# bibtab

bibtype: article
filename: elefunt.bib
label: Bunch:1991:DFA
author: K. J. Bunch and W. N. Cain and R. W. Grow
title: A data fitting approach to series convergence acceleration
journal: j-APPL-MATH-COMP
volume: 42
number: 2 (part II)
pages: 189--195
year: 1991
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/0096-3003(91)90050-W
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
MRclass: 65B10 (65D10)
MRnumber: 1094414 (91k:65015)
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: Applied Mathematics and Computation
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: K. J. Bunch and W. N. Cain and R. W. Grow
rawtitle: A data fitting approach to series convergence acceleration
entry:
@Article{Bunch:1991:DFA,
  author =       "K. J. Bunch and W. N. Cain and R. W. Grow",
  title =        "A data fitting approach to series convergence
                 acceleration",
  journal =      j-APPL-MATH-COMP,
  volume =       "42",
  number =       "2 (part II)",
  pages =        "189--195",
  month =        "????",
  year =         "1991",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(91)90050-W",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65B10 (65D10)",
  MRnumber =     "1094414 (91k:65015)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1991:TEI
author: B. C. Carlson
title: A table of elliptic integrals: One quadratic factor
journal: j-MATH-COMPUT
volume: 56
number: 193
pages: 267--280
month: jan
monthnumber: 1
year: 1991
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33E05 (65A05)
MRnumber: 92b:33056
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: Dept. of Math., Iowa State Univ., Ames, IA, USA
journalURL: http://www.ams.org/mcom/
treatment: P Practical
rawauthor: B. C. Carlson
rawtitle: A table of elliptic integrals: {One} quadratic factor
keywords:
conjugate complex zeros; elliptic integrals; Fortran programs; integral equations; integration; polynomial; R-functions; square root

classcodes:
B0290R (Integral equations); B0290M (Numerical integration and differentiation); C4180 (Integral equations); C4160 (Numerical integration and differentiation)

entry:
@Article{Carlson:1991:TEI,
  author =       "B. C. Carlson",
  title =        "A table of elliptic integrals: {One} quadratic
                 factor",
  journal =      j-MATH-COMPUT,
  volume =       "56",
  number =       "193",
  pages =        "267--280",
  month =        jan,
  year =         "1991",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33E05 (65A05)",
  MRnumber =     "92b:33056",
  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 =   "B0290R (Integral equations); B0290M (Numerical
                 integration and differentiation); C4180 (Integral
                 equations); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "conjugate complex zeros; elliptic integrals; Fortran
                 programs; integral equations; integration; polynomial;
                 R-functions; square root",
  treatment =    "P Practical",
}


bibtype: techreport
filename: elefunt.bib
label: Cody:1991:CPT
author: W. J. Cody
title: CELEFUNT: a Portable Test Package for Complex Elementary Functions
type: Technical Report
number: ANL-91/1
institution: inst-ANL
address: inst-ANL:adr
pages: iii + 21
month: jan
monthnumber: 1
year: 1991
bibdate: Fri Sep 23 23:39:07 1994
bibtimestamp: 1994.09.23 23:39:07 ???
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawtitle: {CELEFUNT}: a Portable Test Package for Complex Elementary Functions
entry:
@TechReport{Cody:1991:CPT,
  author =       "W. J. Cody",
  title =        "{CELEFUNT}: a Portable Test Package for Complex
                 Elementary Functions",
  type =         "Technical Report",
  number =       "ANL-91/1",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "iii + 21",
  month =        jan,
  year =         "1991",
  bibdate =      "Fri Sep 23 23:39:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Corless:1991:NEA
author: R. M. Corless and D. J. Jeffrey and H. Rasmussen
title: Numerical evaluation of Airy functions with complex arguments
journal: j-J-COMPUT-PHYS
volume: 93
number: 1
pages: 252--253
month: mar
monthnumber: 3
year: 1991
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(91)90089-4
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:47 MST 2012
bibtimestamp: 2012.01.02 07:55:47 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999191900894
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. M. Corless and D. J. Jeffrey and H. Rasmussen
rawtitle: Numerical evaluation of {Airy} functions with complex arguments
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib

entry:
@Article{Corless:1991:NEA,
  author =       "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
  title =        "Numerical evaluation of {Airy} functions with complex
                 arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "93",
  number =       "1",
  pages =        "252--253",
  month =        mar,
  year =         "1991",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(91)90089-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:47 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999191900894",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Crenshaw:1991:SRS
author: J. W. Crenshaw
title: Square roots are simple?
journal: j-EMBED-SYS-PROG
volume: 4
number: 11
pages: 30--52
month: nov
monthnumber: 11
year: 1991
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Wed Sep 14 19:14:52 1994
bibtimestamp: 1994.09.14 19:14:52 ???
fjournal: Embedded Systems Programming
acknowledgement: ack-nj
rawauthor: J. W. Crenshaw
rawtitle: Square roots are simple?
entry:
@Article{Crenshaw:1991:SRS,
  author =       "J. W. Crenshaw",
  title =        "Square roots are simple?",
  journal =      j-EMBED-SYS-PROG,
  volume =       "4",
  number =       "11",
  pages =        "30--52",
  month =        nov,
  year =         "1991",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Wed Sep 14 19:14:52 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 =     "Embedded Systems Programming",
}


bibtype: article
filename: elefunt.bib
label: DeDoelder:1991:SSC
author: P. J. De Doelder
journal: j-J-COMPUT-APPL-MATH
volume: 37
number: 1--3
pages: 125--141
day: 18
month: nov
monthnumber: 11
year: 1991
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(91)90112-W
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:22 MST 2017
bibtimestamp: 2017.02.25 13:02:22 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279190112W
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: P. J. {De Doelder}
title:
On some series containing $ psi (x) - psi (y >) $ and $ (psi (x) - psi (y >))^2 $ for certain values of $x$ and $y$

rawtitle:
On some series containing $ \psi (x) - \psi (y >) $ and $ (\psi (x) - \psi (y >))^2 $ for certain values of $x$ and $y$

entry:
@Article{DeDoelder:1991:SSC,
  author =       "P. J. {De Doelder}",
  title =        "On some series containing $ \psi (x) - \psi (y >) $
                 and $ (\psi (x) - \psi (y >))^2 $ for certain values of
                 $x$ and $y$",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "37",
  number =       "1--3",
  pages =        "125--141",
  day =          "18",
  month =        nov,
  year =         "1991",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(91)90112-W",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190112W",
  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: Dritz:1991:IPS
author: Kenneth W. Dritz
title: Introduction to the proposed standard for the elementary functions in Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 3--8
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics)
corpsource: Dept. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Kenneth W. Dritz
rawtitle: Introduction to the proposed standard for the elementary functions in {Ada}
keywords:
Ada; committees; elementary functions; generic package; ISO standard; mathematics computing; secondary; standards

entry:
@Article{Dritz:1991:IPS,
  author =       "Kenneth W. Dritz",
  title =        "Introduction to the proposed standard for the
                 elementary functions in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "3--8",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics)",
  corpsource =   "Dept. of Math. and Comput. Sci., Argonne Nat. Lab.,
                 IL, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; committees; elementary functions; generic
                 package; ISO standard; mathematics computing;
                 secondary; standards",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Dritz:1991:PSGa
author: K. W. Dritz
title: Proposed standard for a generic package of elementary functions for Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 9--46
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C6110B (Software engineering techniques); C7310 (Mathematics)
corpsource: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: K. W. Dritz
rawtitle: Proposed standard for a generic package of elementary functions for {Ada}
keywords:
ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics Working Group; basic; elementary functions; ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package; GENERIC-ELEMENTARY-FUNCTIONS; Group; international standard; joint proposal; mathematical routines; mathematics computing; NRG; Rapporteur Group; reusable applications; SC22; software reusability; specification; standards; WG9 Numerics

entry:
@Article{Dritz:1991:PSGa,
  author =       "K. W. Dritz",
  title =        "Proposed standard for a generic package of elementary
                 functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "9--46",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C6110B (Software
                 engineering techniques); C7310 (Mathematics)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics
                 Working Group; basic; elementary functions;
                 ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package;
                 GENERIC-ELEMENTARY-FUNCTIONS; Group; international
                 standard; joint proposal; mathematical routines;
                 mathematics computing; NRG; Rapporteur Group; reusable
                 applications; SC22; software reusability;
                 specification; standards; WG9 Numerics",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Dritz:1991:PSGb
author: K. W. Dritz
title: Proposed standard for a generic package of primitive functions for Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 66--82
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics)
corpsource: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: K. W. Dritz
rawtitle: Proposed standard for a generic package of primitive functions for {Ada}
keywords:
Ada; compliable Ada; elementary functions; generic package; GENERIC-; mathematical; mathematics computing; primitive functions; primitive operations; PRIMITIVE-FUNCTIONS; software; specification; standards

entry:
@Article{Dritz:1991:PSGb,
  author =       "K. W. Dritz",
  title =        "Proposed standard for a generic package of primitive
                 functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "66--82",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; compliable Ada; elementary functions; generic
                 package; GENERIC-; mathematical; mathematics computing;
                 primitive functions; primitive operations;
                 PRIMITIVE-FUNCTIONS; software; specification;
                 standards",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Dritz:1991:RPS
author: K. W. Dritz
title: Rationale for the proposed standard for a generic package of elementary functions for Ada
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 47--65
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics); C6110 (Systems analysis and programming)
corpsource: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: K. W. Dritz
rawtitle: Rationale for the proposed standard for a generic package of elementary functions for {Ada}
keywords:
ACM SIGAda Numerics Working Group; Ada; Ada-Europe Numerics; collateral; elementary functions standard; mathematics computing; numerical software; portability; programming; robustness; standards; Working Group

entry:
@Article{Dritz:1991:RPS,
  author =       "K. W. Dritz",
  title =        "Rationale for the proposed standard for a generic
                 package of elementary functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "47--65",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110 (Systems analysis and programming)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda Numerics Working Group; Ada; Ada-Europe
                 Numerics; collateral; elementary functions standard;
                 mathematics computing; numerical software; portability;
                 programming; robustness; standards; Working Group",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Duprat:1991:WND
author: J. Duprat and J.-M. Muller
title: Writing numbers differently for faster calculation
journal: j-TECHNIQUE-SCI-INFORMATIQUES
volume: 10
number: 3
pages: 211--224
year: 1991
CODEN: TTSIDJ
ISSN: 0752-4072, 0264-7419 OR 07524072, 02647419
ISSNL: 0752-4072 OR 07524072
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:20:21 MST
fjournal: Technique et science informatiques : TSI
language: French
acknowledgement: ack-nhfb
affiliation: Ecole Normale Superieure de Lyon, France
thesaurus: Digital arithmetic
rawauthor: J. Duprat and J.-M. Muller
rawtitle: Writing numbers differently for faster calculation
abstract:
Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.

keywords:
Addition; Borrow save; Carry save methods; Cordic algorithm; Floating point arithmetic; Multiplication; Pseudo normalisation; Shifting; Subtraction; Zero

rawabstract:
Instead of Avizienis' or the carry save methods a borrow save (BS) notation is proposed. Examples are given of BS addition, subtraction, shifting and multiplication with the necessary elementary cells being proposed and circuits for testing zero and sign being described. Floating point arithmetic is explained, involving pseudo normalisation and applications are covered including the Cordic algorithm.

entry:
@Article{Duprat:1991:WND,
  author =       "J. Duprat and J.-M. Muller",
  title =        "Writing numbers differently for faster calculation",
  journal =      j-TECHNIQUE-SCI-INFORMATIQUES,
  volume =       "10",
  number =       "3",
  pages =        "211--224",
  month =        "????",
  year =         "1991",
  CODEN =        "TTSIDJ",
  ISSN =         "0752-4072, 0264-7419",
  ISSN-L =       "0752-4072",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Instead of Avizienis' or the carry save methods a
                 borrow save (BS) notation is proposed. Examples are
                 given of BS addition, subtraction, shifting and
                 multiplication with the necessary elementary cells
                 being proposed and circuits for testing zero and sign
                 being described. Floating point arithmetic is
                 explained, involving pseudo normalisation and
                 applications are covered including the Cordic
                 algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon, France",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Technique et science informatiques : TSI",
  keywords =     "Addition; Borrow save; Carry save methods; Cordic
                 algorithm; Floating point arithmetic; Multiplication;
                 Pseudo normalisation; Shifting; Subtraction; Zero",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Digital arithmetic",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ferguson:1991:AMA
author: W. E. Ferguson, Jr. and T. Brightman
title: Accurate and Monotone Approximations of Some Transcendental Functions
crossref: Kornerup:1991:PIS
pages: 237--244
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.11.27 12:40:58 MST
acknowledgement: ack-nj
rawauthor: W. E. {Ferguson, Jr.} and T. Brightman
rawtitle: Accurate and Monotone Approximations of Some Transcendental Functions
entry:
@InProceedings{Ferguson:1991:AMA,
  author =       "W. E. {Ferguson, Jr.} and T. Brightman",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  crossref =     "Kornerup:1991:PIS",
  pages =        "237--244",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gal:1991:AEM
author: Shmuel Gal and Boris Bachelis
title: An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard
journal: j-TOMS
volume: 17
number: 1
pages: 26--45
month: mar
monthnumber: 3
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20 (65-04 65D15)
MRnumber: 92a:65069
bibdate: Sun Sep 04 23:33:02 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.04 23:33:02 ???
URL: http://www.acm.org/pubs/toc/Abstracts/toms/103151.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Shmuel Gal and Boris Bachelis
rawtitle: An Accurate Elementary Mathematical Library for the {IEEE} Floating Point Standard
abstract:
The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values. par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation.

rawabstract:
The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values. \par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.

entry:
@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65-04 65D15)",
  MRnumber =     "92a:65069",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/103151.html",
  abstract =     "The algorithms used by the IBM Israel Scientific
                 Center for the elementary mathematical library using
                 the IEEE standard for binary floating point arithmetic
                 are described. The algorithms are based on the
                 ``accurate tables method.'' This methodology achieves
                 high performance and produces very accurate results. It
                 overcomes one of the main problems encountered in
                 elementary mathematical functions computations:
                 achieving last bit accuracy. The results obtained are
                 correctly rounded for almost all argument values.
                 \par

