonnegative. Only rational operations and square roots are required. An appendix contains a recurrence relation and two new representations (in terms of elementary symmetric functions and power sums) for $R$-polynomials, as well as an upper bound for the error made in truncating the Taylor series of an $R$-function.

keywords:
convergence; duplication theory; elliptic integral; integration; numerical methods; R-polynomial; Taylor series

rawabstract:
Logarithms, arctangents, and elliptic integrals of all three kinds (including complete integrals) are evaluated numerically by successive applications of the duplication theorem. When the convergence is improved by including a fixed number of terms of Taylor's series, the error ultimately decreases by a factor of 4096 in each cycle of iteration. Except for Cauchy principal values there is no separation of cases according to the values of the variables, and no serious cancellations occur if the variables are real and nonnegative. Only rational operations and square roots are required. An appendix contains a recurrence relation and two new representations (in terms of elementary symmetric functions and power sums) for $R$-polynomials, as well as an upper bound for the error made in truncating the Taylor series of an $R$-function.

entry:
@Article{Carlson:1979:CEI,
  author =       "B. C. Carlson",
  title =        "Computing elliptic integrals by duplication",
  journal =      j-NUM-MATH,
  volume =       "33",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "1979",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20",
  MRnumber =     "80h:65008",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Logarithms, arctangents, and elliptic integrals of all
                 three kinds (including complete integrals) are
                 evaluated numerically by successive applications of the
                 duplication theorem. When the convergence is improved
                 by including a fixed number of terms of Taylor's
                 series, the error ultimately decreases by a factor of
                 4096 in each cycle of iteration. Except for Cauchy
                 principal values there is no separation of cases
                 according to the values of the variables, and no
                 serious cancellations occur if the variables are real
                 and nonnegative. Only rational operations and square
                 roots are required. An appendix contains a recurrence
                 relation and two new representations (in terms of
                 elementary symmetric functions and power sums) for
                 $R$-polynomials, as well as an upper bound for the
                 error made in truncating the Taylor series of an
                 $R$-function.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classification = "C4180 (Integral equations)",
  corpsource =   "Dept. of Math. and Phys., Iowa Univ., Ames, IA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence; duplication theory; elliptic integral;
                 integration; numerical methods; R-polynomial; Taylor
                 series",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Cole:1979:EI
author: R. J. Cole and C. Pescatore
title: Evaluation of the Integral $ int _0^infty t^n exp ( - t^2 - x / t) d t $
journal: j-J-COMPUT-PHYS
volume: 32
number: 2
pages: 280--287
month: aug
monthnumber: 8
year: 1979
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(79)90135-9
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:34 MST 2012
bibtimestamp: 2012.01.01 09:15:34 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999179901359
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. J. Cole and C. Pescatore
rawtitle: Evaluation of the Integral $ \int_0^\infty t^n \exp ( - t^2 - x / t) \, d t $
abstract:
The main purpose of this paper is to provide a unified approach to the treatment of linear recurrence relations for single or pairs of order statistics. Suppose such a relation has been proved in the simplest case when $ X_1, ldots , X_n $ are independent variates having an arbitrary absolutely continuous distribution. It is pointed out that the same relation continues to hold when the $X$'s are exchangeable, whether continuous or not. As has recently become well known, further generalizations are possible when the $X$'s have any joint distribution. Attention is also drawn to a useful nonlinear recurrence relation due to Boncelet (1987).

rawabstract:
The main purpose of this paper is to provide a unified approach to the treatment of linear recurrence relations for single or pairs of order statistics. Suppose such a relation has been proved in the simplest case when $ X_1, \ldots {}, X_n $ are independent variates having an arbitrary absolutely continuous distribution. It is pointed out that the same relation continues to hold when the $X$'s are exchangeable, whether continuous or not. As has recently become well known, further generalizations are possible when the $X$'s have any joint distribution. Attention is also drawn to a useful nonlinear recurrence relation due to Boncelet (1987).

entry:
@Article{Cole:1979:EI,
  author =       "R. J. Cole and C. Pescatore",
  title =        "Evaluation of the Integral $ \int_0^\infty t^n \exp (
                 - t^2 - x / t) \, d t $",
  journal =      j-J-COMPUT-PHYS,
  volume =       "32",
  number =       "2",
  pages =        "280--287",
  month =        aug,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90135-9",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:34 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/0021999179901359",
  abstract =     "The main purpose of this paper is to provide a unified
                 approach to the treatment of linear recurrence
                 relations for single or pairs of order statistics.
                 Suppose such a relation has been proved in the simplest
                 case when $ X_1, \ldots {}, X_n $ are independent
                 variates having an arbitrary absolutely continuous
                 distribution. It is pointed out that the same relation
                 continues to hold when the $X$'s are exchangeable,
                 whether continuous or not. As has recently become well
                 known, further generalizations are possible when the
                 $X$'s have any joint distribution. Attention is also
                 drawn to a useful nonlinear recurrence relation due to
                 Boncelet (1987).",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Conde:1979:Z
author: S. Conde and Shyam L. Kalla
title: The $ nu $-zeros of $ J_- nu (x) $
journal: j-MATH-COMPUT
volume: 33
number: 145
pages: 423--426
month: jan
monthnumber: 1
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20
MRnumber: 80b:65021
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: With a microfiche supplement.
acknowledgement: ack-nhfb
classcodes: C4170 (Differential equations); C4190 (Other numerical methods)
corpsource: Facultad de Ingenieria, Univ. del Zulia, Maracaibo, Venezuela
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: S. Conde and Shyam L. Kalla
rawtitle: The $ \nu $-zeros of {$ J_{- \nu }(x) $}
keywords:
Bessel function; boundary value; boundary-value problems; J/sub -v/(x); partial differential equations; poles and zeros; problems; transforms; v-zeros

entry:
@Article{Conde:1979:Z,
  author =       "S. Conde and Shyam L. Kalla",
  title =        "The $ \nu $-zeros of {$ J_{- \nu }(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "145",
  pages =        "423--426",
  month =        jan,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "80b:65021",
  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 =   "C4170 (Differential equations); C4190 (Other numerical
                 methods)",
  corpsource =   "Facultad de Ingenieria, Univ. del Zulia, Maracaibo,
                 Venezuela",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; boundary value; boundary-value
                 problems; J/sub -v/(x); partial differential equations;
                 poles and zeros; problems; transforms; v-zeros",
  remark =       "Fullerton: With a microfiche supplement.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Delic:1979:CSS
author: G. Delic
title: Chebyshev series for the spherical Bessel function $ j_l(r) $
journal: j-COMP-PHYS-COMM
volume: 18
number: 1
pages: 73--86
month: sep
monthnumber: 9
year: 1979
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(79)90025-0
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 06:01:26 MST 2012
bibtimestamp: 2012.02.13 06:01:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465579900250
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: G. Delic
rawtitle: {Chebyshev} series for the spherical {Bessel} function $ j_l(r) $
entry:
@Article{Delic:1979:CSS,
  author =       "G. Delic",
  title =        "{Chebyshev} series for the spherical {Bessel} function
                 $ j_l(r) $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "18",
  number =       "1",
  pages =        "73--86",
  month =        sep,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90025-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:26 MST 2012",
  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/0010465579900250",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Divgi:1979:CUB
author: D. R. Divgi
title: Calculation of Univariate and Bivariate Normal Probability Functions
journal: j-ANN-STAT
volume: 7
number: 4
pages: 903--910
month: jul
monthnumber: 7
year: 1979
CODEN: ASTSC7
DOI: https://doi.org/10.1214/aos/1176344739
ISSN: 0090-5364 (print), 2168-8966 (electronic) OR 00905364 (print), 21688966 (electronic)
ISSNL: 0090-5364 OR 00905364
bibdate: Wed Jun 4 06:39:50 MDT 2014
bibtimestamp: 2014.06.04 06:39:50 MDT
URL: http://projecteuclid.org/euclid.aos/1176344739
fjournal: Annals of Statistics
acknowledgement: ack-nhfb
journalURL: http://projecteuclid.org/all/euclid.aos/
rawauthor: D. R. Divgi
rawtitle: Calculation of Univariate and Bivariate Normal Probability Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/annstat1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Divgi:1979:CUB,
  author =       "D. R. Divgi",
  title =        "Calculation of Univariate and Bivariate Normal
                 Probability Functions",
  journal =      j-ANN-STAT,
  volume =       "7",
  number =       "4",
  pages =        "903--910",
  month =        jul,
  year =         "1979",
  CODEN =        "ASTSC7",
  DOI =          "https://doi.org/10.1214/aos/1176344739",
  ISSN =         "0090-5364 (print), 2168-8966 (electronic)",
  ISSN-L =       "0090-5364",
  bibdate =      "Wed Jun 4 06:39:50 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annstat1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://projecteuclid.org/euclid.aos/1176344739",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aos/",
}


bibtype: article
filename: elefunt.bib
label: Einarsson:1979:BEN
author: Bo Einarsson
title: Bibliography on the evaluation of numerical software
journal: j-J-COMPUT-APPL-MATH
volume: 5
number: 2
pages: 145--159
month: jun
monthnumber: 6
year: 1979
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0771-050X(79)90011-1
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Thu Oct 28 17:14:49 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.28 17:14:49 ???
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Bo Einarsson
rawtitle: Bibliography on the evaluation of numerical software
abstract:
This bibliography on the evaluation of numerical software has been written at the request of the IFIP Working Group on Numerical Software (IFIP WG 2.5), and is divided into nine different sections. Within each section the references are given in alphabetical order by the first author. The aim of the bibliography is to be useful in the production and evaluation of good software for numerical mathematics.