                 Our main idea in the accurate tables method is to use
                 ``nonstandard tables,'' which are different from the
                 natural tables of equally spaced points in which the
                 rounding error prevents obtaining last bit accuracy. In
                 order to achieve a small error we use the following
                 idea: Perturb the original, equally spaced, points in
                 such a way that the table value (or tables values in
                 case we need several tables) will be very close to
                 numbers which can be exactly represented by the
                 computer (much closer than the usual double precision
                 representation). Thus we were able to control the error
                 introduced by the computer representation of real
                 numbers and extended the accuracy without actually
                 using extended precision arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation.",
}


bibtype: article
filename: elefunt.bib
label: Gray:1991:GMA
author: H. L. Gray and Suojin Wang
title: A General Method for Approximating Tail Probabilities
journal: j-J-AM-STAT-ASSOC
volume: 86
number: 413
pages: 159--166
month: mar
monthnumber: 3
year: 1991
CODEN: JSTNAL
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
bibdate: Wed Jan 25 08:06:12 MST 2012
bibtimestamp: 2012.01.25 08:06:12 MST
URL: http://www.jstor.org/stable/2289726
fjournal: Journal of the American Statistical Association
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uasa20
rawauthor: H. L. Gray and Suojin Wang
rawtitle: A General Method for Approximating Tail Probabilities
bibsource:
http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314297; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1990.bib

entry:
@Article{Gray:1991:GMA,
  author =       "H. L. Gray and Suojin Wang",
  title =        "A General Method for Approximating Tail
                 Probabilities",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "86",
  number =       "413",
  pages =        "159--166",
  month =        mar,
  year =         "1991",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:06:12 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314297;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1990.bib",
  URL =          "http://www.jstor.org/stable/2289726",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gustafson:1991:CAA
author: Sven-AA ke Gustafson and Frank Stenger
crossref: Bowers:1991:CCI
pages: 161--171
year: 1991
MRclass: 41A30 (93B40)
MRnumber: MR1140021
bibdate: Thu May 10 16:31:10 2007
bibtimestamp: 2007.05.10 16:31:10 ???
keywords: Chebyshev acceleration; convergence acceleration
ZMnumber: 0746.41034
acknowledgement: ack-nhfb
reviewer: Zhang Ganglu (Dongying)
rawauthor: Sven-{\AA}ke Gustafson and Frank Stenger
title:
Convergence acceleration applied to Sinc approximation with application to approximation of $ |x|^alpha $

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
The author studies mainly the role of Chebyshev acceleration of Sinc approximation. Then he considers various methods of approximating $ vert x vert ^alpha $ and applies Chebyshev acceleration to the various type of approximants for the case of $ alpha = 1 $.

rawabstract:
The author studies mainly the role of Chebyshev acceleration of Sinc approximation. Then he considers various methods of approximating $ \vert x \vert^\alpha $ and applies Chebyshev acceleration to the various type of approximants for the case of $ \alpha = 1 $.

rawtitle:
Convergence acceleration applied to {Sinc} approximation with application to approximation of $ |x|^\alpha $

entry:
@InProceedings{Gustafson:1991:CAA,
  author =       "Sven-{\AA}ke Gustafson and Frank Stenger",
  title =        "Convergence acceleration applied to {Sinc}
                 approximation with application to approximation of $
                 |x|^\alpha $",
  crossref =     "Bowers:1991:CCI",
  pages =        "161--171",
  year =         "1991",
  MRclass =      "41A30 (93B40)",
  MRnumber =     "MR1140021",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0746.41034",
  abstract =     "The author studies mainly the role of Chebyshev
                 acceleration of Sinc approximation. Then he considers
                 various methods of approximating $ \vert x \vert^\alpha
                 $ and applies Chebyshev acceleration to the various
                 type of approximants for the case of $ \alpha = 1 $.",
  acknowledgement = ack-nhfb,
  classmath =    "*41A65 (Abstract approximation theory)",
  keywords =     "Chebyshev acceleration; convergence acceleration",
  reviewer =     "Zhang Ganglu (Dongying)",
}


bibtype: article
filename: elefunt.bib
label: Hamza:1991:MBD
author: K. M. Hamza and M. A. H. Abdul-Karim
title: Microprocessor Based Direct Square Root Extractor
journal: Modelling
volume: 34
number: 1
pages: 45--48
year: 1991
bibdate: Thu Sep 1 10:15:42 1994
bibtimestamp: 1994.09.01 10:15:42 ???
acknowledgement: ack-nj
rawauthor: K. M. Hamza and M. A. H. Abdul-Karim
rawtitle: Microprocessor Based Direct Square Root Extractor
entry:
@Article{Hamza:1991:MBD,
  author =       "K. M. Hamza and M. A. H. Abdul-Karim",
  title =        "Microprocessor Based Direct Square Root Extractor",
  journal =      "Modelling",
  volume =       "34",
  number =       "1",
  pages =        "45--48",
  month =        "????",
  year =         "1991",
  bibdate =      "Thu Sep 1 10:15:42 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,
}


bibtype: article
filename: elefunt.bib
label: Ifantis:1991:PZS
author: E. K. Ifantis and C. G. Kokologiannaki and C. B. Kouris
title: On the positive zeros of the second derivative of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 34
number: 1
pages: 21--31
day: 10
month: feb
monthnumber: 2
year: 1991
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:48 MST 2017
bibtimestamp: 2017.02.25 12:20:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042791901449
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: E. K. Ifantis and C. G. Kokologiannaki and C. B. Kouris
rawtitle: On the positive zeros of the second derivative of {Bessel} functions
entry:
@Article{Ifantis:1991:PZS,
  author =       "E. K. Ifantis and C. G. Kokologiannaki and C. B.
                 Kouris",
  title =        "On the positive zeros of the second derivative of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "34",
  number =       "1",
  pages =        "21--31",
  day =          "10",
  month =        feb,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042791901449",
  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: Ikebe:1991:CZO
author: Yasuhiko Ikebe and Yasushi Kikuchi and Issei Fujishiro
title: Computing zeros and orders of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 38
number: 1--3
pages: 169--184
day: 23
month: dec
monthnumber: 12
year: 1991
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:23 MST 2017
bibtimestamp: 2017.02.25 13:02:23 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279190169K
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Yasuhiko Ikebe and Yasushi Kikuchi and Issei Fujishiro
rawtitle: Computing zeros and orders of {Bessel} functions
entry:
@Article{Ikebe:1991:CZO,
  author =       "Yasuhiko Ikebe and Yasushi Kikuchi and Issei
                 Fujishiro",
  title =        "Computing zeros and orders of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "38",
  number =       "1--3",
  pages =        "169--184",
  day =          "23",
  month =        dec,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:23 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190169K",
  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: Iserles:1991:CDC
author: A. Iserles
title: Complex dynamics of convergence acceleration
journal: j-IMA-J-NUMER-ANAL
volume: 11
number: 2
pages: 205--240
year: 1991
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65B05 (65E05)
MRnumber: 92h:65006
bibdate: Sat Dec 23 17:06:35 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: A. Iserles
rawtitle: Complex dynamics of convergence acceleration
entry:
@Article{Iserles:1991:CDC,
  author =       "A. Iserles",
  title =        "Complex dynamics of convergence acceleration",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "11",
  number =       "2",
  pages =        "205--240",
  year =         "1991",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65B05 (65E05)",
  MRnumber =     "92h:65006",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Laforgia:1991:BMB
author: Andrea Laforgia
title: Bounds for modified Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 34
number: 3
pages: 263--267
day: 26
month: apr
monthnumber: 4
year: 1991
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:49 MST 2017
bibtimestamp: 2017.02.25 12:20:49 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279190087Z
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Andrea Laforgia
rawtitle: Bounds for modified {Bessel} functions
entry:
@Article{Laforgia:1991:BMB,
  author =       "Andrea Laforgia",
  title =        "Bounds for modified {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "34",
  number =       "3",
  pages =        "263--267",
  day =          "26",
  month =        apr,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:49 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190087Z",
  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: Levrie:1991:CAF
author: Paul Levrie
title: Convergence acceleration for $n$-fractions
journal: j-APPL-NUM-MATH
volume: 7
number: 6
pages: 481--492
month: jun
monthnumber: 6
year: 1991
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 40A15 (65B05)
MRnumber: 92k:40001
MRreviewer: Claude Brezinski
bibdate: Sat Feb 8 10:09:54 MST 1997
bibtimestamp: 1997.02.08 10:09:54 MST
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Paul Levrie
rawtitle: Convergence acceleration for $n$-fractions
bibsource:
https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Levrie:1991:CAF,
  author =       "Paul Levrie",
  title =        "Convergence acceleration for $n$-fractions",
  journal =      j-APPL-NUM-MATH,
  volume =       "7",
  number =       "6",
  pages =        "481--492",
  month =        jun,
  year =         "1991",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "40A15 (65B05)",
  MRnumber =     "92k:40001",
  MRreviewer =   "Claude Brezinski",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Levrie:1991:CFC
author: Paul Levrie
journal: j-APPL-NUM-MATH
volume: 8
number: 3
pages: 225--242
month: oct
monthnumber: 10
year: 1991
CODEN: ANMAEL
DOI: https://doi.org/10.1090/surv/037
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65B99 (65Q05)
MRnumber: 92m:65012
MRreviewer: J. Albrycht
bibdate: Sat Feb 8 10:09:54 MST 1997
bibtimestamp: 1997.02.08 10:09:54 MST
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Paul Levrie
title:
$ G $-continued fractions and convergence acceleration in the solution of third-order linear recurrence relations of Poincare type

rawtitle:
$ {G} $-continued fractions and convergence acceleration in the solution of third-order linear recurrence relations of {Poincar{\'e}} type

entry:
@Article{Levrie:1991:CFC,
  author =       "Paul Levrie",
  title =        "$ {G} $-continued fractions and convergence
                 acceleration in the solution of third-order linear
                 recurrence relations of {Poincar{\'e}} type",
  journal =      j-APPL-NUM-MATH,
  volume =       "8",
  number =       "3",
  pages =        "225--242",
  month =        oct,
  year =         "1991",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1090/surv/037",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B99 (65Q05)",
  MRnumber =     "92m:65012",
  MRreviewer =   "J. Albrycht",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lyons:1991:FMF
author: Ken Lyons
title: A fast method for finding an integer square root
crossref: Koopman:1991:PST
pages: 27--30
year: 1991
bibdate: Tue May 4 05:57:50 MDT 1999
bibtimestamp: 1999.05.04 05:57:50 MDT
URL: http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/
acknowledgement: ack-nhfb
rawauthor: Ken Lyons
rawtitle: A fast method for finding an integer square root
bibsource:
http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@InProceedings{Lyons:1991:FMF,
  author =       "Ken Lyons",
  title =        "A fast method for finding an integer square root",
  crossref =     "Koopman:1991:PST",
  pages =        "27--30",
  year =         "1991",
  bibdate =      "Tue May 4 05:57:50 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Markstein:1991:WFF
author: V. Markstein and P. Markstein and T. Nguyen and S. Poole
title: Wide Format Floating-Point Math Libraries
crossref: IEEE:1991:PSA
pages: 130--138
year: 1991
bibdate: Wed Dec 13 18:34:51 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.13 18:34:51 ???
acknowledgement: ack-nhfb
affiliation: ISQUARE, Inc., Austin, TX, USA
thesaurus: Digital arithmetic; Mathematics computing; Parallel processing; Performance evaluation
rawauthor: V. Markstein and P. Markstein and T. Nguyen and S. Poole
rawtitle: Wide Format Floating-Point Math Libraries
abstract:
The authors present the performance and accuracy evaluations of eleven transcendental functions found in 64- and 128-bit floating-point formats in math libraries on the Cray Y-MP, the IBM 3090E/VF, the Convex C-240, the Hewlett--Packard 9000/720, and the IBM System/6000. Both architecture and algorithms are shown to impact the results.

keywords:
128 Bit; 64 Bit; Accuracy evaluations; Convex C-240; Cray Y-MP; Floating-point formats; Hewlett--Packard 9000/720; IBM 3090E/VF; IBM System/6000; Math libraries; Performance; Transcendental functions; Wide format floating point math libraries

rawabstract:
The authors present the performance and accuracy evaluations of eleven transcendental functions found in 64- and 128-bit floating-point formats in math libraries on the Cray Y-MP, the IBM 3090E/VF, the Convex C-240, the Hewlett--Packard 9000/720, and the IBM System/6000. Both architecture and algorithms are shown to impact the results.

entry:
@InProceedings{Markstein:1991:WFF,
  author =       "V. Markstein and P. Markstein and T. Nguyen and S.
                 Poole",
  title =        "Wide Format Floating-Point Math Libraries",
  crossref =     "IEEE:1991:PSA",
  pages =        "130--138",
  year =         "1991",
  bibdate =      "Wed Dec 13 18:34:51 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The authors present the performance and accuracy
                 evaluations of eleven transcendental functions found in
                 64- and 128-bit floating-point formats in math
                 libraries on the Cray Y-MP, the IBM 3090E/VF, the
                 Convex C-240, the Hewlett--Packard 9000/720, and the
                 IBM System/6000. Both architecture and algorithms are
                 shown to impact the results.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "ISQUARE, Inc., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods); C5470
                 (Performance evaluation and testing); C7310
                 (Mathematics)",
  confdate =     "18-22 Nov. 1991",
  conflocation = "Albuquerque, NM, USA",
  confsponsor =  "IEEE; ACM",
  keywords =     "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
                 Cray Y-MP; Floating-point formats; Hewlett--Packard
                 9000/720; IBM 3090E/VF; IBM System/6000; Math
                 libraries; Performance; Transcendental functions; Wide
                 format floating point math libraries",
  numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Mathematics computing; Parallel
                 processing; Performance evaluation",
}


bibtype: article
filename: elefunt.bib
label: Maximon:1991:EIP
author: Leonard C. Maximon
title: On the evaluation of the integral over the product of two spherical Bessel functions
journal: j-J-MATH-PHYS
volume: 32
number: 3
pages: 642--648
month: mar
monthnumber: 3
year: 1991
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.529405
ISSNL: 0022-2488 OR 00222488
MRclass: 33C55
MRnumber: 92f:33018
MRreviewer: S. K. Chatterjea
bibdate: Tue Nov 1 08:57:23 MDT 2011
bibtimestamp: 2011.11.01 08:57:23 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v32/i3/p642_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Leonard C. Maximon
rawtitle: On the evaluation of the integral over the product of two spherical {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/jmathphys1990.bib

entry:
@Article{Maximon:1991:EIP,
  author =       "Leonard C. Maximon",
  title =        "On the evaluation of the integral over the product of
                 two spherical {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "32",
  number =       "3",
  pages =        "642--648",
  month =        mar,
  year =         "1991",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.529405",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33C55",
  MRnumber =     "92f:33018",
  MRreviewer =   "S. K. Chatterjea",
  bibdate =      "Tue Nov 1 08:57:23 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/jmathphys1990.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v32/i3/p642_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "7",
}


bibtype: article
filename: elefunt.bib
label: McQuillan:1991:HPV
author: S. E. McQuillan and J. V. McCanny and R. F. Woods
title: High performance VLSI architecture for division and square root
journal: j-ELECT-LETTERS
volume: 27
number: 1
pages: 19--21
day: 3
month: jan
monthnumber: 1
year: 1991
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: S. E. McQuillan and J. V. McCanny and R. F. Woods
rawtitle: High performance {VLSI} architecture for division and square root
entry:
@Article{McQuillan:1991:HPV,
  author =       "S. E. McQuillan and J. V. McCanny and R. F. Woods",
  title =        "High performance {VLSI} architecture for division and
                 square root",
  journal =      j-ELECT-LETTERS,
  volume =       "27",
  number =       "1",
  pages =        "19--21",
  day =          "3",
  month =        jan,
  year =         "1991",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A novel high performance bit parallel architecture to
                 perform square root and division is proposed. Relevant
                 VLSI design issues have been addressed. By employing
                 redundant arithmetic and a semisystolic schedule, the
                 throughput has been made \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: McQuillan:1991:VAM
author: S. E. McQuillan and J. V. McCanny
title: A VLSI architecture for multiplication, division and square root
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1205--1208
year: 1991
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: S. E. McQuillan and J. V. McCanny
rawtitle: A {VLSI} architecture for multiplication, division and square root
booktitle:
1991 International Conference on Acoustics, Speech, and Signal Processing: ICASSP-91, 14--17 April 1991

rawbooktitle:
1991 International Conference on Acoustics, Speech, and Signal Processing: {ICASSP-91, 14--17} April 1991

entry:
@InProceedings{McQuillan:1991:VAM,
  author =       "S. E. McQuillan and J. V. McCanny",
  booktitle =    "1991 International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-91, 14--17} April 1991",
  title =        "A {VLSI} architecture for multiplication, division and
                 square root",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1205--1208",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A high-performance VLSI architecture to perform
                 combined multiply-accumulate, divide, and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control, and can be reconfigured
                 for every cycle. The execution time \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Midy:1991:CSE
author: P. Midy and Y. Yakovlev
title: Computing some elementary functions of a complex variable
journal: j-MATH-COMP-SIM
volume: 33
number: 1
pages: 33--49
year: 1991
CODEN: MCSIDR
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
MRclass: 65Y10 (65D20)
MRnumber: MR1122989
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: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03784754
rawauthor: P. Midy and Y. Yakovlev
rawtitle: Computing some elementary functions of a complex variable
entry:
@Article{Midy:1991:CSE,
  author =       "P. Midy and Y. Yakovlev",
  title =        "Computing some elementary functions of a complex
                 variable",
  journal =      j-MATH-COMP-SIM,
  volume =       "33",
  number =       "1",
  pages =        "33--49",
  year =         "1991",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  MRclass =      "65Y10 (65D20)",
  MRnumber =     "MR1122989",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
}


bibtype: article
filename: elefunt.bib
label: Montuschi:1991:OAE
author: P. Montuschi and M. Mezzalama
title: Optimal Absolute Error Starting Values for Newton--Raphson Calculation of Square Root
journal: j-COMPUTING
volume: 46
number: 1
pages: 67--86
month: mar
monthnumber: 3
year: 1991
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
MRclass: 65H05 (65G99)
MRnumber: 92a:65161
bibdate: Tue Oct 12 16:33:42 MDT 1999
bibtimestamp: 1999.10.12 16:33:42 MDT
fjournal: Computing
acknowledgement: ack-nhfb
affiliation: Politecnico di Torino
affiliationaddress: Torino, Italy
journalURL: http://link.springer.com/journal/607
journalabr: Comput Vienna New York
rawauthor: P. Montuschi and M. Mezzalama
rawtitle: Optimal Absolute Error Starting Values for {Newton--Raphson} Calculation of Square Root
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; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database; OCLC Contents1st database

keywords:
Absolute Error; Computer Programming --- Algorithms; Mathematical Techniques; Newton--Raphson Method; Optimization; Square Roots

entry:
@Article{Montuschi:1991:OAE,
  author =       "P. Montuschi and M. Mezzalama",
  title =        "Optimal Absolute Error Starting Values for
                 {Newton--Raphson} Calculation of Square Root",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "1",
  pages =        "67--86",
  month =        mar,
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65H05 (65G99)",
  MRnumber =     "92a:65161",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  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;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  acknowledgement = ack-nhfb,
  affiliation =  "Politecnico di Torino",
  affiliationaddress = "Torino, Italy",
  classification = "723; 921",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Absolute Error; Computer Programming --- Algorithms;
                 Mathematical Techniques; Newton--Raphson Method;
                 Optimization; Square Roots",
}


bibtype: inproceedings
filename: elefunt.bib
label: Montuschi:1991:SRD
author: Paolo Montuschi and Luigi Ciminiera
title: Simple radix 2 division and square root with skipping of some addition steps
crossref: Kornerup:1991:PIS
pages: 202--209
year: 1991
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf
keywords: ARITH-10
acknowledgement: ack-nhfb
rawauthor: Paolo Montuschi and Luigi Ciminiera
rawtitle: Simple radix 2 division and square root with skipping of some addition steps
entry:
@InProceedings{Montuschi:1991:SRD,
  author =       "Paolo Montuschi and Luigi Ciminiera",
  title =        "Simple radix 2 division and square root with skipping
                 of some addition steps",
  crossref =     "Kornerup:1991:PIS",
  pages =        "202--209",
  year =         "1991",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  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/arith10/papers/ARITH10_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
  summary =      "The authors present a novel algorithm for shared radix
                 2 division and square root whose main characteristic is
                 the ability to avoid any addition when the digit 0 has
                 been selected. The solution presented uses a redundant
                 representation of the \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: OGrady:1991:HOA
author: E. Pearse O'Grady and Baek-Kyu Young
title: A hardware-oriented algorithm for floating-point function generation
journal: j-IEEE-TRANS-COMPUT
volume: 40
number: 2
pages: 237--241
month: feb
monthnumber: 2
year: 1991
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.73596
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. Pearse O'Grady and Baek-Kyu Young
rawtitle: A hardware-oriented algorithm for floating-point function generation
abstract:
An algorithm is presented for performing accurate, high-speed, floating-point function generation for univariate functions defined at arbitrary breakpoints. Rapid identification of the breakdown interval, which includes the input argument, is the key operation in the algorithm. A hardware implementation which makes extensive use of read/write memories illustrates the algorithm.

rawabstract:
An algorithm is presented for performing accurate, high-speed, floating-point function generation for univariate functions defined at arbitrary breakpoints. Rapid identification of the breakdown interval, which includes the input argument, is the key operation in the algorithm. A hardware implementation which makes extensive use of read/write memories illustrates the algorithm.

entry:
@Article{OGrady:1991:HOA,
  author =       "E. Pearse O'Grady and Baek-Kyu Young",
  title =        "A hardware-oriented algorithm for floating-point
                 function generation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "2",
  pages =        "237--241",
  month =        feb,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.73596",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm is presented for performing accurate,
                 high-speed, floating-point function generation for
                 univariate functions defined at arbitrary breakpoints.
                 Rapid identification of the breakdown interval, which
                 includes the input argument, is the key operation in
                 the algorithm. A hardware implementation which makes
                 extensive use of read/write memories illustrates the
                 algorithm.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Okabe:1991:LDC
author: Y. Okabe and N. Takagi and S. Yaima
title: Log-Depth Circuits for Elementary Functions Using Residue Number System
journal: j-ELECTRON-COMMUN-JPN
volume: 74
number: 8
pages: 31--37
year: 1991
CODEN: ECOJAL
ISSN: 0424-8368 OR 04248368
bibdate: Mon May 19 15:16:09 1997
bibtimestamp: 1997.05.19 15:16:09 ???
note: Translated from Denshi Joho Tsushin Gakkai Ronbunshi, vol.21-DI, no.9, September 1990, pp.723-728
fjournal: Electronics and communications in Japan
acknowledgement: ack-nhfb
key: OTY91
rawauthor: Y. Okabe and N. Takagi and S. Yaima
rawtitle: Log-Depth Circuits for Elementary Functions Using Residue Number System
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawnote:
Translated from Denshi Joho Tsushin Gakkai Ronbunshi, vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728

entry:
@Article{Okabe:1991:LDC,
  author =       "Y. Okabe and N. Takagi and S. Yaima",
  key =          "OTY91",
  title =        "Log-Depth Circuits for Elementary Functions Using
                 Residue Number System",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "74",
  number =       "8",
  pages =        "31--37",
  year =         "1991",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  bibdate =      "Mon May 19 15:16:09 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
                 vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}


bibtype: article
filename: elefunt.bib
label: Olver:1991:UEIb
author: F. W. J. Olver
journal: j-SIAM-J-MATH-ANA
volume: 22
number: 5
pages: 1475--1489
month: sep
monthnumber: 9
year: 1991
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 41A60 (33C15)
MRnumber: 92g:41035
MRreviewer: Hans-J{\"u}rgen Glaeske
bibdate: Sun Nov 28 19:25:21 MST 2010
bibtimestamp: 2010.11.28 19:25:21 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: F. W. J. Olver
title:
Uniform, Exponentially Improved, Asymptotic Expansions for the Confluent Hypergeometric Function and Other Integral Transforms

bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMA/22/5; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib

rawtitle:
Uniform, Exponentially Improved, Asymptotic Expansions for the Confluent Hypergeometric Function and Other Integral Transforms

entry:
@Article{Olver:1991:UEIb,
  author =       "F. W. J. Olver",
  title =        "Uniform, Exponentially Improved, Asymptotic Expansions
                 for the Confluent Hypergeometric Function and Other
                 Integral Transforms",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "22",
  number =       "5",
  pages =        "1475--1489",
  month =        sep,
  year =         "1991",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "41A60 (33C15)",
  MRnumber =     "92g:41035",
  MRreviewer =   "Hans-J{\"u}rgen Glaeske",
  bibdate =      "Sun Nov 28 19:25:21 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/22/5;
                 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: Press:1991:BFF
author: William H. Press and Saul A. Teukolsky
title: Bessel Functions of Fractional Order
journal: j-COMPUT-PHYS
volume: 5
number: 2
pages: 244--??
month: mar
monthnumber: 3
year: 1991
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.4822982
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:28 MDT 2019
bibtimestamp: 2019.04.10 08:45:28 MDT
URL: https://aip.scitation.org/doi/10.1063/1.4822982
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William H. Press and Saul A. Teukolsky
rawtitle: {Bessel} Functions of Fractional Order
entry:
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  URL =          "https://aip.scitation.org/doi/10.1063/1.4822982",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Press:1991:MBF
author: William H. Press and Saul A. Teukolsky
title: Modified Bessel Functions of Fractional Order
journal: j-COMPUT-PHYS
volume: 5
number: 3
pages: 330--??
month: may
monthnumber: 5
year: 1991
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.4822991
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:29 MDT 2019
bibtimestamp: 2019.04.10 08:45:29 MDT
URL: https://aip.scitation.org/doi/10.1063/1.4822991
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William H. Press and Saul A. Teukolsky
rawtitle: Modified {Bessel} Functions of Fractional Order
entry:
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  author =       "William H. Press and Saul A. Teukolsky",
  title =        "Modified {Bessel} Functions of Fractional Order",
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  pages =        "330--??",
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  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
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bibtype: book
filename: elefunt.bib
label: Saan:1991:VFP
author: T. Saan
publisher: Eston. Nauchno-Proizvod. Obcdprime ed. Vychisl. Tekhn. Inform., Tartu
pages: 139
year: 1991
MRclass: 65-04 (65D15)
MRnumber: 94f:65008
MRreviewer: W. Govaerts
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: T. Saan
title:
cyr Vychislenie elementarnykh funktsiui s pomoshch'yu drobno-ratsional'nykh priblizheniui . (Russian) [Calculation of elementary functions by means of rational approximations]

rawtitle:
{{\cyr Vychislenie {\`e}lementarnykh funktsi{\u\i}s pomoshch'yu drobno-ratsional'nykh priblizheni{\u\i}}}. ({Russian}) [Calculation of elementary functions by means of rational approximations]

entry:
@Book{Saan:1991:VFP,
  author =       "T. Saan",
  title =        "{{\cyr Vychislenie {\`e}lementarnykh funktsi{\u\i}s
                 pomoshch'yu drobno-ratsional'nykh priblizheni{\u\i}}}.
                 ({Russian}) [Calculation of elementary functions by
                 means of rational approximations]",
  publisher =    "{\`E}ston. Nauchno-Proizvod. Ob\cdprime ed. Vychisl.
                 Tekhn. Inform., Tartu",
  pages =        "139",
  year =         "1991",
  MRclass =      "65-04 (65D15)",
  MRnumber =     "94f:65008",
  MRreviewer =   "W. Govaerts",
  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: Smith:1991:AFP
author: David M. Smith
title: Algorithm 693: A FORTRAN Package for Floating-Point Multiple-Precision Arithmetic
journal: j-TOMS
volume: 17
number: 2
pages: 273--283
month: jun
monthnumber: 6
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 23:44:20 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.04 23:44:20 ???
URL: http://www.acm.org/pubs/toc/Abstracts/toms/108585.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Loyola Marymount Univ., Los Angeles, CA, USA
journalURL: https://dl.acm.org/loi/toms
thesaurus: Digital arithmetic; Function approximation; Mathematics computing; Software packages; Subroutines
rawauthor: David M. Smith
rawtitle: Algorithm 693: {A FORTRAN} Package for Floating-Point Multiple-Precision Arithmetic
abstract:
FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.

keywords:
Accuracy; Algorithms; Elementary functions; Floating-point multiple-precision arithmetic; FM; FORTRAN-77 routines; Mathematical library; Portable software; Rounding off

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.

rawabstract:
FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.

entry:
@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "Algorithm 693: {A FORTRAN} Package for Floating-Point
                 Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/108585.html",
  abstract =     "FM is a collection of FORTRAN-77 routines which
                 performs floating-point multiple-precision arithmetic
                 and elementary functions. Results are almost always
                 correctly rounded, and due to improved algorithms used
                 for elementary functions, reasonable efficiency is
                 obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Loyola Marymount Univ., Los Angeles, CA, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accuracy; Algorithms; Elementary functions;
                 Floating-point multiple-precision arithmetic; FM;
                 FORTRAN-77 routines; Mathematical library; Portable
                 software; Rounding off",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
  thesaurus =    "Digital arithmetic; Function approximation;
                 Mathematics computing; Software packages; Subroutines",
}


bibtype: article
filename: elefunt.bib
label: Squire:1991:ANS
author: Jon S. Squire
title: Ada numerics standardization and testing
journal: j-SIGADA-LETTERS
volume: 11
number: 7
address: New York, NY, USA
pages: 1--286
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.24 15:01:45 MST
fjournal: ACM SIGAda Ada Letters
keywords: Ada (Computer program language)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
rawauthor: Jon S. Squire
rawtitle: {Ada} numerics standardization and testing
annote:
``A special edition from SIGAda ldots presented by SIGAda Numerics Working Group and Ada-Europe Numerics Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics Rapporteur Group.''--Cover. Includes bibliographies. Introduction to the proposed standard for the elementary functions in Ada / Kenneth W. Dritz --- Proposed standard for a generic package of elementary functions for Ada / edited by Kenneth W. Dritz --- Rationale for the proposed standard for a generic package of elementary functions for Ada; Proposed standard for a generic package of primitive functions for Ada; Rationale for the proposed standard for a generic package of primitive functions for Ada / Kenneth W. Dritz --- Proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / edited by Graham S. Hodgson --- Rationale for the proposed standard for packages of real and complex type declarations and basic operations for Ada (including vector and matrix types) / Graham S. Hodgson. Proposed standard for a generic package of complex elementary functions / edited by Jon S. Squire --- Rationale for the proposed standard for a generic package of complex elementary functions / Jon S. Squire --- A portable generic elementary function package in Ada and an accurate test suite / Ping Tak Peter Tang --- Towards validation of generic elementary functions and other standard Ada numerics packages / Jon S. Squire --- Floating point attributes in Ada / Dik T. Winter --- An Ada math library for real-time avionics / Donald A. Celarier and Donald W. Sando --- Predifined floating point type names, uniformity rapporteur group UI-48 / edited by Jon S. Squire.