TOC:
2. Miscellaneous evaluations 3. Linear algebra 4. Optimization and nonlinear equations 5. Functions 6. Quadrature 7. Integral equations 8. Ordinary differential equations 9. Partial differential equations

rawabstract:
This bibliography on the evaluation of numerical software has been written at the request of the IFIP Working Group on Numerical Software (IFIP WG 2.5), and is divided into nine different sections. Within each section the references are given in alphabetical order by the first author. The aim of the bibliography is to be useful in the production and evaluation of good software for numerical mathematics.

rawTOC:
2. Miscellaneous evaluations \\ 3. Linear algebra \\ 4. Optimization and nonlinear equations \\ 5. Functions \\ 6. Quadrature \\ 7. Integral equations \\ 8. Ordinary differential equations \\ 9. Partial differential equations

entry:
@Article{Einarsson:1979:BEN,
  author =       "Bo Einarsson",
  title =        "Bibliography on the evaluation of numerical software",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "5",
  number =       "2",
  pages =        "145--159",
  month =        jun,
  year =         "1979",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0771-050X(79)90011-1",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Oct 28 17:14:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This bibliography on the evaluation of numerical
                 software has been written at the request of the IFIP
                 Working Group on Numerical Software (IFIP WG 2.5), and
                 is divided into nine different sections. Within each
                 section the references are given in alphabetical order
                 by the first author. The aim of the bibliography is to
                 be useful in the production and evaluation of good
                 software for numerical mathematics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  tableofcontents = "2. Miscellaneous evaluations \\
                 3. Linear algebra \\
                 4. Optimization and nonlinear equations \\
                 5. Functions \\
                 6. Quadrature \\
                 7. Integral equations \\
                 8. Ordinary differential equations \\
                 9. Partial differential equations",
}


bibtype: article
filename: elefunt.bib
label: elLozy:1979:RAS
author: Mohamed el Lozy
journal: j-TOMS
volume: 5
number: 2
pages: 238--239
month: jun
monthnumber: 6
year: 1979
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:16 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:16 ???
note: See cite Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Mohamed el Lozy
rawnote: See \cite{Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS}.
title:
Remark on ``Algorithm 395: Student's $t$-Distribution'' and Remark on ``Algorithm 396: Student's Quantiles [S14]''

remark:
Fullerton: The algorithms are corrected for computers with anomalously small word lengths (e.g., IBM and Interdata).

rawtitle:
Remark on ``{Algorithm 395: Student's $t$-Distribution}'' and Remark on ``{Algorithm 396: Student's Quantiles [S14]}''

entry:
@Article{elLozy:1979:RAS,
  author =       "Mohamed el Lozy",
  title =        "Remark on ``{Algorithm 395: Student's
                 $t$-Distribution}'' and Remark on ``{Algorithm 396:
                 Student's Quantiles [S14]}''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "238--239",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:16 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: The algorithms are corrected for computers
                 with anomalously small word lengths (e.g., IBM and
                 Interdata).",
}


bibtype: article
filename: elefunt.bib
label: Epstein:1979:STE
author: H. I. Epstein and B. F. Caviness
title: A structure theorem for the elementary functions and its application to the identity problem
journal: j-INT-J-COMPUT-INF-SCI
volume: 8
number: 1
pages: 9--37
year: 1979
CODEN: IJCIAH
ISSN: 0091-7036 OR 00917036
MRclass: 12H05 (68C05)
MRnumber: 80k:12032
MRreviewer: Michael F. Singer
bibdate: Sat Apr 26 12:45:53 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.04.26 12:45:53 ???
fjournal: International Journal of Computer and Information Sciences
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10766
rawauthor: H. I. Epstein and B. F. Caviness
rawtitle: A structure theorem for the elementary functions and its application to the identity problem
entry:
@Article{Epstein:1979:STE,
  author =       "H. I. Epstein and B. F. Caviness",
  title =        "A structure theorem for the elementary functions and
                 its application to the identity problem",
  journal =      j-INT-J-COMPUT-INF-SCI,
  volume =       "8",
  number =       "1",
  pages =        "9--37",
  year =         "1979",
  CODEN =        "IJCIAH",
  ISSN =         "0091-7036",
  MRclass =      "12H05 (68C05)",
  MRnumber =     "80k:12032",
  MRreviewer =   "Michael F. Singer",
  bibdate =      "Sat Apr 26 12:45:53 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Computer and Information
                 Sciences",
  journal-URL =  "http://link.springer.com/journal/10766",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1979:AEU
author: Henry E. Fettis
title: An asymptotic expansion for the upper percentage points of the $ chi ^2 $-distribution
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1059--1064
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
DOI: https://doi.org/10.2307/2006079
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 62E20
MRnumber: 80h:62014
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: approximation theory; asymptotic expansion; upper percentage point
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4130 (Interpolation and function approximation)
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Henry E. Fettis
rawtitle: An asymptotic expansion for the upper percentage points of the $ \chi^2 $-distribution
entry:
@Article{Fettis:1979:AEU,
  author =       "Henry E. Fettis",
  title =        "An asymptotic expansion for the upper percentage
                 points of the $ \chi^2 $-distribution",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1059--1064",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2006079",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "62E20",
  MRnumber =     "80h:62014",
  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,
  ajournal =     "Math. Comput.",
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximation theory; asymptotic expansion; upper
                 percentage point",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Gabutti:1979:HPM
author: Bruno Gabutti
title: On high precision methods for computing integrals involving Bessel functions
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1049--1057
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D30
MRnumber: 80c:65048
MRreviewer: K. Jetter
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel function integral; computational complexity; exponential function integral; integration
acknowledgement: ack-nhfb
classcodes: C4180 (Integral equations); C4240 (Programming and algorithm theory)
corpsource: Istituto di Calcoli Numerici, Univ. di Torino, Torino, Italy
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Bruno Gabutti
rawtitle: On high precision methods for computing integrals involving {Bessel} functions
entry:
@Article{Gabutti:1979:HPM,
  author =       "Bruno Gabutti",
  title =        "On high precision methods for computing integrals
                 involving {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1049--1057",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D30",
  MRnumber =     "80c:65048",
  MRreviewer =   "K. Jetter",
  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 =   "C4180 (Integral equations); C4240 (Programming and
                 algorithm theory)",
  corpsource =   "Istituto di Calcoli Numerici, Univ. di Torino, Torino,
                 Italy",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function integral; computational complexity;
                 exponential function integral; integration",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Gargantini:1979:NSS
author: Irene Gargantini
title: The Numerical Stability of Simultaneous Iterations Via Square-Rooting
journal: j-COMPUT-MATH-APPL
volume: 5
number: 1
pages: 25--31
year: 1979
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(81)90136-X
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:16 MST 2017
bibtimestamp: 2017.03.01 18:51:16 MST
URL: http://www.sciencedirect.com/science/article/pii/089812218190136X
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-jr
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Irene Gargantini
rawtitle: The Numerical Stability of Simultaneous Iterations Via Square-Rooting
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gargantini:1979:NSS,
  author =       "Irene Gargantini",
  title =        "The Numerical Stability of Simultaneous Iterations Via
                 Square-Rooting",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "5",
  number =       "1",
  pages =        "25--31",
  month =        "????",
  year =         "1979",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(81)90136-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812218190136X",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1979:AIG
author: W. Gautschi
title: Algorithm 542: Incomplete Gamma Functions [S14]
journal: j-TOMS
volume: 5
number: 4
pages: 482--489
month: dec
monthnumber: 12
year: 1979
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355853.355864
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Aug 28 00:39:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.28 00:39:50 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
remark: Fullerton: FORTRAN routines of adjustable accuracy.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. Gautschi
rawtitle: {Algorithm 542}: Incomplete Gamma Functions [{S14}]
entry:
@Article{Gautschi:1979:AIG,
  author =       "W. Gautschi",
  title =        "{Algorithm 542}: Incomplete Gamma Functions [{S14}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "482--489",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355864",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:39:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: FORTRAN routines of adjustable accuracy.",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1979:CPI
author: Walter Gautschi
title: A Computational Procedure for Incomplete Gamma Functions
journal: j-TOMS
volume: 5
number: 4
pages: 466--481
month: dec
monthnumber: 12
year: 1979
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355853.355863
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Aug 28 00:32:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.28 00:32:50 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Walter Gautschi
rawtitle: A Computational Procedure for Incomplete Gamma Functions
remark:
Fullerton: Algorithms for the incomplete gamma function, $ gamma (a, x) $, the complementary function, $ Gamma (a, x) $, and Tricomi's form, $ gamma '(a, x) $, are given.

entry:
@Article{Gautschi:1979:CPI,
  author =       "Walter Gautschi",
  title =        "A Computational Procedure for Incomplete Gamma
                 Functions",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "466--481",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355863",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: Algorithms for the incomplete gamma
                 function, $ \gamma (a, x) $, the complementary
                 function, $ \Gamma (a, x) $, and Tricomi's form, $
                 \gamma '(a, x) $, are given.",
}


bibtype: article
filename: elefunt.bib
label: Glasser:1979:NI
author: M. L. Glasser
journal: j-MATH-COMPUT
volume: 33
number: 146
pages: 792--793
month: apr
monthnumber: 4
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A40
MRnumber: 80d:33004
MRreviewer: T. Erber
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; hypergeometric series; integral; integral equations
acknowledgement: ack-nhfb
classcodes: C1120 (Mathematical analysis); C4180 (Integral equations)
corpsource: Math. and Computer Sci. Dept., Clarkson Coll. of Technol., Potsdam, NY, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: M. L. Glasser
title:
A Note on the Integral $ int ^infty _0 t^2 alpha - 1(1 + t^2)^1 - alpha - beta J_nu (x sqrt 1 + t^2) d t $

rawtitle:
A Note on the Integral $ \int^\infty_0 t^{2 \alpha - 1}(1 + t^2)^{1 - \alpha - \beta } {J}_\nu (x \sqrt {1 + t^2}) d t $