entry:
@Article{Squire:1991:ANS,
  author =       "Jon S. Squire",
  title =        "{Ada} numerics standardization and testing",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  address =      "New York, NY, USA",
  pages =        "1--286",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "``A special edition from SIGAda \ldots{} presented by
                 SIGAda Numerics Working Group and Ada-Europe Numerics
                 Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
                 Rapporteur Group.''--Cover. Includes bibliographies.
                 Introduction to the proposed standard for the
                 elementary functions in Ada / Kenneth W. Dritz ---
                 Proposed standard for a generic package of elementary
                 functions for Ada / edited by Kenneth W. Dritz ---
                 Rationale for the proposed standard for a generic
                 package of elementary functions for Ada; Proposed
                 standard for a generic package of primitive functions
                 for Ada; Rationale for the proposed standard for a
                 generic package of primitive functions for Ada /
                 Kenneth W. Dritz --- Proposed standard for packages of
                 real and complex type declarations and basic operations
                 for Ada (including vector and matrix types) / edited by
                 Graham S. Hodgson --- Rationale for the proposed
                 standard for packages of real and complex type
                 declarations and basic operations for Ada (including
                 vector and matrix types) / Graham S. Hodgson. Proposed
                 standard for a generic package of complex elementary
                 functions / edited by Jon S. Squire --- Rationale for
                 the proposed standard for a generic package of complex
                 elementary functions / Jon S. Squire --- A portable
                 generic elementary function package in Ada and an
                 accurate test suite / Ping Tak Peter Tang --- Towards
                 validation of generic elementary functions and other
                 standard Ada numerics packages / Jon S. Squire ---
                 Floating point attributes in Ada / Dik T. Winter --- An
                 Ada math library for real-time avionics / Donald A.
                 Celarier and Donald W. Sando --- Predifined floating
                 point type names, uniformity rapporteur group UI-48 /
                 edited by Jon S. Squire.",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada (Computer program language)",
}


bibtype: article
filename: elefunt.bib
label: Squire:1991:PSG
author: J. S. Squire
title: Proposed standard for a generic package of complex elementary functions (Ada)
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 140--165
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics); C6110B (Software engineering techniques)
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: J. S. Squire
rawtitle: Proposed standard for a generic package of complex elementary functions ({Ada})
keywords:
ACM SIGAda; Ada; Ada-Europe Numerics Working Group; applications; complex elementary functions; complex mathematical routines; COMPLEX-ELEMENTARY-FUNCTIONS; generic package; GENERIC-; international standard; joint proposal; mathematics computing; Numerics Working Group; portable; reusable; software reusability; standards; WG9 Numerics Rapporteur Group

entry:
@Article{Squire:1991:PSG,
  author =       "J. S. Squire",
  title =        "Proposed standard for a generic package of complex
                 elementary functions ({Ada})",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "140--165",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
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  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda; Ada; Ada-Europe Numerics Working Group;
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                 generic package; GENERIC-; international standard;
                 joint proposal; mathematics computing; Numerics Working
                 Group; portable; reusable; software reusability;
                 standards; WG9 Numerics Rapporteur Group",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Squire:1991:RPS
author: Jon S. Squire
title: Rationale for the proposed standard for a generic package of complex elementary functions (Ada)
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 166--179
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages); C7310 (Mathematics); C6110B (Software engineering techniques)
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Jon S. Squire
rawtitle: Rationale for the proposed standard for a generic package of complex elementary functions ({Ada})
keywords:
ACM SIGAda Numerics Working Group; Ada; Ada-; basic complex mathematical; complex; COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions; error bounds; Europe Numerics Working Group; generic package; GENERIC-; mathematics computing; proposed standard; reusable applications; routines; software reusability; specification; standards

entry:
@Article{Squire:1991:RPS,
  author =       "Jon S. Squire",
  title =        "Rationale for the proposed standard for a generic
                 package of complex elementary functions ({Ada})",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "166--179",
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  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
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  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
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  keywords =     "ACM SIGAda Numerics Working Group; Ada; Ada-; basic
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                 COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions;
                 error bounds; Europe Numerics Working Group; generic
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                 standard; reusable applications; routines; software
                 reusability; specification; standards",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Squire:1991:TVG
author: J. S. Squire
title: Towards validation of generic elementary functions and other standard Ada numerics packages
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 217--243
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: J. S. Squire
rawtitle: Towards validation of generic elementary functions and other standard {Ada} numerics packages
keywords:
Ada; Ada listings; computing; conformance testing; conformance tests; generic elementary functions; implementors guide; mathematics; program testing; proposed ISO; prototype tests; standard Ada numerics packages; standards; test suite

classcodes:
C6150G (Diagnostic, testing, debugging and evaluating systems); C7310 (Mathematics); C6140D (High level languages)

entry:
@Article{Squire:1991:TVG,
  author =       "J. S. Squire",
  title =        "Towards validation of generic elementary functions and
                 other standard {Ada} numerics packages",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "217--243",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150G (Diagnostic, testing, debugging and evaluating
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  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; Ada listings; computing; conformance testing;
                 conformance tests; generic elementary functions;
                 implementors guide; mathematics; program testing;
                 proposed ISO; prototype tests; standard Ada numerics
                 packages; standards; test suite",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Tang:1991:PGE
author: Ping Tak Peter Tang
title: A portable generic elementary function package in Ada and an accurate test suite
journal: j-SIGADA-LETTERS
volume: 11
number: 7
pages: 181--216
month: Fall
year: 1991
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Thu Mar 20 07:41:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.20 07:41:09 MST
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Ping Tak Peter Tang
rawtitle: A portable generic elementary function package in {Ada} and an accurate test suite
keywords:
accurate test; Ada; function libraries; mathematics computing; portability; portable generic elementary function package; program testing; resolution; rigorous analysis; software; suite; test programs

classcodes:
C7310 (Mathematics); C6140D (High level languages); C6110B (Software engineering techniques); C6150G (Diagnostic, testing, debugging and evaluating systems)

entry:
@Article{Tang:1991:PGE,
  author =       "Ping Tak Peter Tang",
  title =        "A portable generic elementary function package in
                 {Ada} and an accurate test suite",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "181--216",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics); C6140D (High level languages);
                 C6110B (Software engineering techniques); C6150G
                 (Diagnostic, testing, debugging and evaluating
                 systems)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "accurate test; Ada; function libraries; mathematics
                 computing; portability; portable generic elementary
                 function package; program testing; resolution; rigorous
                 analysis; software; suite; test programs",
  treatment =    "P Practical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tang:1991:TLA
author: Ping Tak Peter Tang
title: Table-Lookup Algorithms for Elementary Functions and Their Error Analysis
crossref: Kornerup:1991:PIS
pages: 232--236
year: 1991
bibdate: Sat Nov 27 12:40:58 MST 2004
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.11.27 12:40:58 MST
acknowledgement: ack-nj
rawauthor: Ping Tak Peter Tang
rawtitle: Table-Lookup Algorithms for Elementary Functions and Their Error Analysis
entry:
@InProceedings{Tang:1991:TLA,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  crossref =     "Kornerup:1991:PIS",
  pages =        "232--236",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Wong:1991:FHA
author: W. F. Wong and E. Goto
title: Fast Hardware-based Algorithms for Elementary Function Computations
crossref: Anonymous:1991:PIS
pages: 56--65
year: 1991
bibdate: Sat Jan 11 10:14:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 10:14:06 MST
acknowledgement: ack-nhfb
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast Hardware-based Algorithms for Elementary Function Computations
entry:
@InProceedings{Wong:1991:FHA,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-based Algorithms for Elementary Function
                 Computations",
  crossref =     "Anonymous:1991:PIS",
  pages =        "56--65",
  year =         "1991",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  searchkey =    "ti:elementary function",
}


bibtype: article
filename: elefunt.bib
label: Zeilberger:1991:MPP
author: Doron Zeilberger
title: A Maple program for proving hypergeometric identities
journal: j-SIGSAM
volume: 25
number: 3
pages: 4--13
month: jul
monthnumber: 7
year: 1991
CODEN: SIGSBZ
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Fri Feb 8 18:27:01 MST 2002
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.02.08 18:27:01 MST
fjournal: SIGSAM Bulletin
acknowledgement: ack-nhfb
affiliation: Dept. of Math. and Comput. Sci., Drexel Univ., Philadelphia, PA, USA
classcodes: C7310 (Mathematics)
corpsource: Dept. of Math. and Comput. Sci., Drexel Univ., Philadelphia, PA, USA
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
thesaurus: Mathematics computing; Public domain software; Symbol manipulation; Theorem proving
treatment: P Practical
issue: 97
rawauthor: Doron Zeilberger
rawtitle: A {Maple} program for proving hypergeometric identities
abstract:
Gives the listing of a MAPLE program for implementing an algorithm for proving any terminating definite hypergeometric identity, and more generally, for finding the linear recurrence satisfied by any definite hypergeometric sum R(n):= Sigma /sub k/F(n,k), where F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/( alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub i'/)!). The algorithm for definite hypergeometric summation relies on Gosper's (1978) ingenious decision procedure for indefinite summation, but not in the obvious way!.

keywords:
definite; Definite hypergeometric summation; hypergeometric identity; hypergeometric summation; linear recurrence; Linear recurrence; manipulation; MAPLE program; mathematics computing; proofs; Proofs; public domain software; shareware; Shareware; symbol; terminating definite; Terminating definite hypergeometric identity; theorem proving

rawabstract:
Gives the listing of a MAPLE program for implementing an algorithm for proving any terminating definite hypergeometric identity, and more generally, for finding the linear recurrence satisfied by any definite hypergeometric sum R(n):= Sigma /sub k/F(n,k), where F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/( alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub i'/)!). The algorithm for definite hypergeometric summation relies on Gosper's (1978) ingenious decision procedure for indefinite summation, but not in the obvious way!.

entry:
@Article{Zeilberger:1991:MPP,
  author =       "Doron Zeilberger",
  title =        "A {Maple} program for proving hypergeometric
                 identities",
  journal =      j-SIGSAM,
  volume =       "25",
  number =       "3",
  pages =        "4--13",
  month =        jul,
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  CODEN =        "SIGSBZ",
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  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:01 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Gives the listing of a MAPLE program for implementing
                 an algorithm for proving any terminating definite
                 hypergeometric identity, and more generally, for
                 finding the linear recurrence satisfied by any definite
                 hypergeometric sum R(n):= Sigma /sub k/F(n,k), where
                 F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/(
                 alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub
                 i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub
                 i'/)!). The algorithm for definite hypergeometric
                 summation relies on Gosper's (1978) ingenious decision
                 procedure for indefinite summation, but not in the
                 obvious way!.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Drexel Univ.,
                 Philadelphia, PA, USA",
  classcodes =   "C7310 (Mathematics)",
  classification = "C7310 (Mathematics)",
  corpsource =   "Dept. of Math. and Comput. Sci., Drexel Univ.,
                 Philadelphia, PA, USA",
  fjournal =     "SIGSAM Bulletin",
  issue =        "97",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "definite; Definite hypergeometric summation;
                 hypergeometric identity; hypergeometric summation;
                 linear recurrence; Linear recurrence; manipulation;
                 MAPLE program; mathematics computing; proofs; Proofs;
                 public domain software; shareware; Shareware; symbol;
                 terminating definite; Terminating definite
                 hypergeometric identity; theorem proving",
  thesaurus =    "Mathematics computing; Public domain software; Symbol
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  treatment =    "P Practical",
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bibtype: article
filename: elefunt.bib
label: Ziv:1991:FEE
author: Abraham Ziv
title: Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit
journal: j-TOMS
volume: 17
number: 3
pages: 410--423
month: sep
monthnumber: 9
year: 1991
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Sep 1 10:15:31 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:15:31 ???
URL: http://www.acm.org/pubs/toc/Abstracts/toms/116813.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; standardization; theory
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Abraham Ziv
rawtitle: Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit
subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.

entry:
@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/116813.html",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; standardization; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}


bibtype: book
filename: elefunt.bib
label: Achieser:1992:TA
author: N. I. Achieser
title: Theory of Approximation
publisher: pub-DOVER
address: pub-DOVER:adr
pages: x + 307
year: 1992
ISBN: 0-486-67129-1 (paperback) OR 0486671291 (paperback)
ISBN13: 978-0-486-67129-1 (paperback) OR 9780486671291 (paperback)
LCCN: QA221 .A533 1992
bibdate: Fri Oct 20 08:06:59 MDT 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 08:06:59 MDT
series: Dover books on advanced mathematics
subject: Mathematical analysis
acknowledgement: ack-nhfb
rawauthor: N. I. Achieser
rawtitle: Theory of Approximation
remark:
Translation of Russian original, Leketisii po teorii approksimaetisii. Reprint of English translation cite Achieser:1956:TA.

TOC:
Approximation Problems in Linear Normalized Spaces Formulation of the Principal Problem in the Theory of Approximation / 1 The Concept of Metric Space / 1 The Concept of Linear Normalized Space / 2 Examples of Linear Normalized Spaces / 3 The Inequalities of Holder and Minkowski / 4 Additional Examples of Linear Normalized Spaces / 7 Hilbert Space / 8 The Fundamental Theorem of Approximation Theory in Linear Normalized Spaces / 10 Strictly Normalized Spaces / 11 An Example of Approximation in the Space $L^p$ / 12 Geometric Interpretation / 13 Separable and Complete Spaces / 14 Approximation Theorems in Hilbert Space / 15 An Example of Approximation in Hilbert Space / 19 More About the Approximation Problem in Hilbert Space / 21 Orthonormalized Vector Systems in Hilbert Space / 22 Orthogonalization of Vector Systems / 23 Infinite Orthonormalized Systems / 25 An Example of a Non-Separable System / 29 Weierstrass' First Theorem / 29 Weierstrass' Second Theorem / 32 The Separability of the Space C / 33 The Separability of the Space $L^p$ / 34 Generalization of Weierstrass' Theorem to the Space $L^p$ / 37 The Completeness of the Space $L^p$ / 38 Examples of Complete Orthonormalized Systems in L[superscript 2] / 40 Muntz's Theorem / 43 The Concept of the Linear Functional / 46 F. Riesz's Theorem / 47 A Criterion for the Closure of a Set of Vectors in Linear Normalized Spaces / 49 P. L. Tchebysheff's Domain of Ideas Statement of the Problem / 51 A Generalization of the Theorem of de la Vallee-Poussin / 52 The Existence Theorem / 53 Tchebysheff's Theorem / 55 A Special Case of Tchebysheff's Theorem / 57 The Tchebysheff Polynomials of Least Deviation from Zero / 57 A Further Example of P. Tchebysheff's Theorem / 58 An Example for the Application of the General Theorem of de la Vallee-Poussin / 60 An Example for the Application of P. L. Tchebysheff's General Theorem / 62 The Passage to Periodic Functions / 64 An Example of Approximating with the Aid of Periodic Functions / 66 The Weierstrass Function / 66 Haar's Problem / 67 Proof of the Necessity of Haar's Condition / 68 Proof of the Sufficiency of Haar's Condition / 69 An Example Related to Haar's Problem / 72 P. L. Tchebysheff's Systems of Functions / 73 Generalization of P. L. Tchebysheff's Theorem / 74 On a Question Pertaining to the Approximation of a Continuous Function in the Space $L$ / 76 A. A. Markoff's Theorem / 82 Special Cases of the Theorem of A. A. Markoff / 85 Elements of Harmonic Analysis The Simplest Properties of Fourier Series / 89 Fourier Series for Functions of Bounded Variation / 93 The Parseval Equation for Fourier Series / 97 Examples of Fourier Series / 98 Trigonometric Integrals / 101 The Riemann--Lebesgue Theorem / 103 Plancherel's Theory / 104 Watson's Theorem / 106 Plancherel's Theorem / 108 Fejer's Theorem / 110 Integral-Operators of the Fejer Type / 113 The Theorem of Young and Hardy / 116 Examples of Kernels of the Fejer Type / 118 The Fourier Transformation of Integrable Functions / 120 The Faltung of two Functions / 122 V. A. Stekloff's Functions / 123 Multimonotonic Functions / 125 Conjugate Functions / 126 Certain Extremal Properties of Integral Transcendental Functions of the Exponential Type Integral Functions of the Exponential Type / 130 The Borel Transformation / 132 The Theorem of Wiener and Paley / 134 Integral Functions of the Exponential Type which are Bounded along the Real Axis / 137 S. N. Bernstein's Inequality / 140 B. M. Levitan's Polynomials / 146 The Theorem of Fejer and Riesz. A Generalization of This Theorem / 152 A Criterion for the Representation of Continuous Functions as Fourier--Stieltjes Integrals / 154 Questions Regarding the Best Harmonic Approximation of Functions Preliminary Remarks / 160 The Modulus of Continuity / 161 The Generalization to the Space $L^p$ ($p geq 1$) / 162 An Example of Harmonic Approximation / 165 Some Estimates for Fourier Coefficients / 169 More about V. A. Stekloff's Functions / 173 Two Lemmas / 175 The Direct Problem of Harmonic Approximation / 176 A Criterion due to B. Sz.-Nagy / 183 The Best Approximation of Differentiable Functions / 187 Direct Observations Concerning Periodic Functions / 195 Jackson's Second Theorem / 199 The Generalized Fejer Method / 201 Berstein's Theorem / 206 Priwaloff's Theorem / 210 Generalizations of Bernstein's Theorems to the Space $L^p$ ($p geq 1$) / 211 The Best Harmonic Approximation of Analytic Functions / 214 A Different Formulation of the Result of the Preceding Section / 218 The Converse of Bernstein's Theorem / 221 Wiener's Theorem on Approximation Wiener's Problem / 224 The Necessity of Wiener's Condition / 224 Some Definitions and Notation / 225 Several Lemmas / 227 The Wiener--Levy Theorem / 230 Proof of the Sufficiency of Wiener's Condition / 233 Wiener's General Tauber Theorem / 234 Weakly Decreasing Functions / 235 Remarks on the Terminology / 237 Ikehara's Theorem / 238 Carleman's Tauber Theorem / 241 Various Addenda and Problems Elementary Extremal Problems and Certain Closure Criteria / 243 Szego's Theorem and Some of Its Applications / 256 Further Examples of Closed Sequences of Functions / 267 The Caratheodory--Fejer Problem and Similar Problems / 270 Solotareff's Problems and Related Problems / 280 The Best Harmonic Approximation of the Simplest Analytic Functions / 289 Notes / 296 Index / 306

rawTOC:
Approximation Problems in Linear Normalized Spaces \\ Formulation of the Principal Problem in the Theory of Approximation / 1 \\ The Concept of Metric Space / 1 \\ The Concept of Linear Normalized Space / 2 \\ Examples of Linear Normalized Spaces / 3 \\ The Inequalities of Holder and Minkowski / 4 \\ Additional Examples of Linear Normalized Spaces / 7 \\ Hilbert Space / 8 \\ The Fundamental Theorem of Approximation Theory in Linear Normalized Spaces / 10 \\ Strictly Normalized Spaces / 11 \\ An Example of Approximation in the Space $L^p$ / 12 \\ Geometric Interpretation / 13 \\ Separable and Complete Spaces / 14 \\ Approximation Theorems in Hilbert Space / 15 \\ An Example of Approximation in Hilbert Space / 19 \\ More About the Approximation Problem in Hilbert Space / 21 \\ Orthonormalized Vector Systems in Hilbert Space / 22 \\ Orthogonalization of Vector Systems / 23 \\ Infinite Orthonormalized Systems / 25 \\ An Example of a Non-Separable System / 29 \\ Weierstrass' First Theorem / 29 \\ Weierstrass' Second Theorem / 32 \\ The Separability of the Space C / 33 \\ The Separability of the Space $L^p$ / 34 \\ Generalization of Weierstrass' Theorem to the Space $L^p$ / 37 \\ The Completeness of the Space $L^p$ / 38 \\ Examples of Complete Orthonormalized Systems in L[superscript 2] / 40 \\ Muntz's Theorem / 43 \\ The Concept of the Linear Functional / 46 \\ F. Riesz's Theorem / 47 \\ A Criterion for the Closure of a Set of Vectors in Linear Normalized Spaces / 49 \\ P. L. Tchebysheff's Domain of Ideas \\ Statement of the Problem / 51 \\ A Generalization of the Theorem of de la Vallee-Poussin / 52 \\ The Existence Theorem / 53 \\ Tchebysheff's Theorem / 55 \\ A Special Case of Tchebysheff's Theorem / 57 \\ The Tchebysheff Polynomials of Least Deviation from Zero / 57 \\ A Further Example of P. Tchebysheff's Theorem / 58 \\ An Example for the Application of the General Theorem of de la Vallee-Poussin / 60 \\ An Example for the Application of P. L. Tchebysheff's General Theorem / 62 \\ The Passage to Periodic Functions / 64 \\ An Example of Approximating with the Aid of Periodic Functions / 66 \\ The Weierstrass Function / 66 \\ Haar's Problem / 67 \\ Proof of the Necessity of Haar's Condition / 68 \\ Proof of the Sufficiency of Haar's Condition / 69 \\ An Example Related to Haar's Problem / 72 \\ P. L. Tchebysheff's Systems of Functions / 73 \\ Generalization of P. L. Tchebysheff's Theorem / 74 \\ On a Question Pertaining to the Approximation of a Continuous Function in the Space $L$ / 76 \\ A. A. Markoff's Theorem / 82 \\ Special Cases of the Theorem of A. A. Markoff / 85 \\ Elements of Harmonic Analysis \\ The Simplest Properties of Fourier Series / 89 \\ Fourier Series for Functions of Bounded Variation / 93 \\ The Parseval Equation for Fourier Series / 97 \\ Examples of Fourier Series / 98 \\ Trigonometric Integrals / 101 \\ The Riemann--Lebesgue Theorem / 103 \\ Plancherel's Theory / 104 \\ Watson's Theorem / 106 \\ Plancherel's Theorem / 108 \\ Fejer's Theorem / 110 \\ Integral-Operators of the Fejer Type / 113 \\ The Theorem of Young and Hardy / 116 \\ Examples of Kernels of the Fejer Type / 118 \\ The Fourier Transformation of Integrable Functions / 120 \\ The Faltung of two Functions / 122 \\ V. A. Stekloff's Functions / 123 \\ Multimonotonic Functions / 125 \\ Conjugate Functions / 126 \\ Certain Extremal Properties of Integral Transcendental Functions of the Exponential Type \\ Integral Functions of the Exponential Type / 130 \\ The Borel Transformation / 132 \\ The Theorem of Wiener and Paley / 134 \\ Integral Functions of the Exponential Type which are Bounded along the Real Axis / 137 \\ S. N. Bernstein's Inequality / 140 \\ B. M. Levitan's Polynomials / 146 \\ The Theorem of Fejer and Riesz. A Generalization of This Theorem / 152 \\ A Criterion for the Representation of Continuous Functions as Fourier--Stieltjes Integrals / 154 \\ Questions Regarding the Best Harmonic Approximation of Functions Preliminary Remarks / 160 \\ The Modulus of Continuity / 161 \\ The Generalization to the Space $L^p$ ($p \geq 1$) / 162 \\ An Example of Harmonic Approximation / 165 \\ Some Estimates for Fourier Coefficients / 169 \\ More about V. A. Stekloff's Functions / 173 \\ Two Lemmas / 175 \\ The Direct Problem of Harmonic Approximation / 176 \\ A Criterion due to B. Sz.-Nagy / 183 \\ The Best Approximation of Differentiable Functions / 187 \\ Direct Observations Concerning Periodic Functions / 195 \\ Jackson's Second Theorem / 199 \\ The Generalized Fejer Method / 201 \\ Berstein's Theorem / 206 \\ Priwaloff's Theorem / 210 \\ Generalizations of Bernstein's Theorems to the Space $L^p$ ($p \geq 1$) / 211 \\ The Best Harmonic Approximation of Analytic Functions / 214 \\ A Different Formulation of the Result of the Preceding Section / 218 \\ The Converse of Bernstein's Theorem / 221 \\ Wiener's Theorem on Approximation \\ Wiener's Problem / 224 \\ The Necessity of Wiener's Condition / 224 \\ Some Definitions and Notation / 225 \\ Several Lemmas / 227 \\ The Wiener--Levy Theorem / 230 \\ Proof of the Sufficiency of Wiener's Condition / 233 \\ Wiener's General Tauber Theorem / 234 \\ Weakly Decreasing Functions / 235 \\ Remarks on the Terminology / 237 \\ Ikehara's Theorem / 238 \\ Carleman's Tauber Theorem / 241 \\ Various Addenda and Problems \\ Elementary Extremal Problems and Certain Closure Criteria / 243 \\ Szego's Theorem and Some of Its Applications / 256 \\ Further Examples of Closed Sequences of Functions / 267 \\ The Caratheodory--Fejer Problem and Similar Problems / 270 \\ Solotareff's Problems and Related Problems / 280 \\ The Best Harmonic Approximation of the Simplest Analytic Functions / 289 \\ Notes / 296 \\ Index / 306

entry:
@Book{Achieser:1992:TA,
  author =       "N. I. Achieser",
  title =        "Theory of Approximation",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "x + 307",
  year =         "1992",
  ISBN =         "0-486-67129-1 (paperback)",
  ISBN-13 =      "978-0-486-67129-1 (paperback)",
  LCCN =         "QA221 .A533 1992",
  bibdate =      "Fri Oct 20 08:06:59 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover books on advanced mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Russian original, Lek{\"e}t{\`\i}sii po
                 teorii approksima{\"e}t{\`\i}sii. Reprint of English
                 translation \cite{Achieser:1956:TA}.",
  subject =      "Mathematical analysis",
  tableofcontents = "Approximation Problems in Linear Normalized Spaces
                 \\
                 Formulation of the Principal Problem in the Theory of
                 Approximation / 1 \\
                 The Concept of Metric Space / 1 \\
                 The Concept of Linear Normalized Space / 2 \\
                 Examples of Linear Normalized Spaces / 3 \\
                 The Inequalities of Holder and Minkowski / 4 \\
                 Additional Examples of Linear Normalized Spaces / 7 \\
                 Hilbert Space / 8 \\
                 The Fundamental Theorem of Approximation Theory in
                 Linear Normalized Spaces / 10 \\
                 Strictly Normalized Spaces / 11 \\
                 An Example of Approximation in the Space $L^p$ / 12 \\
                 Geometric Interpretation / 13 \\
                 Separable and Complete Spaces / 14 \\
                 Approximation Theorems in Hilbert Space / 15 \\
                 An Example of Approximation in Hilbert Space / 19 \\
                 More About the Approximation Problem in Hilbert Space /
                 21 \\
                 Orthonormalized Vector Systems in Hilbert Space / 22
                 \\
                 Orthogonalization of Vector Systems / 23 \\
                 Infinite Orthonormalized Systems / 25 \\
                 An Example of a Non-Separable System / 29 \\
                 Weierstrass' First Theorem / 29 \\
                 Weierstrass' Second Theorem / 32 \\
                 The Separability of the Space C / 33 \\
                 The Separability of the Space $L^p$ / 34 \\
                 Generalization of Weierstrass' Theorem to the Space
                 $L^p$ / 37 \\
                 The Completeness of the Space $L^p$ / 38 \\
                 Examples of Complete Orthonormalized Systems in
                 L[superscript 2] / 40 \\
                 Muntz's Theorem / 43 \\
                 The Concept of the Linear Functional / 46 \\
                 F. Riesz's Theorem / 47 \\
                 A Criterion for the Closure of a Set of Vectors in
                 Linear Normalized Spaces / 49 \\
                 P. L. Tchebysheff's Domain of Ideas \\
                 Statement of the Problem / 51 \\
                 A Generalization of the Theorem of de la Vallee-Poussin
                 / 52 \\
                 The Existence Theorem / 53 \\
                 Tchebysheff's Theorem / 55 \\
                 A Special Case of Tchebysheff's Theorem / 57 \\
                 The Tchebysheff Polynomials of Least Deviation from
                 Zero / 57 \\
                 A Further Example of P. Tchebysheff's Theorem / 58 \\
                 An Example for the Application of the General Theorem
                 of de la Vallee-Poussin / 60 \\
                 An Example for the Application of P. L. Tchebysheff's
                 General Theorem / 62 \\
                 The Passage to Periodic Functions / 64 \\
                 An Example of Approximating with the Aid of Periodic
                 Functions / 66 \\
                 The Weierstrass Function / 66 \\
                 Haar's Problem / 67 \\
                 Proof of the Necessity of Haar's Condition / 68 \\
                 Proof of the Sufficiency of Haar's Condition / 69 \\
                 An Example Related to Haar's Problem / 72 \\
                 P. L. Tchebysheff's Systems of Functions / 73 \\
                 Generalization of P. L. Tchebysheff's Theorem / 74 \\
                 On a Question Pertaining to the Approximation of a
                 Continuous Function in the Space $L$ / 76 \\
                 A. A. Markoff's Theorem / 82 \\
                 Special Cases of the Theorem of A. A. Markoff / 85 \\
                 Elements of Harmonic Analysis \\
                 The Simplest Properties of Fourier Series / 89 \\
                 Fourier Series for Functions of Bounded Variation / 93
                 \\
                 The Parseval Equation for Fourier Series / 97 \\
                 Examples of Fourier Series / 98 \\
                 Trigonometric Integrals / 101 \\
                 The Riemann--Lebesgue Theorem / 103 \\
                 Plancherel's Theory / 104 \\
                 Watson's Theorem / 106 \\
                 Plancherel's Theorem / 108 \\
                 Fejer's Theorem / 110 \\
                 Integral-Operators of the Fejer Type / 113 \\
                 The Theorem of Young and Hardy / 116 \\
                 Examples of Kernels of the Fejer Type / 118 \\
                 The Fourier Transformation of Integrable Functions /
                 120 \\
                 The Faltung of two Functions / 122 \\
                 V. A. Stekloff's Functions / 123 \\
                 Multimonotonic Functions / 125 \\
                 Conjugate Functions / 126 \\
                 Certain Extremal Properties of Integral Transcendental
                 Functions of the Exponential Type \\
                 Integral Functions of the Exponential Type / 130 \\
                 The Borel Transformation / 132 \\
                 The Theorem of Wiener and Paley / 134 \\
                 Integral Functions of the Exponential Type which are
                 Bounded along the Real Axis / 137 \\
                 S. N. Bernstein's Inequality / 140 \\
                 B. M. Levitan's Polynomials / 146 \\
                 The Theorem of Fejer and Riesz. A Generalization of
                 This Theorem / 152 \\
                 A Criterion for the Representation of Continuous
                 Functions as Fourier--Stieltjes Integrals / 154 \\
                 Questions Regarding the Best Harmonic Approximation of
                 Functions Preliminary Remarks / 160 \\
                 The Modulus of Continuity / 161 \\
                 The Generalization to the Space $L^p$ ($p \geq 1$) /
                 162 \\
                 An Example of Harmonic Approximation / 165 \\
                 Some Estimates for Fourier Coefficients / 169 \\
                 More about V. A. Stekloff's Functions / 173 \\
                 Two Lemmas / 175 \\
                 The Direct Problem of Harmonic Approximation / 176 \\
                 A Criterion due to B. Sz.-Nagy / 183 \\
                 The Best Approximation of Differentiable Functions /
                 187 \\
                 Direct Observations Concerning Periodic Functions / 195
                 \\
                 Jackson's Second Theorem / 199 \\
                 The Generalized Fejer Method / 201 \\
                 Berstein's Theorem / 206 \\
                 Priwaloff's Theorem / 210 \\
                 Generalizations of Bernstein's Theorems to the Space
                 $L^p$ ($p \geq 1$) / 211 \\
                 The Best Harmonic Approximation of Analytic Functions /
                 214 \\
                 A Different Formulation of the Result of the Preceding
                 Section / 218 \\
                 The Converse of Bernstein's Theorem / 221 \\
                 Wiener's Theorem on Approximation \\
                 Wiener's Problem / 224 \\
                 The Necessity of Wiener's Condition / 224 \\
                 Some Definitions and Notation / 225 \\
                 Several Lemmas / 227 \\
                 The Wiener--Levy Theorem / 230 \\
                 Proof of the Sufficiency of Wiener's Condition / 233
                 \\
                 Wiener's General Tauber Theorem / 234 \\
                 Weakly Decreasing Functions / 235 \\
                 Remarks on the Terminology / 237 \\
                 Ikehara's Theorem / 238 \\
                 Carleman's Tauber Theorem / 241 \\
                 Various Addenda and Problems \\
                 Elementary Extremal Problems and Certain Closure
                 Criteria / 243 \\
                 Szego's Theorem and Some of Its Applications / 256 \\
                 Further Examples of Closed Sequences of Functions / 267
                 \\
                 The Caratheodory--Fejer Problem and Similar Problems /
                 270 \\
                 Solotareff's Problems and Related Problems / 280 \\
                 The Best Harmonic Approximation of the Simplest
                 Analytic Functions / 289 \\
                 Notes / 296 \\
                 Index / 306",
}