entry:
@Article{Glasser:1979:NI,
  author =       "M. L. Glasser",
  title =        "A Note on the Integral $ \int^\infty_0 t^{2 \alpha -
                 1}(1 + t^2)^{1 - \alpha - \beta } {J}_\nu (x \sqrt {1 +
                 t^2}) d t $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "792--793",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40",
  MRnumber =     "80d:33004",
  MRreviewer =   "T. Erber",
  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 =   "C1120 (Mathematical analysis); C4180 (Integral
                 equations)",
  corpsource =   "Math. and Computer Sci. Dept., Clarkson Coll. of
                 Technol., Potsdam, NY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; hypergeometric series; integral;
                 integral equations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Haavie:1979:GNT
author: Tore Haa vie
title: Generalized Neville type extrapolation schemes
journal: j-BIT
volume: 19
number: 2
pages: 204--213
month: jun
monthnumber: 6
year: 1979
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01930850
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65B05 (65D05 65D30)
MRnumber: 80f:65005
MRreviewer: Siegfried Filippi
bibdate: Wed Jan 4 18:52:16 MST 2006
bibtimestamp: 2006.01.04 18:52:16 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=2&spage=204
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Tore H{\aa}vie
rawtitle: Generalized {Neville} type extrapolation schemes
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Haavie:1979:GNT,
  author =       "Tore H{\aa}vie",
  title =        "Generalized {Neville} type extrapolation schemes",
  journal =      j-BIT,
  volume =       "19",
  number =       "2",
  pages =        "204--213",
  month =        jun,
  year =         "1979",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01930850",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65B05 (65D05 65D30)",
  MRnumber =     "80f:65005",
  MRreviewer =   "Siegfried Filippi",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&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=19&issue=2&spage=204",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Johnson:1979:RAF
author: Donald B. Johnson and Webb Miller and Brian Minnihan and Celia Wrathall
title: Reducibility Among Floating-Point Graphs
journal: j-J-ACM
volume: 26
number: 4
pages: 739--760
month: oct
monthnumber: 10
year: 1979
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 65G05
MRnumber: 80i:65045
bibdate: Fri Dec 08 11:55:10 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.08 11:55:10 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: Donald B. Johnson and Webb Miller and Brian Minnihan and Celia Wrathall
rawtitle: Reducibility Among Floating-Point Graphs
abstract:
The graph-theoretic models of this paper can be used to compare the rounding-error behavior of numerical programs. The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors in each arithmetic operation. Models constructed on this assumption are more tractable than would be the case under more realistic assumptions. There are identified two easily tested conditions on programs which guarantee that error analyses are relatively insensitive to the particular graph model employed. The development has the additional benefit of sometimes providing an elementary proof that one program is comparable in stability to another. Examples of such results are given.

rawabstract:
The graph-theoretic models of this paper can be used to compare the rounding-error behavior of numerical programs. The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors in each arithmetic operation. Models constructed on this assumption are more tractable than would be the case under more realistic assumptions. There are identified two easily tested conditions on programs which guarantee that error analyses are relatively insensitive to the particular graph model employed. The development has the additional benefit of sometimes providing an elementary proof that one program is comparable in stability to another. Examples of such results are given.

entry:
@Article{Johnson:1979:RAF,
  author =       "Donald B. Johnson and Webb Miller and Brian Minnihan
                 and Celia Wrathall",
  title =        "Reducibility Among Floating-Point Graphs",
  journal =      j-J-ACM,
  volume =       "26",
  number =       "4",
  pages =        "739--760",
  month =        oct,
  year =         "1979",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "80i:65045",
  bibdate =      "Fri Dec 08 11:55:10 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The graph-theoretic models of this paper can be used
                 to compare the rounding-error behavior of numerical
                 programs. The models follow the approach, popularized
                 by Wilkinson, of assuming independent rounding errors
                 in each arithmetic operation. Models constructed on
                 this assumption are more tractable than would be the
                 case under more realistic assumptions. There are
                 identified two easily tested conditions on programs
                 which guarantee that error analyses are relatively
                 insensitive to the particular graph model employed. The
                 development has the additional benefit of sometimes
                 providing an elementary proof that one program is
                 comparable in stability to another. Examples of such
                 results are given.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}


bibtype: article
filename: elefunt.bib
label: Kobayashi:1979:UEF
author: Y. Kobayashi and M. Ohkita and M. Inoue
title: On the use of an exponential function in approximation of elliptic integrals
journal: j-MATH-COMPUT-SIMUL
volume: 21
number: 2
pages: 226--230
month: aug
monthnumber: 8
year: 1979
CODEN: MCSIDR
DOI: https://doi.org/10.1016/0378-4754(79)90138-1
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Fri Aug 15 13:24:19 MDT 2025
bibtimestamp: 2025.08.15 13:24:19 MDT
URL: https://www.sciencedirect.com/science/article/pii/0378475479901381
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: Y. Kobayashi and M. Ohkita and M. Inoue
rawtitle: On the use of an exponential function in approximation of elliptic integrals
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1970.bib

entry:
@Article{Kobayashi:1979:UEF,
  author =       "Y. Kobayashi and M. Ohkita and M. Inoue",
  title =        "On the use of an exponential function in approximation
                 of elliptic integrals",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "21",
  number =       "2",
  pages =        "226--230",
  month =        aug,
  year =         "1979",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(79)90138-1",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Aug 15 13:24:19 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1970.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0378475479901381",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: article
filename: elefunt.bib
label: Kusterer:1979:SEP
author: Roland Kusterer and Manfred Reimer
title: Stable Evaluation of Polynomials in Time $ log n $
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1019--1031
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1979-0528054-X; https://doi.org/10.2307/2006075
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65G05 (68C25)
MRnumber: 80d:65050 (528054)
MRreviewer: C. W. Clenshaw
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: algorithm; approximation theory; number of multiplications to evaluate a polynomial; polynomials
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Math. Inst., University of Dortmund, Dortmund, West Germany
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Roland Kusterer and Manfred Reimer
rawtitle: Stable Evaluation of Polynomials in Time $ \log n $
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; 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; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database

entry:
@Article{Kusterer:1979:SEP,
  author =       "Roland Kusterer and Manfred Reimer",
  title =        "Stable Evaluation of Polynomials in Time $ \log n $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1019--1031",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1979-0528054-X;
                 https://doi.org/10.2307/2006075",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G05 (68C25)",
  MRnumber =     "80d:65050 (528054)",
  MRreviewer =   "C. W. Clenshaw",
  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/bibnet/authors/c/clenshaw-charles-w.bib;
                 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;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Math. Inst., University of Dortmund, Dortmund, West
                 Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm; approximation theory; number of
                 multiplications to evaluate a polynomial; polynomials",
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Leung:1979:AFE
author: K. V. Leung and S. S. Ghaderpanah
journal: j-MATH-COMPUT
volume: 33
number: 148
pages: 1299--1306
month: oct
monthnumber: 10
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33-04)
MRnumber: 80e:65024
MRreviewer: R. P. Boas, Jr.
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4140 (Linear algebra)
corpsource: Dept. of Computer Sci., Concordia Univ., Montreal, Que., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: K. V. Leung and S. S. Ghaderpanah
title:
An application of the finite element approximation method to find the complex zeros of the modified Bessel function $ K_n(z) $

keywords:
Bessel function; complex zeros; finite element analysis; finite element approximation method; iterative optimisation scheme; modified; poles and zeros

rawtitle:
An application of the finite element approximation method to find the complex zeros of the modified {Bessel} function $ {K}_n(z) $

entry:
@Article{Leung:1979:AFE,
  author =       "K. V. Leung and S. S. Ghaderpanah",
  title =        "An application of the finite element approximation
                 method to find the complex zeros of the modified
                 {Bessel} function $ {K}_n(z) $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "148",
  pages =        "1299--1306",
  month =        oct,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33-04)",
  MRnumber =     "80e:65024",
  MRreviewer =   "R. P. Boas, Jr.",
  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 =   "C4140 (Linear algebra)",
  corpsource =   "Dept. of Computer Sci., Concordia Univ., Montreal,
                 Que., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; complex zeros; finite element
                 analysis; finite element approximation method;
                 iterative optimisation scheme; modified; poles and
                 zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Lindstrom:1979:MSM
author: F. T. Lindstrom
title: A Modified $3$-Spline Method for Evaluating the Euler Digamma Function
journal: j-TECHNOMETRICS
volume: 21
number: 3
pages: 307--311
month: aug
monthnumber: 8
year: 1979
CODEN: TCMTA2
DOI: https://doi.org/10.2307/1267752
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
bibdate: Sat Jun 21 13:18:50 MDT 2014
bibtimestamp: 2014.06.21 13:18:50 MDT
URL: http://www.jstor.org/stable/1267752
fjournal: Technometrics
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00401706.html
rawauthor: F. T. Lindstrom
rawtitle: A Modified $3$-Spline Method for Evaluating the {Euler} Digamma Function
bibsource:
http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254300; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib

entry:
@Article{Lindstrom:1979:MSM,
  author =       "F. T. Lindstrom",
  title =        "A Modified $3$-Spline Method for Evaluating the
                 {Euler} Digamma Function",
  journal =      j-TECHNOMETRICS,
  volume =       "21",
  number =       "3",
  pages =        "307--311",
  month =        aug,
  year =         "1979",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.2307/1267752",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Sat Jun 21 13:18:50 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00401706.html;
                 http://www.jstor.org/stable/i254300;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
  URL =          "http://www.jstor.org/stable/1267752",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}


bibtype: article
filename: elefunt.bib
label: Ling:1979:EWZ
author: C. B. Ling
title: Evaluation of Weierstrass Zeta Functions
journal: j-SIAM-REVIEW
volume: 21
number: 1
pages: 146--147
year: 1979
CODEN: SIREAD
DOI: https://doi.org/10.1137/1021020
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Fri Jun 21 11:25:02 MDT 2013
bibtimestamp: 2013.06.21 11:25:02 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
rawauthor: C. B. Ling
rawtitle: Evaluation of {Weierstrass} Zeta Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Ling:1979:EWZ,
  author =       "C. B. Ling",
  title =        "Evaluation of {Weierstrass} Zeta Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "21",
  number =       "1",
  pages =        "146--147",
  month =        "????",
  year =         "1979",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1021020",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "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",
}


bibtype: article
filename: elefunt.bib
label: Maurone:1979:ABD
author: Philip A. Maurone and Alain J. Phares
title: On the asymptotic behavior of the derivatives of Airy functions
journal: j-J-MATH-PHYS
volume: 20
number: 11
pages: 2191--2191
month: nov
monthnumber: 11
year: 1979
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.523997
ISSNL: 0022-2488 OR 00222488
MRclass: 33A60
MRnumber: 80j:33014
bibdate: Sat Oct 29 11:28:40 MDT 2011
bibtimestamp: 2011.10.29 11:28:40 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v20/i11/p2191_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
corpsource: Dept. of Phys., Villanova Univ., Villanova, PA, USA
journalURL: http://jmp.aip.org/
onlinedate: 29 July 2008
treatment: T Theoretical or Mathematical
rawauthor: Philip A. Maurone and Alain J. Phares
rawtitle: On the asymptotic behavior of the derivatives of {Airy} functions
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1975.bib

keywords:
Airy functions; angular momentum theory; asymptotic behavior; derivatives; functional analysis; noniterative functional solution; quantum theory; quark confinement; recursion relation

entry:
@Article{Maurone:1979:ABD,
  author =       "Philip A. Maurone and Alain J. Phares",
  title =        "On the asymptotic behavior of the derivatives of
                 {Airy} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "20",
  number =       "11",
  pages =        "2191--2191",
  month =        nov,
  year =         "1979",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.523997",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33A60",
  MRnumber =     "80j:33014",
  bibdate =      "Sat Oct 29 11:28:40 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/jmathphys1975.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v20/i11/p2191_s1",
  acknowledgement = ack-nhfb,
  classification = "A0230 (Function theory, analysis); A0365D
                 (Functional analytical methods in quantum theory);
                 A1235 (Composite models of particles)",
  corpsource =   "Dept. of Phys., Villanova Univ., Villanova, PA, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "Airy functions; angular momentum theory; asymptotic
                 behavior; derivatives; functional analysis;
                 noniterative functional solution; quantum theory; quark
                 confinement; recursion relation",
  onlinedate =   "29 July 2008",
  pagecount =    "1",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Morris:1979:DFR
author: Robert Morris
title: The Dilogarithm Function of a Real Argument
journal: j-MATH-COMPUT
volume: 33
number: 146
pages: 778--787
month: apr
monthnumber: 4
year: 1979
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1979-0521291-X
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33A70)
MRnumber: 80e:65025
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: algorithm theory; dilogarithm function; real argument
acknowledgement: ack-nhfb
classcodes: C4240 (Programming and algorithm theory)
corpsource: Bell Labs., Murray Hill, NJ, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Robert Morris
rawtitle: The Dilogarithm Function of a Real Argument
remark:
Fullerton: Relative errors down to $ 10^-24 $ for $ operatorname Li_2 (z) = - int _0^z frac log (1 - z)z d z $. $ operatorname Li_2 (z) $ is a form of Spence's integral.

entry:
@Article{Morris:1979:DFR,
  author =       "Robert Morris",
  title =        "The Dilogarithm Function of a Real Argument",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "778--787",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1979-0521291-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A70)",
  MRnumber =     "80e:65025",
  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,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4240 (Programming and algorithm theory)",
  corpsource =   "Bell Labs., Murray Hill, NJ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm theory; dilogarithm function; real
                 argument",
  received =     "22 May 1978",
  remark =       "Fullerton: Relative errors down to $ 10^{-24} $ for $
                 \operatorname {Li}_2 (z) = - \int_0^z \frac {\log (1 -
                 z)z} \, d z $. $ \operatorname {Li}_2 (z) $ is a form
                 of Spence's integral.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Pexton:1979:DRT
author: Robert L. Pexton and Arno D. Steiger
title: Degenerate roots of three transcendental equations involving spherical Bessel functions
journal: j-MATH-COMPUT
volume: 33
number: 147
pages: 1041--1048
month: jul
monthnumber: 7
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: loose microfiche suppl. 65H10 (65D20)
MRnumber: 80g:65057
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: function approximation; spherical Bessel function; transcendental equation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Lawrence Livermore Lab., Univ. of California, Livermore, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: Robert L. Pexton and Arno D. Steiger
rawtitle: Degenerate roots of three transcendental equations involving spherical {Bessel} functions
entry:
@Article{Pexton:1979:DRT,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Degenerate roots of three transcendental equations
                 involving spherical {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1041--1048",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "loose microfiche suppl. 65H10 (65D20)",
  MRnumber =     "80g:65057",
  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 =   "Lawrence Livermore Lab., Univ. of California,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function approximation; spherical Bessel function;
                 transcendental equation",
  treatment =    "A Application; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Phillips:1979:FAC
author: G. Phillips
title: A fast approximation to the complementary error function for use in fitting gamma-ray peaks
journal: j-NUCL-INSTR-METH
volume: 164
pages: 561--563
month: sep
monthnumber: 9
year: 1979
CODEN: NUIMAL
DOI: https://doi.org/10.1016/0029-554X(79)90094-6
ISSN: 0029-554x (print), 1878-3759 (electronic) OR 0029554x (print), 18783759 (electronic)
ISSNL: 0029-554X OR 0029554X
bibdate: Mon Oct 24 11:37:20 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
URL: http://adsabs.harvard.edu/abs/1979NucIM.164..561P
fjournal: Nuclear Instruments and Methods
acknowledgement: ack-nhfb
rawauthor: G. Phillips
rawtitle: A fast approximation to the complementary error function for use in fitting gamma-ray peaks
abstract:
A fast approximation to the complementary error function has been programmed and tested for use in the peak-shape function for fitting peaks in gamma-ray spectra. The function was compared for speed and accuracy on the NRL ASC 7 computer to the mathematical library version of the complementary error function. The approximation has resulted in a 50% time savings in the computer program HYPERMET which was developed at NRL for automatic analysis of gamma-ray spectra from germanium detectors.

rawabstract:
A fast approximation to the complementary error function has been programmed and tested for use in the peak-shape function for fitting peaks in gamma-ray spectra. The function was compared for speed and accuracy on the NRL ASC 7 computer to the mathematical library version of the complementary error function. The approximation has resulted in a 50\% time savings in the computer program HYPERMET which was developed at NRL for automatic analysis of gamma-ray spectra from germanium detectors.

entry:
@Article{Phillips:1979:FAC,
  author =       "G. Phillips",
  title =        "A fast approximation to the complementary error
                 function for use in fitting gamma-ray peaks",
  journal =      j-NUCL-INSTR-METH,
  volume =       "164",
  number =       "??",
  pages =        "561--563",
  month =        sep,
  year =         "1979",
  CODEN =        "NUIMAL",
  DOI =          "https://doi.org/10.1016/0029-554X(79)90094-6",
  ISSN =         "0029-554x (print), 1878-3759 (electronic)",
  ISSN-L =       "0029-554X",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://adsabs.harvard.edu/abs/1979NucIM.164..561P",
  abstract =     "A fast approximation to the complementary error
                 function has been programmed and tested for use in the
                 peak-shape function for fitting peaks in gamma-ray
                 spectra. The function was compared for speed and
                 accuracy on the NRL ASC 7 computer to the mathematical
                 library version of the complementary error function.
                 The approximation has resulted in a 50\% time savings
                 in the computer program HYPERMET which was developed at
                 NRL for automatic analysis of gamma-ray spectra from
                 germanium detectors.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nuclear Instruments and Methods",
}


bibtype: article
filename: elefunt.bib
label: Reeves:1979:AB
author: C. M. Reeves
title: Algorithm 9: Boyserf
journal: j-COMP-J
volume: 22
number: 1
pages: 89--90
month: feb
monthnumber: 2
year: 1979
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/22.1.86; https://doi.org/10.1093/comjnl/22.1.89
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Thu Oct 05 15:40:50 2000
bibtimestamp: 2000.10.05 15:40:50 ???
note: Reprinted from booktitle The Computer Bulletin, September 1964, p. 67.
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: C. M. Reeves
rawnote: Reprinted from \booktitle{The Computer Bulletin}, September 1964, p. 67.
rawtitle: Algorithm 9: {Boyserf}
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_22/Issue_01/; https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_22/Issue_01/tiff/89.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_22/Issue_01/tiff/90.tif

remark:
The boyserf() function computes $ F(x) = int _0^1 exp ( - x * t**2) d t $. A Maple simplification says that $ F(x) = sqrt pi erf (sqrt x) / (2 sqrt x) $.

entry:
@Article{Reeves:1979:AB,
  author =       "C. M. Reeves",
  title =        "Algorithm 9: {Boyserf}",
  journal =      j-COMP-J,
  volume =       "22",
  number =       "1",
  pages =        "89--90",
  month =        feb,
  year =         "1979",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/22.1.86;
                 https://doi.org/10.1093/comjnl/22.1.89",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Oct 05 15:40:50 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_22/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprinted from \booktitle{The Computer Bulletin},
                 September 1964, p. 67.",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_22/Issue_01/tiff/89.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_22/Issue_01/tiff/90.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  remark =       "The boyserf() function computes $ F(x) = \int_0^1 \exp
                 ( - x * t**2) \, d t $. A Maple simplification says
                 that $ F(x) = \sqrt {\pi } \erf (\sqrt {x}) / (2 \sqrt
                 {x}) $.",
}


bibtype: article
filename: elefunt.bib
label: Risch:1979:APE
author: Robert H. Risch
title: Algebraic properties of the elementary functions of analysis
journal: j-AM-J-MATH
volume: 101
number: 4
pages: 743--759
year: 1979
CODEN: AJMAAN
ISSN: 0002-9327 (print), 1080-6377 (electronic) OR 00029327 (print), 10806377 (electronic)
ISSNL: 0002-9327 OR 00029327
MRclass: 12H05
MRnumber: 81b:12029
MRreviewer: J. L. Johnson
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: American Journal of Mathematics
acknowledgement: ack-nhfb
rawauthor: Robert H. Risch
rawtitle: Algebraic properties of the elementary functions of analysis
entry:
@Article{Risch:1979:APE,
  author =       "Robert H. Risch",
  title =        "Algebraic properties of the elementary functions of
                 analysis",
  journal =      j-AM-J-MATH,
  volume =       "101",
  number =       "4",
  pages =        "743--759",
  year =         "1979",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327 (print), 1080-6377 (electronic)",
  ISSN-L =       "0002-9327",
  MRclass =      "12H05",
  MRnumber =     "81b:12029",
  MRreviewer =   "J. L. Johnson",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Mathematics",
}