bibtype: article
filename: elefunt.bib
label: Anderson:1992:FIH
author: G. D. Anderson and M. K. Vamanamurthy and M. Vuorinen
title: Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 23
number: 2
pages: 512--524
month: mar
monthnumber: 3
year: 1992
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33C05 (33C75)
MRnumber: 93b:33001
MRreviewer: J. M. H. Peters
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: G. D. Anderson and M. K. Vamanamurthy and M. Vuorinen
rawtitle: Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
entry:
@Article{Anderson:1992:FIH,
  author =       "G. D. Anderson and M. K. Vamanamurthy and M.
                 Vuorinen",
  title =        "Functional Inequalities for Hypergeometric Functions
                 and Complete Elliptic Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "23",
  number =       "2",
  pages =        "512--524",
  month =        mar,
  year =         "1992",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33C05 (33C75)",
  MRnumber =     "93b:33001",
  MRreviewer =   "J. M. H. Peters",
  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: book
filename: elefunt.bib
label: Baker:1992:CMF
author: Louis Baker
title: C Mathematical Function Handbook
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: xviii + 757
year: 1992
ISBN: 0-07-911158-0 OR 0079111580
ISBN13: 978-0-07-911158-6 OR 9780079111586
LCCN: QA351.B17 1991; QA351 .B17 1992
bibdate: Fri Aug 31 18:54:02 MDT 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.08.31 18:54:02 MDT
series: McGraw-Hill programming tools for scientists and engineers
remark: System requirements for computer disk: PC; C or C++ compiler.
subject: Functions, Special; Computer programs; C (Computer program language)
acknowledgement: ack-nhfb
rawauthor: Louis Baker
rawtitle: {C} Mathematical Function Handbook
TOC:
Preface / xv 1. Special Functions and Numerical Analysis / 1 Correspondence with Abramowitz and Stegun / 1 Numerical Analysis / 1 The IEEE-754 Standard / 1 Practical Considerations / 3 Reference / 6 2. Special Functions in C and C++ / 8 C and C++ / 8 Portability, ANSI C, and C++ / 8 Infinite Loops / 9 Header Files COMPLEX.H, CMLIB.H, PROTOM.H / 10 Error Handling / 10 Pitfalls with Special Functions / 11 Normalization Conventions / 12 Tips and Pitfalls in C / 12 Calling C from C++ / 14 References / 15 Cmlib.h / 16 COMPLEX.H Header File / 17 Prototypes for booktitle C Mathematical Function Handbook / 19 3. Elementary Analytical Methods / 33 Powers and Roots / 33 Complex Numbers / 34 Roots of Polynomials / 35 Quadratics / 35 Cubics / 35 Quartics (biquadratics) / 36 Implementation Considerations / 37 Ouintics / 38 References / 38 Complex Variable Auxiliary Routines / 39 Powers and Roots / 45 Polynomial Root Finders / 48 Test Driver for Programs of Chapters 3-4 / 60 4. Elementary Transcendental Functions / 72 Elementary Functions / 72 Complex Elementary Functions / 73 Gudermannian / 74 References / 74 5. Exponential Integral and Relatives / 75 Exponential and Related Integrals / 75 Methods / 76 References / 76 Shi(x) and Chi(x) / 76 Exponential Integral / 78 Test Driver Results: Exponential Integral and Relatives / 95 6. Gamma Function and Related Integrals / 100 Gamma Function and Relatives / 100 The Pochhammer Symbol / 100 Methods / 101 Asymptotic Series / 101 Reference / 101 Gamma Function and Relatives / 102 Digamma and First 2 Polygamma Functions / 111 7. Error Function and Relatives / 115 Error Function and Relatives / 115 Methods / 117 Recurrence Relations / 117 C Code / 118 References / 118 Figure: Dawson's Integral / 118 Plasma Dispersion Function / 120 Iterated Error Function / 127 Boehmer (generalized Fresnel) Integral / 129 Complementary Error Function for Complex Arguments / 133 Test Driver Chapter 7 / 134 8. Legendre Functions / 142 Legendre Functions / 142 Derivatives / 143 Applications / 143 Methods / 144 References / 144 Legendre and Associated Legendre Functions / 146 Legendre Functions for $|x| > 1$ / 155 Toroidal $P|x| > 1$ / 163 Mehler (Conical Legendre) Functions / 164 Test Driver for Legendre Functions of Chapter 8 / 166 9. Bessel Functions / 177 Struve Functions / 178 Anger and Weber Functions / 179 Relationship to Confluent Hypergeometric Function / 179 Derivatives / 179 Other Related Functions / 179 Zeros of Bessel Functions / 180 Applications / 180 Methods / 180 References / 181 Bessel Functions for Complex Arguments / 182 Bessel Functions: Rational Approximations / 194 Bessel Function Tables as a Function of (Integral) n / 201 Zeros of Bessel Functions / 205 Test Driver for Bessel Functions / 211 Test Driver Bessel Zero / 220 Output of Bessel Function Test Driver / 221 Output of Test Driver for Zerobess() / 237 10. Bessel Functions of Fractional Order / 239 Introduction / 239 Spherical Bessel Functions / 239 Airy Functions / 239 Applications / 240 Asymptotics / 240 Caustics / 240 Schroedinger's Equation, Turning Points and the WKB Method / 242 Methods / 243 The $|A|$ Function / 243 References / 244 Spherical Bessel Functions and Allied Routines / 245 Airy, Bessel Functions and Integrals Thereof / 250 11. Integrals of Bessel Functions / 265 Introduction / 265 Applications / 265 Methods / 265 Bickley Functions / 265 Adaptive Quadrature / 266 Repeated Integrals of Jn / 266 Other Integrals / 266 References / 266 Figures of Integrals of Bessel Functions / 267 Integrals of Bessel Functions / 277 Adaptive Integration Routine / 242 12. Struve and Anger--Weber Functions / 284 Introduction / 284 Struve Functions / 284 Anger--Weber Functions / 284 Methods / 285 References / 285 Figures / 286 Struve Functions General Order / 289 Struve Functions Lowest Order / 291 Integrals of Struve HO, HO/t, LO / 295 Integral of Anger--Weber Function / 297 13. Confluent Hypergeometric Functions and Relatives / 301 Introduction / 301 Airy Functions / 303 Applications / 303 Methods / 304 References / 304 Confluent Hypergeometric Function Complex Arguments / 305 Test Drive Confluent Hypergeometric Function / 318 Confluent Hypergeometric Function U / 322 Test Driver U.c / 331 Test Output: Confluent-Hypergeometric Function / 332 Test Output: U / 334 14. Coulomb Wave Functions / 335 Introduction / 335 Methods / 336 References / 337 Coulomb Wave Functions / 339 Test Driver Coulomb Wave Functions / 343 Test Output: Coulomb wave Functions / 344 15. The Hypergeometric Function / 345 Introduction / 345 Applications / 346 Methods / 346 References / 346 Hypergeometric Function Complex Arguments / 347 Legendre Function $P$ for Complex Parameters / 364 Legendre $Q$ for Complex Arguments / 366 Test Driver $_2F_1$ / 369 Output: Gauss Hypergeometric Functions / 370 Real Hypergeometric Function and Relatives / 371 16. The Elliptic Functions / 373 Introduction / 373 Applications / 376 Methods / 376 References / 377 Figure / 378 Basic Elliptic Functions Real Arguments / 380 Elliptic Integral of Third Kind / 391 Jacobian Elliptic Function Complex Argument / 397 Complex Elliptic Theta Functions / 406 Output: Test Driver for Elliptic Functions / 411 17. The Elliptic Integrals / 416 Introduction / 415 Caveat / 416 References / 417 Figures / 417 18. The Weierstrass Elliptic Function and Relatives / 425 Introduction / 425 Methods / 427 References / 427 Inverse of Weierstrass Elliptic P . / 428 Brent Root Finder / 430 19. The Parabolic Cylinder Functions / 432 Introduction / 432 Methods / 432 Figures / 432 Parabolic Cylinder Functions / 435 Test Driver Parabolic Cylinder Function / 442 20. The Mathieu Functions / 444 Introduction / 444 Method / 443 References / 445 Figures / 445 Mathieu Functions / 449 Mathieu Functions Test Driver / 465 Test Output: Mathieu Functions / 467 21. The Spheroidal Wave Functions / 475 Introduction / 475 Spheroidal Wave Functions / 475 Generalized Spheroidal Wave Functions / 477 Caveat / 477 Method / 477 References / 478 Figures / 478 Spheroidal Wave Functions / 486 Legptable Pn,m for n = m to ntop / 500 Test Driver Spheroidal Wave Functions / 501 Test Output: Spheroidal Wave Functions / 504 22. Orthogonal Polynomials / 509 Introduction / 509 Contents / 509 Applications / 509 Method / 509 Orthogonal Polynomials / 510 Test Driver Orthogonal Polynomials / 513 23. Bernoulli and Euler Numbers and Polynomials, Riemann Zeta Function / 516 Introduction / 516 Riemann Zeta Function / 516 Bernoulli Polynomials and Numbers / 517 Euler Polynomials and Numbers / 517 Methods / 517 References / 517 Riemann Zeta (real arguments) / 519 Test Driver Riemann Zeta (Real) / 527 Test Output: Riemann Zeta, Bernoulli, Euler Numbers / 324 24. Combinatorics. Stirling Numbers / 529 Introduction / 529 Methods / 529 References / 529 Stirling Numbers First and Second Kind / 530 Fibonacci Numbers / 531 Binomial Coefficients / 532 Test Driver for Stirling Numbers / 533 Test Output: Stirling, Fibonacci, Binomial Coefficients / 534 25. Numerical Analysis / 535 Discussion / 535 Reference / 536 26. Statistical Functions, Probability Distributions, and Random Variables / 537 Introduction / 537 Methods / 537 References / 537 Random Numbers / 538 Random Distributions / 544 Test Driver for Random Number / 551 Test Output: Random Numbers and Distributions / 560 Calculator Version of Stat.c Routines / 565 27. Miscellaneous Functions / 592 Introduction / 592 Debye Functions / 592 Method / 593 Sievert / 593 Method / 593 Abramowitz and Kruse--Ramsey / 593 Method / 593 Ritchie / 593 Method / 593 Dilogarithm and Polylogarithms / 593 Method / 594 Claussen / 594 Method / 594 Lobachevsky / 594 Method / 594 Clebsch--Gordon and Relatives / 594 Method / 595 v and Relatives / 595 Method / 596 References / 596 Figures / 595 Sievert Integral Chapter 27 / 605 Dilogarithm / 606 Polylogarithm Function / 607 ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 / 608 Nu and Mu Integrals of Erdelyi Vol III p. 217 / 612 Lobachevsky Function / 614 Test Driver Miscellaneous Functions / 616 Test Driver Ritchie's Integral / 619 Test Output: Miscellaneous Functions / 620 Test Output: Ritchie's Integral / 624 Clebsch--Gordon, Wigner, Related Coefficients / 625 Test Driver Wigner / 631 Wigner Sample Output / 635 28. Scales of Notation / 636 29. C++ Programs / 637 Hurwitz Zeta and Lerch Phi Transcendent / 638 Methods / 638 Meijer $G$ and Generalized Hypergeometric Functions / 638 Methods / 639 Elliptic Functions / 639 Applications / 639 Methods / 639 Fock Functions / 640 Methods / 541 References / 641 // Complex.hpp / 643 Elliptic Functions / 646 Arithmetic--Geometric Mean (AGM) Supplemental / 656 Test Driver for: Elliptic Functions / 662 // Cvector.hpp / 665 // cmatrix.hpp / 666 Test Output: Elliptic Functions / 667 Complex C++ Utilities / 669 Fock Functions / 674 Test Output: Fock Functions / 682 ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 / 697 Test Output: Abramowitz Functions, Complex Arguments / 701 Riemann and Hurwitz / 712 Riemann and Hurwitz: Pade / 716 Lerch Phi Transcendent / 720 Generalized Hypergeometric Function and Meijer $G$ / 723 Test Output: Meijer $G$ / 730 Generalized Hypergeometric Function and Meijer $G$ / 731 Test Output: Meijer $G$ with Pade / 738 MacRobert E Function / 739 30. Xref / 740 Other Listings / 741 Adaptive Quadrature (from C loops) / 741 Test Driver Chaps. 16--18 / 743 Index to C Functions / 747 Index / 753