bibtype: article
filename: elefunt.bib
label: Schulten:1979:AEC
author: Z. (or K. ??) Schulten and D. G. M. Anderson and R. G. Gordon
title: An Algorithm for the Evaluation of the Complex Airy Functions
journal: j-J-COMPUT-PHYS
volume: 31
number: 1
pages: 60--75
month: apr
monthnumber: 4
year: 1979
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(79)90062-7
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sat Oct 30 10:34:34 2010
bibtimestamp: 2010.10.30 10:34:34 ???
fjournal: Journal of Computational Physics
remark: Fullerton: Simple formulae over the whole complex plane are presented.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Z. (or K. ??) Schulten and D. G. M. Anderson and R. G. Gordon
rawtitle: An Algorithm for the Evaluation of the Complex {Airy} Functions
entry:
@Article{Schulten:1979:AEC,
  author =       "Z. (or K. ??) Schulten and D. G. M. Anderson and R. G.
                 Gordon",
  title =        "An Algorithm for the Evaluation of the Complex {Airy}
                 Functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "31",
  number =       "1",
  pages =        "60--75",
  month =        apr,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90062-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 10:34:34 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/",
  remark =       "Fullerton: Simple formulae over the whole complex
                 plane are presented.",
}


bibtype: article
filename: elefunt.bib
label: Smith:1979:ALL
author: David A. Smith and William F. Ford
title: Acceleration of Linear and Logarithmic Convergence
journal: j-SIAM-J-NUMER-ANAL
volume: 16
number: 2
pages: 223--240
month: apr
monthnumber: 4
year: 1979
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65B10
MRnumber: 82a:65012
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: David A. Smith and William F. Ford
rawtitle: Acceleration of Linear and Logarithmic Convergence
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database

entry:
@Article{Smith:1979:ALL,
  author =       "David A. Smith and William F. Ford",
  title =        "Acceleration of Linear and Logarithmic Convergence",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "16",
  number =       "2",
  pages =        "223--240",
  month =        apr,
  year =         "1979",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65B10",
  MRnumber =     "82a:65012",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: article
filename: elefunt.bib
label: Takemasa:1979:CFC
author: T. Takemasa and T. Tamura and H. H. Wolter
title: Coulomb Functions with Complex Angular Momenta
journal: j-COMP-PHYS-COMM
volume: 17
number: 4
pages: 351--355
month: jul
monthnumber: 7
year: 1979
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(79)90097-3
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Oct 30 11:14:02 2010
bibtimestamp: 2010.10.30 11:14:02 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: T. Takemasa and T. Tamura and H. H. Wolter
rawtitle: {Coulomb} Functions with Complex Angular Momenta
remark:
Fullerton: Description of program CCOULOM, which works only in the part of the $ (rho , eta ) $-plane where $ eta ^2 ll rho $ and $ | ell |^2 ll rho $.

entry:
@Article{Takemasa:1979:CFC,
  author =       "T. Takemasa and T. Tamura and H. H. Wolter",
  title =        "{Coulomb} Functions with Complex Angular Momenta",
  journal =      j-COMP-PHYS-COMM,
  volume =       "17",
  number =       "4",
  pages =        "351--355",
  month =        jul # "\slash " # aug,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90097-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 11:14:02 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",
  remark =       "Fullerton: Description of program CCOULOM, which works
                 only in the part of the $ (\rho, \eta) $-plane where $
                 \eta^2 \ll \rho $ and $ | \ell |^2 \ll \rho $.",
}


bibtype: article
filename: elefunt.bib
label: Temme:1979:AAP
author: N. M. Temme
journal: j-J-COMPUT-PHYS
volume: 32
number: 2
pages: 270--279
month: aug
monthnumber: 8
year: 1979
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(79)90134-7
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sat Oct 30 11:23:13 2010
bibtimestamp: 2010.10.30 11:23:13 ???
fjournal: Journal of Computational Physics
remark: Fullerton: An adjustable-accuracy 100 line Algol procedure is discussed.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: N. M. Temme
title:
An Algorithm with ALGOL 60 Program for the Computation of the Zeros of Ordinary Bessel Functions and those of their Derivatives

rawtitle:
An Algorithm with {ALGOL 60} Program for the Computation of the Zeros of Ordinary {Bessel} Functions and those of their Derivatives

entry:
@Article{Temme:1979:AAP,
  author =       "N. M. Temme",
  title =        "An Algorithm with {ALGOL 60} Program for the
                 Computation of the Zeros of Ordinary {Bessel} Functions
                 and those of their Derivatives",
  journal =      j-J-COMPUT-PHYS,
  volume =       "32",
  number =       "2",
  pages =        "270--279",
  month =        aug,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90134-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 11:23:13 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/",
  remark =       "Fullerton: An adjustable-accuracy 100 line Algol
                 procedure is discussed.",
}


bibtype: article
filename: elefunt.bib
label: Temme:1979:AEI
author: N. M. Temme
title: The asymptotic expansion of the incomplete gamma functions
journal: j-SIAM-J-MATH-ANA
volume: 10
number: 4
pages: 757--766
month: jul
monthnumber: 7
year: 1979
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33A15
MRnumber: 80i:33002
MRreviewer: E. Rieksti\lfhook n{\v{s}}
bibdate: Sun Nov 28 19:22:16 MST 2010
bibtimestamp: 2010.11.28 19:22:16 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: N. M. Temme
rawtitle: The asymptotic expansion of the incomplete gamma functions
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMA/10/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib

entry:
@Article{Temme:1979:AEI,
  author =       "N. M. Temme",
  title =        "The asymptotic expansion of the incomplete gamma
                 functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "10",
  number =       "4",
  pages =        "757--766",
  month =        jul,
  year =         "1979",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A15",
  MRnumber =     "80i:33002",
  MRreviewer =   "E. Rieksti\lfhook n{\v{s}}",
  bibdate =      "Sun Nov 28 19:22:16 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/10/4;
                 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",
}


bibtype: article
filename: elefunt.bib
label: Terras:1979:DIG
author: Riho Terras
title: The determination of incomplete gamma functions through analytic integration
journal: j-J-COMPUT-PHYS
volume: 31
number: 1
pages: 146--151
month: apr
monthnumber: 4
year: 1979
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(79)90066-4
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:33 MST 2012
bibtimestamp: 2012.01.01 09:15:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999179900664
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Riho Terras
rawtitle: The determination of incomplete gamma functions through analytic integration
entry:
@Article{Terras:1979:DIG,
  author =       "Riho Terras",
  title =        "The determination of incomplete gamma functions
                 through analytic integration",
  journal =      j-J-COMPUT-PHYS,
  volume =       "31",
  number =       "1",
  pages =        "146--151",
  month =        apr,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90066-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:33 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/0021999179900664",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Thacher:1979:NBR
author: Henry C. Thacher, Jr.
title: New Backward Recurrences for Bessel Functions
journal: j-MATH-COMPUT
volume: 33
number: 146
pages: 744--764
month: apr
monthnumber: 4
year: 1979
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33A40)
MRnumber: 81b:65019
MRreviewer: R. G. Langebartel
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: backward recurrences; Bessel functions; converges
acknowledgement: ack-nhfb
classcodes: C1120 (Mathematical analysis)
corpsource: Dept. of Computer Sci., Univ. of Kentucky, Lexington, KY, USA
journalURL: http://www.ams.org/mcom/
treatment: N New Development; T Theoretical or Mathematical
rawauthor: Henry C. {Thacher, Jr.}
rawtitle: New Backward Recurrences for {Bessel} Functions
entry:
@Article{Thacher:1979:NBR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "New Backward Recurrences for {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "744--764",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A40)",
  MRnumber =     "81b:65019",
  MRreviewer =   "R. G. Langebartel",
  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 =   "C1120 (Mathematical analysis)",
  corpsource =   "Dept. of Computer Sci., Univ. of Kentucky, Lexington,
                 KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "backward recurrences; Bessel functions; converges",
  treatment =    "N New Development; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Amos:1980:CEI
author: Donald E. Amos
title: Computation of Exponential Integrals
journal: j-TOMS
volume: 6
number: 3
pages: 365--377
month: sep
monthnumber: 9
year: 1980
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355900.355908
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D30 (68-04)
MRnumber: 82b:65011
bibdate: Mon Aug 29 10:57:24 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1994.08.29 10:57:24 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: exponential integral; Miller algorithm; recursion; Taylor series
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
reviewer: M. M. Chawla
rawauthor: Donald E. Amos
rawtitle: Computation of Exponential Integrals
entry:
@Article{Amos:1980:CEI,
  author =       "Donald E. Amos",
  title =        "Computation of Exponential Integrals",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "365--377",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355908",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (68-04)",
  MRnumber =     "82b:65011",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "exponential integral; Miller algorithm; recursion;
                 Taylor series",
  reviewer =     "M. M. Chawla",
}


bibtype: article
filename: elefunt.bib
label: Brent:1980:SNA
author: Richard P. Brent and Edwin M. McMillan
title: Some new algorithms for high-precision computation of Euler's constant
journal: j-MATH-COMPUT
volume: 34
number: 149
pages: 305--312
month: jan
monthnumber: 1
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 10-04 (10A40 68C05)
MRnumber: 82g:10002
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; computation; Euler's constant; function evaluation; high precision
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Univ. of California, Berkeley, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: N New Development; T Theoretical or Mathematical
rawauthor: Richard P. Brent and Edwin M. McMillan
rawtitle: Some new algorithms for high-precision computation of {Euler}'s constant
remark:
Fullerton: Calculation to 30,100 places is discussed, but only a 3-digit value appears in the paper.

entry:
@Article{Brent:1980:SNA,
  author =       "Richard P. Brent and Edwin M. McMillan",
  title =        "Some new algorithms for high-precision computation of
                 {Euler}'s constant",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "149",
  pages =        "305--312",
  month =        jan,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "10-04 (10A40 68C05)",
  MRnumber =     "82g:10002",
  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 =   "Univ. of California, Berkeley, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; computation; Euler's constant;
                 function evaluation; high precision",
  remark =       "Fullerton: Calculation to 30,100 places is discussed,
                 but only a 3-digit value appears in the paper.",
  treatment =    "N New Development; T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Brent:1980:UAE
author: R. P. Brent
title: Unrestricted Algorithms for Elementary and Special Functions
crossref: Lavington:1980:IPP
pages: 613--619
year: 1980
bibdate: Thu Sep 01 11:55:31 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 11:55:31 ???
URL: http://maths-people.anu.edu.au/~brent/pub/pub052.html
acknowledgement: ack-nj
rawauthor: R. P. Brent
rawtitle: Unrestricted Algorithms for Elementary and Special Functions
remark:
From the author's Web site: Errata for original version:par Page 615, remove the absolute value signs in equation (13) and the following paragraph (x should be large and positive here).par Page 616, second half of equation (26): insert a minus sign after the equals sign.par Page 617, equation (39): delete `` / j ! ''.par Page 617, equation (42): the assumption ``j < k'' should be added. Also, the contour C needs to be enlarged slightly.par Page 617, left-hand-side of equation (44): replace ``Sj,k'' by ``S2j,k''.par Page 617, ten lines after equation (44): replace ``O(jn2)'' by ``O(j2n)''.

entry:
@InProceedings{Brent:1980:UAE,
  author =       "R. P. Brent",
  title =        "Unrestricted Algorithms for Elementary and Special
                 Functions",
  crossref =     "Lavington:1980:IPP",
  pages =        "613--619",
  year =         "1980",
  bibdate =      "Thu Sep 01 11:55:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://maths-people.anu.edu.au/~brent/pub/pub052.html",
  acknowledgement = ack-nj,
  remark =       "From the author's Web site: Errata for original
                 version:\par Page 615, remove the absolute value signs
                 in equation (13) and the following paragraph (x should
                 be large and positive here).\par

                 Page 616, second half of equation (26): insert a minus
                 sign after the equals sign.\par

                 Page 617, equation (39): delete `` / j ! ''.\par

                 Page 617, equation (42): the assumption ``j < k''
                 should be added. Also, the contour C needs to be
                 enlarged slightly.\par

                 Page 617, left-hand-side of equation (44): replace
                 ``Sj,k'' by ``S2j,k''.\par

                 Page 617, ten lines after equation (44): replace
                 ``O(jn2)'' by ``O(j2n)''.",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:1980:GEA
author: C. Brezinski
title: A general extrapolation algorithm
journal: j-NUM-MATH
volume: 35
number: 2
pages: 175--187
month: jun
monthnumber: 6
year: 1980
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65B05
MRnumber: 81j:65015
MRreviewer: L. Fox
bibdate: Mon May 26 11:49:34 MDT 1997
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: UER IEEA, Univ. de Lille 1, Villeneuve d'Ascq, France
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: C. Brezinski
rawtitle: A general extrapolation algorithm
keywords:
convergence acceleration; extrapolation; extrapolation algorithm; linear extrapolation; rational extrapolation; recursive algorithm; sequence transformations

entry:
@Article{Brezinski:1980:GEA,
  author =       "C. Brezinski",
  title =        "A general extrapolation algorithm",
  journal =      j-NUM-MATH,
  volume =       "35",
  number =       "2",
  pages =        "175--187",
  month =        jun,
  year =         "1980",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B05",
  MRnumber =     "81j:65015",
  MRreviewer =   "L. Fox",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation)",
  corpsource =   "UER IEEA, Univ. de Lille 1, Villeneuve d'Ascq,
                 France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration; extrapolation; extrapolation
                 algorithm; linear extrapolation; rational
                 extrapolation; recursive algorithm; sequence
                 transformations",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Char:1980:SCF
author: Bruce W. Char
title: On Stieltjes' continued fraction for the gamma function
journal: j-MATH-COMPUT
volume: 34
number: 150
pages: 547--551
month: apr
monthnumber: 4
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05 (65D20)
MRnumber: 81b:65008
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: The first 41 coefficients to 40 digits are given.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Bruce W. Char
rawtitle: On {Stieltjes}' continued fraction for the gamma function
entry:
@Article{Char:1980:SCF,
  author =       "Bruce W. Char",
  title =        "On {Stieltjes}' continued fraction for the gamma
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "150",
  pages =        "547--551",
  month =        apr,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "81b:65008",
  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 first 41 coefficients to 40 digits are
                 given.",
}


bibtype: article
filename: elefunt.bib
label: Clenshaw:1980:UAE
author: C. W. Clenshaw and Frank W. J. Olver
title: An unrestricted algorithm for the exponential function
journal: j-SIAM-J-NUMER-ANAL
volume: 17
number: 2
pages: 310--331
month: apr
monthnumber: 4
year: 1980
CODEN: SJNAAM
DOI: https://doi.org/10.1137/0717026
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 65D20
MRnumber: 567276
MRreviewer: A. M. Cohen
bibdate: Sun Nov 12 06:18:24 2023
bibtimestamp: 2023.11.12 06:18:24 ???
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: C. W. Clenshaw and Frank W. J. Olver
rawtitle: An unrestricted algorithm for the exponential function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
An algorithm is presented for the computation of the exponential function of real argument. There are no restrictions on the range of the argument or on the precision that may be demanded in the results.

authordates:
Charles William Clenshaw (15 March 1926--23 September 2004); Frank William John Olver (15 December 1924--23 April 2013)

rawabstract:
An algorithm is presented for the computation of the exponential function of real argument. There are no restrictions on the range of the argument or on the precision that may be demanded in the results.

entry:
@Article{Clenshaw:1980:UAE,
  author =       "C. W. Clenshaw and Frank W. J. Olver",
  title =        "An unrestricted algorithm for the exponential
                 function",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "17",
  number =       "2",
  pages =        "310--331",
  month =        apr,
  year =         "1980",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0717026",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65D20",
  MRnumber =     "567276",
  MRreviewer =   "A. M. Cohen",
  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/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm is presented for the computation of the
                 exponential function of real argument. There are no
                 restrictions on the range of the argument or on the
                 precision that may be demanded in the results.",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004); Frank William John Olver (15 December 1924--23
                 April 2013)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}


bibtype: book
filename: elefunt.bib
label: Cody:1980:SME
author: William J. Cody, Jr. and William Waite
title: Software Manual for the Elementary Functions
publisher: pub-PH
address: pub-PH:adr
pages: x + 269
year: 1980
ISBN: 0-13-822064-6 OR 0138220646
ISBN13: 978-0-13-822064-8 OR 9780138220648
LCCN: QA331 .C635 1980
bibdate: Tue Dec 14 23:28:38 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 1993.12.14 23:28:38 ???
acknowledgement: ack-nhfb
rawauthor: William J. {Cody, Jr.} and William Waite
rawtitle: Software Manual for the Elementary Functions
TOC:
Preface / ix 1. Introduction / 1 2. Preliminaries / 3 3. Performance Testing / 11 4. SQRT / 17 a. General Discussion / 17 b. Flow Chart for SQRT(X) / 18 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 19 d. Implementation Notes, Binary Floating-Point Machines / 23 e. Implementation Notes, Non-Binary Floating-Point Machines / 25 f. Testing / 28 5. ALOG/ALOG10 / 35 a. General Discussion / 35 b. Flow Chart for ALOG(X)/ALOG10(X) / 37 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 38 d. Implementation Notes, Non-Decimal Floating-Point Machines / 42 e. Implementation Notes, Decimal Floating-Point Machines / 46 f. Testing / 49 6. EXP / 60 a. General Discussion / 60 b. Flow Chart for EXP(X) / 62 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 63 d. Implementation Notes, Non-Decimal Floating-Point Machines / 67 e. Implementation Notes, Decimal Floating-Point Machines / 71 f. Testing / 75 7. POWER (**) / 84 a. General Discussion / 84 b. Flow Chart for POWER(X,Y) / 88 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 90 d. Implementation Notes, Non-Decimal Floating-Point Machines / 97 e. Implementation Notes, Decimal Floating-Point Machines / 106 f. Testing / 113 8. SIN/COS / 125 a. General Discussion / 125 b. Flow Chart for SIN(X)/COS(X) / 127 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 129 d. Implementation Notes, All Floating-Point Machines / 134 e. Testing / 139 9. TAN/COT / 150 a. General Discussion / 150 b. Flow Chart for TAN(X)/COTAN(X) / 152 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 154 d. Implementation Notes, All Floating-Point Machines / 159 e. Testing / 164 10. ASIN/ACOS / 174 a. General Discuss i on / 174 b. Flow Chart for AS IN(X)/ACOS(X) / 176 c. Implementation Not es, Non-Decimal Fixed-Point Machines / 177 d. Implementation Notes, All Floating-Point Machines / 181 e. Testing / 185 11. ATAN/ATAN2 / 194 a. General Discussion / 194 b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 198 d. Implementation Notes, All Floating-Point Machines / 203 e. Testing / 207 12. SINH/COSH / 217 a. General Discussion / 217 b. Flow Chart for SINH(X)/COSH(X) / 220 c. Implementation Notes, Non-Decimal Fixed-Point Machines / 221 d. Implementation Notes, All Floating-Point Machines / 225 e. Testing / 229

shortTOC:
Preface / ix 1. Introduction / 1 2. Preliminaries / 3 3. Performance Testing / 11 4. SQRT / 17 5. ALOG/ALOG10 / 35 6. EXP / 60 7. POWER (**) / 84 8. SIN/COS / 125 9. TAN/COT / 150 10. ASIN/ACOS / 174 11. ATAN/ATAN2 / 194 12. SINH/COSH / 217

rawshortTOC:
Preface / ix \\ 1. Introduction / 1 \\ 2. Preliminaries / 3 \\ 3. Performance Testing / 11 \\ 4. SQRT / 17 \\ 5. ALOG/ALOG10 / 35 \\ 6. EXP / 60 \\ 7. POWER (**) / 84 \\ 8. SIN/COS / 125 \\ 9. TAN/COT / 150 \\ 10. ASIN/ACOS / 174 \\ 11. ATAN/ATAN2 / 194 \\ 12. SINH/COSH / 217