rawTOC:
Preface / xv \\ 1. Special Functions and Numerical Analysis / 1 \\ \\ Correspondence with Abramowitz and Stegun / 1 \\ Numerical Analysis / 1 \\ The IEEE-754 Standard / 1 \\ Practical Considerations / 3 \\ Reference / 6 \\ \\ 2. Special Functions in C and C++ / 8 \\ C and C++ / 8 \\ Portability, ANSI C, and C++ / 8 \\ Infinite Loops / 9 \\ Header Files COMPLEX.H, CMLIB.H, PROTOM.H / 10 \\ Error Handling / 10 \\ Pitfalls with Special Functions / 11 \\ Normalization Conventions / 12 \\ Tips and Pitfalls in C / 12 \\ Calling C from C++ / 14 \\ References / 15 \\ Cmlib.h / 16 \\ COMPLEX.H Header File / 17 \\ Prototypes for \booktitle{C Mathematical Function Handbook} / 19 \\ \\ 3. Elementary Analytical Methods / 33 \\ Powers and Roots / 33 \\ Complex Numbers / 34 \\ Roots of Polynomials / 35 \\ Quadratics / 35 \\ Cubics / 35 \\ Quartics (biquadratics) / 36 \\ Implementation Considerations / 37 \\ Ouintics / 38 \\ References / 38 \\ Complex Variable Auxiliary Routines / 39 \\ Powers and Roots / 45 \\ Polynomial Root Finders / 48 \\ Test Driver for Programs of Chapters 3-4 / 60 \\ \\ 4. Elementary Transcendental Functions / 72 \\ Elementary Functions / 72 \\ Complex Elementary Functions / 73 \\ Gudermannian / 74 \\ References / 74 \\ \\ 5. Exponential Integral and Relatives / 75 \\ Exponential and Related Integrals / 75 \\ Methods / 76 \\ References / 76 \\ Shi(x) and Chi(x) / 76 \\ Exponential Integral / 78 \\ Test Driver Results: Exponential Integral and Relatives / 95 \\ \\ 6. Gamma Function and Related Integrals / 100 \\ Gamma Function and Relatives / 100 \\ The Pochhammer Symbol / 100 \\ Methods / 101 \\ Asymptotic Series / 101 \\ Reference / 101 \\ Gamma Function and Relatives / 102 \\ Digamma and First 2 Polygamma Functions / 111 \\ \\ 7. Error Function and Relatives / 115 \\ Error Function and Relatives / 115 \\ Methods / 117 \\ Recurrence Relations / 117 \\ C Code / 118 \\ References / 118 \\ Figure: Dawson's Integral / 118 \\ Plasma Dispersion Function / 120 \\ Iterated Error Function / 127 \\ Boehmer (generalized Fresnel) Integral / 129 \\ Complementary Error Function for Complex Arguments / 133 \\ Test Driver Chapter 7 / 134 \\ \\ 8. Legendre Functions / 142 \\ Legendre Functions / 142 \\ Derivatives / 143 \\ Applications / 143 \\ Methods / 144 \\ References / 144 \\ Legendre and Associated Legendre Functions / 146 \\ Legendre Functions for $|x| > 1$ / 155 \\ Toroidal $P|x| > 1$ / 163 \\ Mehler (Conical Legendre) Functions / 164 \\ Test Driver for Legendre Functions of Chapter 8 / 166 \\ \\ 9. Bessel Functions / 177 \\ Struve Functions / 178 \\ Anger and Weber Functions / 179 \\ Relationship to Confluent Hypergeometric Function / 179 \\ Derivatives / 179 \\ Other Related Functions / 179 \\ Zeros of Bessel Functions / 180 \\ Applications / 180 \\ Methods / 180 \\ References / 181 \\ Bessel Functions for Complex Arguments / 182 \\ Bessel Functions: Rational Approximations / 194 \\ Bessel Function Tables as a Function of (Integral) n / 201 \\ Zeros of Bessel Functions / 205 \\ Test Driver for Bessel Functions / 211 \\ Test Driver Bessel Zero / 220 \\ Output of Bessel Function Test Driver / 221 \\ Output of Test Driver for Zerobess() / 237 \\ \\ 10. Bessel Functions of Fractional Order / 239 \\ Introduction / 239 \\ Spherical Bessel Functions / 239 \\ Airy Functions / 239 \\ Applications / 240 \\ Asymptotics / 240 \\ Caustics / 240 \\ Schroedinger's Equation, Turning Points and the WKB Method / 242 \\ Methods / 243 \\ The $|A|$ Function / 243 \\ References / 244 \\ Spherical Bessel Functions and Allied Routines / 245 \\ Airy, Bessel Functions and Integrals Thereof / 250 \\ \\ 11. Integrals of Bessel Functions / 265 \\ Introduction / 265 \\ Applications / 265 \\ Methods / 265 \\ Bickley Functions / 265 \\ Adaptive Quadrature / 266 \\ Repeated Integrals of Jn / 266 \\ Other Integrals / 266 \\ References / 266 \\ Figures of Integrals of Bessel Functions / 267 \\ Integrals of Bessel Functions / 277 \\ Adaptive Integration Routine / 242 \\ \\ 12. Struve and Anger--Weber Functions / 284 \\ Introduction / 284 \\ Struve Functions / 284 \\ Anger--Weber Functions / 284 \\ Methods / 285 \\ References / 285 \\ Figures / 286 \\ Struve Functions General Order / 289 \\ Struve Functions Lowest Order / 291 \\ Integrals of Struve HO, HO/t, LO / 295 \\ Integral of Anger--Weber Function / 297 \\ \\ 13. Confluent Hypergeometric Functions and Relatives / 301 \\ Introduction / 301 \\ Airy Functions / 303 \\ Applications / 303 \\ Methods / 304 \\ References / 304 \\ Confluent Hypergeometric Function Complex Arguments / 305 \\ Test Drive Confluent Hypergeometric Function / 318 \\ Confluent Hypergeometric Function U / 322 \\ Test Driver U.c / 331 \\ Test Output: Confluent-Hypergeometric Function / 332 \\ Test Output: U / 334 \\ \\ 14. Coulomb Wave Functions / 335 \\ Introduction / 335 \\ Methods / 336 \\ References / 337 \\ Coulomb Wave Functions / 339 \\ Test Driver Coulomb Wave Functions / 343 \\ Test Output: Coulomb wave Functions / 344 \\ \\ 15. The Hypergeometric Function / 345 \\ Introduction / 345 \\ Applications / 346 \\ Methods / 346 \\ References / 346 \\ Hypergeometric Function Complex Arguments / 347 \\ Legendre Function $P$ for Complex Parameters / 364 \\ Legendre $Q$ for Complex Arguments / 366 \\ Test Driver $_2F_1$ / 369 \\ Output: Gauss Hypergeometric Functions / 370 \\ Real Hypergeometric Function and Relatives / 371 \\ \\ 16. The Elliptic Functions / 373 \\ Introduction / 373 \\ Applications / 376 \\ Methods / 376 \\ References / 377 \\ Figure / 378 \\ Basic Elliptic Functions Real Arguments / 380 \\ Elliptic Integral of Third Kind / 391 \\ Jacobian Elliptic Function Complex Argument / 397 \\ Complex Elliptic Theta Functions / 406 \\ Output: Test Driver for Elliptic Functions / 411 \\ \\ 17. The Elliptic Integrals / 416 \\ Introduction / 415 \\ Caveat / 416 \\ References / 417 \\ Figures / 417 \\ \\ 18. The Weierstrass Elliptic Function and Relatives / 425 \\ Introduction / 425 \\ Methods / 427 \\ References / 427 \\ Inverse of Weierstrass Elliptic P . / 428 \\ Brent Root Finder / 430 \\ \\ 19. The Parabolic Cylinder Functions / 432 \\ Introduction / 432 \\ Methods / 432 \\ Figures / 432 \\ Parabolic Cylinder Functions / 435 \\ Test Driver Parabolic Cylinder Function / 442 \\ \\ 20. The Mathieu Functions / 444 \\ Introduction / 444 \\ Method / 443 \\ References / 445 \\ Figures / 445 \\ Mathieu Functions / 449 \\ Mathieu Functions Test Driver / 465 \\ Test Output: Mathieu Functions / 467 \\ \\ 21. The Spheroidal Wave Functions / 475 \\ Introduction / 475 \\ Spheroidal Wave Functions / 475 \\ Generalized Spheroidal Wave Functions / 477 \\ Caveat / 477 \\ Method / 477 \\ References / 478 \\ Figures / 478 \\ Spheroidal Wave Functions / 486 \\ Legptable Pn,m for n = m to ntop / 500 \\ Test Driver Spheroidal Wave Functions / 501 \\ Test Output: Spheroidal Wave Functions / 504 \\ \\ 22. Orthogonal Polynomials / 509 \\ Introduction / 509 \\ Contents / 509 \\ Applications / 509 \\ Method / 509 \\ Orthogonal Polynomials / 510 \\ Test Driver Orthogonal Polynomials / 513 \\ \\ 23. Bernoulli and Euler Numbers and Polynomials, Riemann Zeta Function / 516 \\ Introduction / 516 \\ Riemann Zeta Function / 516 \\ Bernoulli Polynomials and Numbers / 517 \\ Euler Polynomials and Numbers / 517 \\ Methods / 517 \\ References / 517 \\ Riemann Zeta (real arguments) / 519 \\ Test Driver Riemann Zeta (Real) / 527 \\ Test Output: Riemann Zeta, Bernoulli, Euler Numbers / 324 \\ \\ 24. Combinatorics. Stirling Numbers / 529 \\ Introduction / 529 \\ Methods / 529 \\ References / 529 \\ Stirling Numbers First and Second Kind / 530 \\ Fibonacci Numbers / 531 \\ Binomial Coefficients / 532 \\ Test Driver for Stirling Numbers / 533 \\ Test Output: Stirling, Fibonacci, Binomial Coefficients / 534 \\ \\ 25. Numerical Analysis / 535 \\ Discussion / 535 \\ Reference / 536 \\ \\ 26. Statistical Functions, Probability Distributions, and Random Variables / 537 \\ Introduction / 537 \\ Methods / 537 \\ References / 537 \\ Random Numbers / 538 \\ Random Distributions / 544 \\ Test Driver for Random Number / 551 \\ Test Output: Random Numbers and Distributions / 560 \\ Calculator Version of Stat.c Routines / 565 \\ \\ 27. Miscellaneous Functions / 592 \\ Introduction / 592 \\ Debye Functions / 592 \\ Method / 593 \\ Sievert / 593 \\ Method / 593 \\ Abramowitz and Kruse--Ramsey / 593 \\ Method / 593 \\ Ritchie / 593 \\ Method / 593 \\ Dilogarithm and Polylogarithms / 593 \\ Method / 594 \\ Claussen / 594 \\ Method / 594 \\ Lobachevsky / 594 \\ Method / 594 \\ Clebsch--Gordon and Relatives / 594 \\ Method / 595 \\ v and Relatives / 595 \\ Method / 596 \\ References / 596 \\ Figures / 595 \\ Sievert Integral Chapter 27 / 605 \\ Dilogarithm / 606 \\ Polylogarithm Function / 607 \\ ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 / 608 \\ Nu and Mu Integrals of Erdelyi Vol III p. 217 / 612 \\ Lobachevsky Function / 614 \\ Test Driver Miscellaneous Functions / 616 \\ Test Driver Ritchie's Integral / 619 \\ Test Output: Miscellaneous Functions / 620 \\ Test Output: Ritchie's Integral / 624 \\ Clebsch--Gordon, Wigner, Related Coefficients / 625 \\ Test Driver Wigner / 631 \\ Wigner Sample Output / 635 \\ \\ 28. Scales of Notation / 636 \\ \\ 29. C++ Programs / 637 \\ Hurwitz Zeta and Lerch Phi Transcendent / 638 \\ Methods / 638 \\ Meijer $G$ and Generalized Hypergeometric Functions / 638 \\ Methods / 639 \\ Elliptic Functions / 639 \\ Applications / 639 \\ Methods / 639 \\ Fock Functions / 640 \\ Methods / 541 \\ References / 641 \\ // Complex.hpp / 643 \\ Elliptic Functions / 646 \\ Arithmetic--Geometric Mean (AGM) Supplemental / 656 \\ Test Driver for: Elliptic Functions / 662 \\ // Cvector.hpp / 665 \\ // cmatrix.hpp / 666 \\ Test Output: Elliptic Functions / 667 \\ Complex C++ Utilities / 669 \\ Fock Functions / 674 \\ Test Output: Fock Functions / 682 \\ ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 / 697 \\ Test Output: Abramowitz Functions, Complex Arguments / 701 \\ Riemann and Hurwitz / 712 \\ Riemann and Hurwitz: Pad{\'e} / 716 \\ Lerch Phi Transcendent / 720 \\ Generalized Hypergeometric Function and Meijer $G$ / 723 \\ Test Output: Meijer $G$ / 730 \\ Generalized Hypergeometric Function and Meijer $G$ / 731 \\ Test Output: Meijer $G$ with Pad{\'e} / 738 \\ MacRobert E Function / 739 \\ \\ 30. Xref / 740 \\ Other Listings / 741 \\ Adaptive Quadrature (from C loops) / 741 \\ Test Driver Chaps. 16--18 / 743 \\ Index to C Functions / 747 \\ Index / 753