rawTOC:
Preface / ix \\ 1. Introduction / 1 \\ 2. Preliminaries / 3 \\ 3. Performance Testing / 11 \\ 4. SQRT / 17 \\ a. General Discussion / 17 \\ b. Flow Chart for SQRT(X) / 18 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 19 \\ d. Implementation Notes, Binary Floating-Point Machines / 23 \\ e. Implementation Notes, Non-Binary Floating-Point Machines / 25 \\ f. Testing / 28 \\ 5. ALOG/ALOG10 / 35 \\ a. General Discussion / 35 \\ b. Flow Chart for ALOG(X)/ALOG10(X) / 37 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 38 \\ d. Implementation Notes, Non-Decimal Floating-Point Machines / 42 \\ e. Implementation Notes, Decimal Floating-Point Machines / 46 \\ f. Testing / 49 \\ 6. EXP / 60 \\ a. General Discussion / 60 \\ b. Flow Chart for EXP(X) / 62 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 63 \\ d. Implementation Notes, Non-Decimal Floating-Point Machines / 67 \\ e. Implementation Notes, Decimal Floating-Point Machines / 71 \\ f. Testing / 75 \\ 7. POWER (**) / 84 \\ a. General Discussion / 84 \\ b. Flow Chart for POWER(X,Y) / 88 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 90 \\ d. Implementation Notes, Non-Decimal Floating-Point Machines / 97 \\ e. Implementation Notes, Decimal Floating-Point Machines / 106 \\ f. Testing / 113 \\ 8. SIN/COS / 125 \\ a. General Discussion / 125 \\ b. Flow Chart for SIN(X)/COS(X) / 127 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 129 \\ d. Implementation Notes, All Floating-Point Machines / 134 \\ e. Testing / 139 \\ 9. TAN/COT / 150 \\ a. General Discussion / 150 \\ b. Flow Chart for TAN(X)/COTAN(X) / 152 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 154 \\ d. Implementation Notes, All Floating-Point Machines / 159 \\ e. Testing / 164 \\ 10. ASIN/ACOS / 174 \\ a. General Discuss i on / 174 \\ b. Flow Chart for AS IN(X)/ACOS(X) / 176 \\ c. Implementation Not es, Non-Decimal Fixed-Point Machines / 177 \\ d. Implementation Notes, All Floating-Point Machines / 181 \\ e. Testing / 185 \\ 11. ATAN/ATAN2 / 194 \\ a. General Discussion / 194 \\ b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 198 \\ d. Implementation Notes, All Floating-Point Machines / 203 \\ e. Testing / 207 \\ 12. SINH/COSH / 217 \\ a. General Discussion / 217 \\ b. Flow Chart for SINH(X)/COSH(X) / 220 \\ c. Implementation Notes, Non-Decimal Fixed-Point Machines / 221 \\ d. Implementation Notes, All Floating-Point Machines / 225 \\ e. Testing / 229

entry:
@Book{Cody:1980:SME,
  author =       "William J. {Cody, Jr.} and William Waite",
  title =        "Software Manual for the Elementary Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 269",
  year =         "1980",
  ISBN =         "0-13-822064-6",
  ISBN-13 =      "978-0-13-822064-8",
  LCCN =         "QA331 .C635 1980",
  bibdate =      "Tue Dec 14 23:28:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Preface / ix \\
                 1. Introduction / 1 \\
                 2. Preliminaries / 3 \\
                 3. Performance Testing / 11 \\
                 4. SQRT / 17 \\
                 5. ALOG/ALOG10 / 35 \\
                 6. EXP / 60 \\
                 7. POWER (**) / 84 \\
                 8. SIN/COS / 125 \\
                 9. TAN/COT / 150 \\
                 10. ASIN/ACOS / 174 \\
                 11. ATAN/ATAN2 / 194 \\
                 12. SINH/COSH / 217",
  tableofcontents = "Preface / ix \\
                 1. Introduction / 1 \\
                 2. Preliminaries / 3 \\
                 3. Performance Testing / 11 \\
                 4. SQRT / 17 \\
                 a. General Discussion / 17 \\
                 b. Flow Chart for SQRT(X) / 18 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 19 \\
                 d. Implementation Notes, Binary Floating-Point Machines
                 / 23 \\
                 e. Implementation Notes, Non-Binary Floating-Point
                 Machines / 25 \\
                 f. Testing / 28 \\
                 5. ALOG/ALOG10 / 35 \\
                 a. General Discussion / 35 \\
                 b. Flow Chart for ALOG(X)/ALOG10(X) / 37 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 38 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 42 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 46 \\
                 f. Testing / 49 \\
                 6. EXP / 60 \\
                 a. General Discussion / 60 \\
                 b. Flow Chart for EXP(X) / 62 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 63 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 67 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 71 \\
                 f. Testing / 75 \\
                 7. POWER (**) / 84 \\
                 a. General Discussion / 84 \\
                 b. Flow Chart for POWER(X,Y) / 88 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 90 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 97 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 106 \\
                 f. Testing / 113 \\
                 8. SIN/COS / 125 \\
                 a. General Discussion / 125 \\
                 b. Flow Chart for SIN(X)/COS(X) / 127 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 129 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 134 \\
                 e. Testing / 139 \\
                 9. TAN/COT / 150 \\
                 a. General Discussion / 150 \\
                 b. Flow Chart for TAN(X)/COTAN(X) / 152 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 154 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 159 \\
                 e. Testing / 164 \\
                 10. ASIN/ACOS / 174 \\
                 a. General Discuss i on / 174 \\
                 b. Flow Chart for AS IN(X)/ACOS(X) / 176 \\
                 c. Implementation Not es, Non-Decimal Fixed-Point
                 Machines / 177 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 181 \\
                 e. Testing / 185 \\
                 11. ATAN/ATAN2 / 194 \\
                 a. General Discussion / 194 \\
                 b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 198 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 203 \\
                 e. Testing / 207 \\
                 12. SINH/COSH / 217 \\
                 a. General Discussion / 217 \\
                 b. Flow Chart for SINH(X)/COSH(X) / 220 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 221 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 225 \\
                 e. Testing / 229",
}


bibtype: article
filename: elefunt.bib
label: Coleman:1980:FSB
author: J. P. Coleman
title: A Fortran subroutine for the Bessel function $ J_n(x) $ of order $0$ to $ 10 $
journal: j-COMP-PHYS-COMM
volume: 21
number: 1
pages: 109--118
day: 1
month: dec
monthnumber: 12
year: 1980
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(80)90080-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 06:01:19 MST 2012
bibtimestamp: 2012.02.13 06:01:19 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465580900806
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. P. Coleman
rawtitle: A {Fortran} subroutine for the {Bessel} function {$ J_n(x) $} of order $0$ to $ 10 $
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib

entry:
@Article{Coleman:1980:FSB,
  author =       "J. P. Coleman",
  title =        "A {Fortran} subroutine for the {Bessel} function {$
                 J_n(x) $} of order $0$ to $ 10 $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "21",
  number =       "1",
  pages =        "109--118",
  day =          "1",
  month =        dec,
  year =         "1980",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(80)90080-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:19 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465580900806",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Delahaye:1980:RNA
author: J. P. Delahaye and B. Germain-Bonne
journal: j-NUM-MATH
volume: 35
number: 4
pages: 443--457
month: nov
monthnumber: 11
year: 1980
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65B99 (40A99)
MRnumber: 81k:65007
MRreviewer: Claude Brezinski
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
language: French
acknowledgement: ack-nhfb
corpsource: Univ. des Sci. et Tech. de Lille I, Villeneuve d'Ascq, France
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: J. P. Delahaye and B. Germain-Bonne
title:
Resultats negatifs en acceleration de la convergence. (French) [Negative results in convergence acceleration]

keywords:
acceleration; algorithm; approximation theory; computational complexity; convergence; convergence acceleration; convergence of numerical methods

rawtitle:
{R}{\'e}sultats n{\'e}gatifs en acc{\'e}l{\'e}ration de la convergence. ({French}) [{Negative} results in convergence acceleration]

entry:
@Article{Delahaye:1980:RNA,
  author =       "J. P. Delahaye and B. Germain-Bonne",
  title =        "{R}{\'e}sultats n{\'e}gatifs en acc{\'e}l{\'e}ration
                 de la convergence. ({French}) [{Negative} results in
                 convergence acceleration]",
  journal =      j-NUM-MATH,
  volume =       "35",
  number =       "4",
  pages =        "443--457",
  month =        nov,
  year =         "1980",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B99 (40A99)",
  MRnumber =     "81k:65007",
  MRreviewer =   "Claude Brezinski",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  corpsource =   "Univ. des Sci. et Tech. de Lille I, Villeneuve d'Ascq,
                 France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "acceleration; algorithm; approximation theory;
                 computational complexity; convergence; convergence
                 acceleration; convergence of numerical methods",
  language =     "French",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Ditkin:1980:CSF
author: V. A. Ditkin and K. A. Karpov and M. K. Kerimov
title: The computation of special functions
journal: j-USSR-COMP-MATH-MATH-PHYS
volume: 20
number: 5
pages: 3--12
year: 1980
CODEN: CMMPA9
ISSN: 0041-5553, 0502-9902 OR 00415553, 05029902
ISSNL: 0041-5553 OR 00415553
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: U.S.S.R. Computational Mathematics and Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00415553
journalabr: USSR Comput. Math. Math. Phys
rawauthor: V. A. Ditkin and K. A. Karpov and M. K. Kerimov
rawtitle: The computation of special functions
subject:
G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Ditkin:1980:CSF,
  author =       "V. A. Ditkin and K. A. Karpov and M. K. Kerimov",
  title =        "The computation of special functions",
  journal =      j-USSR-COMP-MATH-MATH-PHYS,
  volume =       "20",
  number =       "5",
  pages =        "3--12",
  year =         "1980",
  CODEN =        "CMMPA9",
  ISSN =         "0041-5553, 0502-9902",
  ISSN-L =       "0041-5553",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.2.1; G.1.2",
  CRclass =      "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Generating functions; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "U.S.S.R. Computational Mathematics and Mathematical
                 Physics",
  genterm =      "algorithms; design",
  guideno =      "09092",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00415553",
  journalabr =   "USSR Comput. Math. Math. Phys",
  jrldate =      "1980",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Eckhardt:1980:AWE
author: Ulrich Eckhardt
title: Algorithm 549: Weierstrass' Elliptic Functions [S21]
journal: j-TOMS
volume: 6
number: 1
pages: 112--120
month: mar
monthnumber: 3
year: 1980
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355873.355884
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Aug 29 10:31:24 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.29 10:31:24 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: Weierstrass' elliptic functions
remark: Fullerton: A complex FORTRAN algorithm with accuracy down to $ 10^-18 $ is given
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ulrich Eckhardt
rawtitle: {Algorithm 549}: {Weierstrass}' Elliptic Functions [{S21}]
entry:
@Article{Eckhardt:1980:AWE,
  author =       "Ulrich Eckhardt",
  title =        "{Algorithm 549}: {Weierstrass}' Elliptic Functions
                 [{S21}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "112--120",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355884",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:31:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Weierstrass' elliptic functions",
  remark =       "Fullerton: A complex FORTRAN algorithm with accuracy
                 down to $ 10^{-18} $ is given",
}


bibtype: article
filename: elefunt.bib
label: Fransen:1980:HPV
author: Arne Fransen and Staffan Wrigge
title: High-precision values of the gamma function and of some related coefficients
journal: j-MATH-COMPUT
volume: 34
number: 150
pages: 553--566
month: apr
monthnumber: 4
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05 (65D20)
MRnumber: 81f:65004
MRreviewer: F. W. J. Olver
bibdate: Sat Apr 01 10:12:58 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 2000.04.01 10:12:58 ???
note: See addendum and corrigendum cite Fransen:1981:ACH.
fjournal: Mathematics of Computation
remark: Fullerton: 80D values of coefficients in the Taylor series for $ Gamma ^m(s + x) $ are given.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Arne Frans{\'e}n and Staffan Wrigge
rawnote: See addendum and corrigendum \cite{Fransen:1981:ACH}.
rawtitle: High-precision values of the gamma function and of some related coefficients
entry:
@Article{Fransen:1980:HPV,
  author =       "Arne Frans{\'e}n and Staffan Wrigge",
  title =        "High-precision values of the gamma function and of
                 some related coefficients",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "150",
  pages =        "553--566",
  month =        apr,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "81f:65004",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Sat Apr 01 10:12:58 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  note =         "See addendum and corrigendum
                 \cite{Fransen:1981:ACH}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 80D values of coefficients in the Taylor
                 series for $ \Gamma^m(s + x) $ are given.",
}


bibtype: techreport
filename: elefunt.bib
label: Fullerton:1980:BEM
author: L. W. Fullerton
title: A Bibliography on the Evaluation of Mathematical Functions
type: Technical report
number: TM 80-1274-4 and CSTR 86
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
pages: 553--566
month: sep
monthnumber: 9
year: 1980
bibdate: Sat Feb 05 17:39:14 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.02.05 17:39:14 ???
acknowledgement: ack-nhfb
rawauthor: L. W. Fullerton
rawtitle: A Bibliography on the Evaluation of Mathematical Functions
entry:
@TechReport{Fullerton:1980:BEM,
  author =       "L. W. Fullerton",
  title =        "A Bibliography on the Evaluation of Mathematical
                 Functions",
  type =         "Technical report",
  number =       "TM 80-1274-4 and CSTR 86",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  month =        sep,
  year =         "1980",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gargantini:1980:PSR
author: Irene Gargantini
title: Parallel Square-Root Iterations for Multiple Roots
journal: j-COMPUT-MATH-APPL
volume: 6
number: 3
pages: 279--288
year: 1980
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:19 MST 2017
bibtimestamp: 2017.03.01 18:51:19 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122180900358
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-jr
journalURL: http://www.sciencedirect.com/science/journal/08981221/
rawauthor: Irene Gargantini
rawtitle: Parallel Square-Root Iterations for Multiple Roots
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gargantini:1980:PSR,
  author =       "Irene Gargantini",
  title =        "Parallel Square-Root Iterations for Multiple Roots",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "3",
  pages =        "279--288",
  month =        "????",
  year =         "1980",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122180900358",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}


bibtype: unpublished
filename: elefunt.bib
label: Kahan:1980:SPI
author: W. Kahan
title: Software $ sqrt x $ for the Proposed IEEE Floating-Point Standard
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
day: 25
month: aug
monthnumber: 8
year: 1980
bibdate: Mon Apr 25 18:24:02 2005
bibtimestamp: 2005.04.25 18:24:02 ???
note: Manuscript
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Manuscript
rawtitle: Software $ \sqrt x $ for the Proposed {IEEE Floating-Point Standard}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.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

entry:
@Unpublished{Kahan:1980:SPI,
  author =       "W. Kahan",
  title =        "Software $ \sqrt x $ for the Proposed {IEEE
                 Floating-Point Standard}",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "????",
  day =          "25",
  month =        aug,
  year =         "1980",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.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",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  mynote =       "Dated August 25 1980",
}


bibtype: article
filename: elefunt.bib
label: Kasperkovitz:1980:AAM
author: P. Kasperkovitz
title: Asymptotic approximations for modified Bessel functions
journal: j-J-MATH-PHYS
volume: 21
number: 1
pages: 6--13
month: jan
monthnumber: 1
year: 1980
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.524310
ISSNL: 0022-2488 OR 00222488
MRclass: 33A40
MRnumber: 81a:33012
MRreviewer: N. Hayek Calil
bibdate: Sat Oct 29 18:18:22 MDT 2011
bibtimestamp: 2011.10.29 18:18:22 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v21/i1/p6_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
onlinedate: 21 July 2008
rawauthor: P. Kasperkovitz
rawtitle: Asymptotic approximations for modified {Bessel} functions
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib

entry:
@Article{Kasperkovitz:1980:AAM,
  author =       "P. Kasperkovitz",
  title =        "Asymptotic approximations for modified {Bessel}
                 functions",
  journal =      j-J-MATH-PHYS,
  volume =       "21",
  number =       "1",
  pages =        "6--13",
  month =        jan,
  year =         "1980",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.524310",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33A40",
  MRnumber =     "81a:33012",
  MRreviewer =   "N. Hayek Calil",
  bibdate =      "Sat Oct 29 18:18:22 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/jmathphys1980.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v21/i1/p6_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "21 July 2008",
  pagecount =    "8",
}


bibtype: article
filename: elefunt.bib
label: Langebartel:1980:FER
author: R. G. Langebartel
title: Fourier expansions of rational fractions of elliptic integrals and Jacobian elliptic functions
journal: j-SIAM-J-MATH-ANA
volume: 11
number: 3
pages: 506--513
month: may
monthnumber: 5
year: 1980
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 42A16 (33A25)
MRnumber: 81e:42008
MRreviewer: R. C. Varma
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: R. G. Langebartel
rawtitle: {Fourier} expansions of rational fractions of elliptic integrals and {Jacobian} elliptic functions
entry:
@Article{Langebartel:1980:FER,
  author =       "R. G. Langebartel",
  title =        "{Fourier} expansions of rational fractions of elliptic
                 integrals and {Jacobian} elliptic functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "11",
  number =       "3",
  pages =        "506--513",
  month =        may,
  year =         "1980",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "42A16 (33A25)",
  MRnumber =     "81e:42008",
  MRreviewer =   "R. C. Varma",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: inproceedings
filename: elefunt.bib
label: Maksymiv:1980:APT
author: E. M. Maksymiv
booktitle: Differentsialnye Uravneniya i ikh Prilozhen
title: Approximate properties of Thiele's formula in a class of elementary functions. (Russian)
volume: 141
publisher: Vestnik L'vov. Politekhn. Inst.
address: L'vov, USSR
pages: 55--56
year: 1980
MRclass: 119.65D20
MRnumber: 81i:65021
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: E. M. Maksymiv
rawbooktitle: Differentsialnye Uravneniya i ikh Prilozhen
rawtitle: Approximate properties of {Thiele}'s formula in a class of elementary functions. ({Russian})
entry:
@InProceedings{Maksymiv:1980:APT,
  author =       "E. M. Maksymiv",
  booktitle =    "Differentsialnye Uravneniya i ikh Prilozhen",
  title =        "Approximate properties of {Thiele}'s formula in a
                 class of elementary functions. ({Russian})",
  volume =       "141",
  publisher =    "Vestnik L'vov. Politekhn. Inst.",
  address =      "L'vov, USSR",
  pages =        "55--56",
  year =         "1980",
  MRclass =      "119.65D20",
  MRnumber =     "81i:65021",
  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",
}


bibtype: article
filename: elefunt.bib
label: Meinardus:1980:OPN
author: Gunter Meinardus and G. D. Taylor
title: Optimal Partitioning of Newton's Method for Calculating Roots
journal: j-MATH-COMPUT
volume: 35
number: 152
pages: 1221--1230
month: oct
monthnumber: 10
year: 1980
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65H05 (41A30)
MRnumber: 81j:65069
MRreviewer: Derek W. Arthur
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
classcodes: C4130 (Interpolation and function approximation)
corpsource: Fachbereich Math., University of Siegen, Siegen, West Germany
journalURL: http://www.ams.org/mcom/
treatment: A Application; T Theoretical or Mathematical
rawauthor: G{\"u}nter Meinardus and G. D. Taylor
rawtitle: Optimal Partitioning of {Newton}'s Method for Calculating Roots
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; JSTOR database

keywords:
cube root; domain interval; function approximation; iterative methods; method; Newton; optimal partitioning; reciprocal square root; square root; subinterval

entry:
@Article{Meinardus:1980:OPN,
  author =       "G{\"u}nter Meinardus and G. D. Taylor",
  title =        "Optimal Partitioning of {Newton}'s Method for
                 Calculating Roots",
  journal =      j-MATH-COMPUT,
  volume =       "35",
  number =       "152",
  pages =        "1221--1230",
  month =        oct,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65H05 (41A30)",
  MRnumber =     "81j:65069",
  MRreviewer =   "Derek W. Arthur",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  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;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Fachbereich Math., University of Siegen, Siegen, West
                 Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "cube root; domain interval; function approximation;
                 iterative methods; method; Newton; optimal
                 partitioning; reciprocal square root; square root;
                 subinterval",
  treatment =    "A Application; T Theoretical or Mathematical",
}