entry:
@Book{Baker:1992:CMF,
  author =       "Louis Baker",
  title =        "{C} Mathematical Function Handbook",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xviii + 757",
  year =         "1992",
  ISBN =         "0-07-911158-0",
  ISBN-13 =      "978-0-07-911158-6",
  LCCN =         "QA351.B17 1991; QA351 .B17 1992",
  bibdate =      "Fri Aug 31 18:54:02 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "McGraw-Hill programming tools for scientists and
                 engineers",
  acknowledgement = ack-nhfb,
  remark =       "System requirements for computer disk: PC; C or C++
                 compiler.",
  subject =      "Functions, Special; Computer programs; C (Computer
                 program language)",
  tableofcontents = "Preface / xv \\
                 1. Special Functions and Numerical Analysis / 1 \\
                 \\
                 Correspondence with Abramowitz and Stegun / 1 \\
                 Numerical Analysis / 1 \\
                 The IEEE-754 Standard / 1 \\
                 Practical Considerations / 3 \\
                 Reference / 6 \\
                 \\
                 2. Special Functions in C and C++ / 8 \\
                 C and C++ / 8 \\
                 Portability, ANSI C, and C++ / 8 \\
                 Infinite Loops / 9 \\
                 Header Files COMPLEX.H, CMLIB.H, PROTOM.H / 10 \\
                 Error Handling / 10 \\
                 Pitfalls with Special Functions / 11 \\
                 Normalization Conventions / 12 \\
                 Tips and Pitfalls in C / 12 \\
                 Calling C from C++ / 14 \\
                 References / 15 \\
                 Cmlib.h / 16 \\
                 COMPLEX.H Header File / 17 \\
                 Prototypes for \booktitle{C Mathematical Function
                 Handbook} / 19 \\
                 \\
                 3. Elementary Analytical Methods / 33 \\
                 Powers and Roots / 33 \\
                 Complex Numbers / 34 \\
                 Roots of Polynomials / 35 \\
                 Quadratics / 35 \\
                 Cubics / 35 \\
                 Quartics (biquadratics) / 36 \\
                 Implementation Considerations / 37 \\
                 Ouintics / 38 \\
                 References / 38 \\
                 Complex Variable Auxiliary Routines / 39 \\
                 Powers and Roots / 45 \\
                 Polynomial Root Finders / 48 \\
                 Test Driver for Programs of Chapters 3-4 / 60 \\
                 \\
                 4. Elementary Transcendental Functions / 72 \\
                 Elementary Functions / 72 \\
                 Complex Elementary Functions / 73 \\
                 Gudermannian / 74 \\
                 References / 74 \\
                 \\
                 5. Exponential Integral and Relatives / 75 \\
                 Exponential and Related Integrals / 75 \\
                 Methods / 76 \\
                 References / 76 \\
                 Shi(x) and Chi(x) / 76 \\
                 Exponential Integral / 78 \\
                 Test Driver Results: Exponential Integral and Relatives
                 / 95 \\
                 \\
                 6. Gamma Function and Related Integrals / 100 \\
                 Gamma Function and Relatives / 100 \\
                 The Pochhammer Symbol / 100 \\
                 Methods / 101 \\
                 Asymptotic Series / 101 \\
                 Reference / 101 \\
                 Gamma Function and Relatives / 102 \\
                 Digamma and First 2 Polygamma Functions / 111 \\
                 \\
                 7. Error Function and Relatives / 115 \\
                 Error Function and Relatives / 115 \\
                 Methods / 117 \\
                 Recurrence Relations / 117 \\
                 C Code / 118 \\
                 References / 118 \\
                 Figure: Dawson's Integral / 118 \\
                 Plasma Dispersion Function / 120 \\
                 Iterated Error Function / 127 \\
                 Boehmer (generalized Fresnel) Integral / 129 \\
                 Complementary Error Function for Complex Arguments /
                 133 \\
                 Test Driver Chapter 7 / 134 \\
                 \\
                 8. Legendre Functions / 142 \\
                 Legendre Functions / 142 \\
                 Derivatives / 143 \\
                 Applications / 143 \\
                 Methods / 144 \\
                 References / 144 \\
                 Legendre and Associated Legendre Functions / 146 \\
                 Legendre Functions for $|x| > 1$ / 155 \\
                 Toroidal $P|x| > 1$ / 163 \\
                 Mehler (Conical Legendre) Functions / 164 \\
                 Test Driver for Legendre Functions of Chapter 8 / 166
                 \\
                 \\
                 9. Bessel Functions / 177 \\
                 Struve Functions / 178 \\
                 Anger and Weber Functions / 179 \\
                 Relationship to Confluent Hypergeometric Function / 179
                 \\
                 Derivatives / 179 \\
                 Other Related Functions / 179 \\
                 Zeros of Bessel Functions / 180 \\
                 Applications / 180 \\
                 Methods / 180 \\
                 References / 181 \\
                 Bessel Functions for Complex Arguments / 182 \\
                 Bessel Functions: Rational Approximations / 194 \\
                 Bessel Function Tables as a Function of (Integral) n /
                 201 \\
                 Zeros of Bessel Functions / 205 \\
                 Test Driver for Bessel Functions / 211 \\
                 Test Driver Bessel Zero / 220 \\
                 Output of Bessel Function Test Driver / 221 \\
                 Output of Test Driver for Zerobess() / 237 \\
                 \\
                 10. Bessel Functions of Fractional Order / 239 \\
                 Introduction / 239 \\
                 Spherical Bessel Functions / 239 \\
                 Airy Functions / 239 \\
                 Applications / 240 \\
                 Asymptotics / 240 \\
                 Caustics / 240 \\
                 Schroedinger's Equation, Turning Points and the WKB
                 Method / 242 \\
                 Methods / 243 \\
                 The $|A|$ Function / 243 \\
                 References / 244 \\
                 Spherical Bessel Functions and Allied Routines / 245
                 \\
                 Airy, Bessel Functions and Integrals Thereof / 250 \\
                 \\
                 11. Integrals of Bessel Functions / 265 \\
                 Introduction / 265 \\
                 Applications / 265 \\
                 Methods / 265 \\
                 Bickley Functions / 265 \\
                 Adaptive Quadrature / 266 \\
                 Repeated Integrals of Jn / 266 \\
                 Other Integrals / 266 \\
                 References / 266 \\
                 Figures of Integrals of Bessel Functions / 267 \\
                 Integrals of Bessel Functions / 277 \\
                 Adaptive Integration Routine / 242 \\
                 \\
                 12. Struve and Anger--Weber Functions / 284 \\
                 Introduction / 284 \\
                 Struve Functions / 284 \\
                 Anger--Weber Functions / 284 \\
                 Methods / 285 \\
                 References / 285 \\
                 Figures / 286 \\
                 Struve Functions General Order / 289 \\
                 Struve Functions Lowest Order / 291 \\
                 Integrals of Struve HO, HO/t, LO / 295 \\
                 Integral of Anger--Weber Function / 297 \\
                 \\
                 13. Confluent Hypergeometric Functions and Relatives /
                 301 \\
                 Introduction / 301 \\
                 Airy Functions / 303 \\
                 Applications / 303 \\
                 Methods / 304 \\
                 References / 304 \\
                 Confluent Hypergeometric Function Complex Arguments /
                 305 \\
                 Test Drive Confluent Hypergeometric Function / 318 \\
                 Confluent Hypergeometric Function U / 322 \\
                 Test Driver U.c / 331 \\
                 Test Output: Confluent-Hypergeometric Function / 332
                 \\
                 Test Output: U / 334 \\
                 \\
                 14. Coulomb Wave Functions / 335 \\
                 Introduction / 335 \\
                 Methods / 336 \\
                 References / 337 \\
                 Coulomb Wave Functions / 339 \\
                 Test Driver Coulomb Wave Functions / 343 \\
                 Test Output: Coulomb wave Functions / 344 \\
                 \\
                 15. The Hypergeometric Function / 345 \\
                 Introduction / 345 \\
                 Applications / 346 \\
                 Methods / 346 \\
                 References / 346 \\
                 Hypergeometric Function Complex Arguments / 347 \\
                 Legendre Function $P$ for Complex Parameters / 364 \\
                 Legendre $Q$ for Complex Arguments / 366 \\
                 Test Driver $_2F_1$ / 369 \\
                 Output: Gauss Hypergeometric Functions / 370 \\
                 Real Hypergeometric Function and Relatives / 371 \\
                 \\
                 16. The Elliptic Functions / 373 \\
                 Introduction / 373 \\
                 Applications / 376 \\
                 Methods / 376 \\
                 References / 377 \\
                 Figure / 378 \\
                 Basic Elliptic Functions Real Arguments / 380 \\
                 Elliptic Integral of Third Kind / 391 \\
                 Jacobian Elliptic Function Complex Argument / 397 \\
                 Complex Elliptic Theta Functions / 406 \\
                 Output: Test Driver for Elliptic Functions / 411 \\
                 \\
                 17. The Elliptic Integrals / 416 \\
                 Introduction / 415 \\
                 Caveat / 416 \\
                 References / 417 \\
                 Figures / 417 \\
                 \\
                 18. The Weierstrass Elliptic Function and Relatives /
                 425 \\
                 Introduction / 425 \\
                 Methods / 427 \\
                 References / 427 \\
                 Inverse of Weierstrass Elliptic P . / 428 \\
                 Brent Root Finder / 430 \\
                 \\
                 19. The Parabolic Cylinder Functions / 432 \\
                 Introduction / 432 \\
                 Methods / 432 \\
                 Figures / 432 \\
                 Parabolic Cylinder Functions / 435 \\
                 Test Driver Parabolic Cylinder Function / 442 \\
                 \\
                 20. The Mathieu Functions / 444 \\
                 Introduction / 444 \\
                 Method / 443 \\
                 References / 445 \\
                 Figures / 445 \\
                 Mathieu Functions / 449 \\
                 Mathieu Functions Test Driver / 465 \\
                 Test Output: Mathieu Functions / 467 \\
                 \\
                 21. The Spheroidal Wave Functions / 475 \\
                 Introduction / 475 \\
                 Spheroidal Wave Functions / 475 \\
                 Generalized Spheroidal Wave Functions / 477 \\
                 Caveat / 477 \\
                 Method / 477 \\
                 References / 478 \\
                 Figures / 478 \\
                 Spheroidal Wave Functions / 486 \\
                 Legptable Pn,m for n = m to ntop / 500 \\
                 Test Driver Spheroidal Wave Functions / 501 \\
                 Test Output: Spheroidal Wave Functions / 504 \\
                 \\
                 22. Orthogonal Polynomials / 509 \\
                 Introduction / 509 \\
                 Contents / 509 \\
                 Applications / 509 \\
                 Method / 509 \\
                 Orthogonal Polynomials / 510 \\
                 Test Driver Orthogonal Polynomials / 513 \\
                 \\
                 23. Bernoulli and Euler Numbers and Polynomials,
                 Riemann Zeta Function / 516 \\
                 Introduction / 516 \\
                 Riemann Zeta Function / 516 \\
                 Bernoulli Polynomials and Numbers / 517 \\
                 Euler Polynomials and Numbers / 517 \\
                 Methods / 517 \\
                 References / 517 \\
                 Riemann Zeta (real arguments) / 519 \\
                 Test Driver Riemann Zeta (Real) / 527 \\
                 Test Output: Riemann Zeta, Bernoulli, Euler Numbers /
                 324 \\
                 \\
                 24. Combinatorics. Stirling Numbers / 529 \\
                 Introduction / 529 \\
                 Methods / 529 \\
                 References / 529 \\
                 Stirling Numbers First and Second Kind / 530 \\
                 Fibonacci Numbers / 531 \\
                 Binomial Coefficients / 532 \\
                 Test Driver for Stirling Numbers / 533 \\
                 Test Output: Stirling, Fibonacci, Binomial Coefficients
                 / 534 \\
                 \\
                 25. Numerical Analysis / 535 \\
                 Discussion / 535 \\
                 Reference / 536 \\
                 \\
                 26. Statistical Functions, Probability Distributions,
                 and Random Variables / 537 \\
                 Introduction / 537 \\
                 Methods / 537 \\
                 References / 537 \\
                 Random Numbers / 538 \\
                 Random Distributions / 544 \\
                 Test Driver for Random Number / 551 \\
                 Test Output: Random Numbers and Distributions / 560 \\
                 Calculator Version of Stat.c Routines / 565 \\
                 \\
                 27. Miscellaneous Functions / 592 \\
                 Introduction / 592 \\
                 Debye Functions / 592 \\
                 Method / 593 \\
                 Sievert / 593 \\
                 Method / 593 \\
                 Abramowitz and Kruse--Ramsey / 593 \\
                 Method / 593 \\
                 Ritchie / 593 \\
                 Method / 593 \\
                 Dilogarithm and Polylogarithms / 593 \\
                 Method / 594 \\
                 Claussen / 594 \\
                 Method / 594 \\
                 Lobachevsky / 594 \\
                 Method / 594 \\
                 Clebsch--Gordon and Relatives / 594 \\
                 Method / 595 \\
                 v and Relatives / 595 \\
                 Method / 596 \\
                 References / 596 \\
                 Figures / 595 \\
                 Sievert Integral Chapter 27 / 605 \\
                 Dilogarithm / 606 \\
                 Polylogarithm Function / 607 \\
                 ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 /
                 608 \\
                 Nu and Mu Integrals of Erdelyi Vol III p. 217 / 612 \\
                 Lobachevsky Function / 614 \\
                 Test Driver Miscellaneous Functions / 616 \\
                 Test Driver Ritchie's Integral / 619 \\
                 Test Output: Miscellaneous Functions / 620 \\
                 Test Output: Ritchie's Integral / 624 \\
                 Clebsch--Gordon, Wigner, Related Coefficients / 625 \\
                 Test Driver Wigner / 631 \\
                 Wigner Sample Output / 635 \\
                 \\
                 28. Scales of Notation / 636 \\
                 \\
                 29. C++ Programs / 637 \\
                 Hurwitz Zeta and Lerch Phi Transcendent / 638 \\
                 Methods / 638 \\
                 Meijer $G$ and Generalized Hypergeometric Functions /
                 638 \\
                 Methods / 639 \\
                 Elliptic Functions / 639 \\
                 Applications / 639 \\
                 Methods / 639 \\
                 Fock Functions / 640 \\
                 Methods / 541 \\
                 References / 641 \\
                 // Complex.hpp / 643 \\
                 Elliptic Functions / 646 \\
                 Arithmetic--Geometric Mean (AGM) Supplemental / 656 \\
                 Test Driver for: Elliptic Functions / 662 \\
                 // Cvector.hpp / 665 \\
                 // cmatrix.hpp / 666 \\
                 Test Output: Elliptic Functions / 667 \\
                 Complex C++ Utilities / 669 \\
                 Fock Functions / 674 \\
                 Test Output: Fock Functions / 682 \\
                 ``Abramowitz'' Functions f1, f2, f3 from Chapter 27 /
                 697 \\
                 Test Output: Abramowitz Functions, Complex Arguments /
                 701 \\
                 Riemann and Hurwitz / 712 \\
                 Riemann and Hurwitz: Pad{\'e} / 716 \\
                 Lerch Phi Transcendent / 720 \\
                 Generalized Hypergeometric Function and Meijer $G$ /
                 723 \\
                 Test Output: Meijer $G$ / 730 \\
                 Generalized Hypergeometric Function and Meijer $G$ /
                 731 \\
                 Test Output: Meijer $G$ with Pad{\'e} / 738 \\
                 MacRobert E Function / 739 \\
                 \\
                 30. Xref / 740 \\
                 Other Listings / 741 \\
                 Adaptive Quadrature (from C loops) / 741 \\
                 Test Driver Chaps. 16--18 / 743 \\
                 Index to C Functions / 747 \\
                 Index / 753",
}


bibtype: article
filename: elefunt.bib
label: Baker:1992:LCE
author: H. G. Baker
title: Less Complex Elementary Functions
journal: j-SIGPLAN
volume: 27
number: 11
pages: 15--16
month: nov
monthnumber: 11
year: 1992
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Thu Sep 08 08:11:27 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 08:11:27 ???
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nj
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: H. G. Baker
rawtitle: Less Complex Elementary Functions
entry:
@Article{Baker:1992:LCE,
  author =       "H. G. Baker",
  title =        "Less Complex Elementary Functions",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "11",
  pages =        "15--16",
  month =        nov,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Sep 08 08:11:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
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bibtype: article
filename: elefunt.bib
label: Bohman:1992:FRP
author: Jan Bohman and Carl-Erik Froberg
title: The $ Gamma $-function revisited: power series expansions and real-imaginary zero lines
journal: j-MATH-COMPUT
volume: 58
number: 197
pages: 315--322
month: jan
monthnumber: 1
year: 1992
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B15 (11Y70 65D20)
MRnumber: 92e:33001
MRreviewer: A. de Castro Brzezicki
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Jan Bohman and Carl-Erik Fr{\"o}berg
rawtitle: The {$ \Gamma $}-function revisited: power series expansions and real-imaginary zero lines
entry:
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  title =        "The {$ \Gamma $}-function revisited: power series
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  journal =      j-MATH-COMPUT,
  volume =       "58",
  number =       "197",
  pages =        "315--322",
  month =        jan,
  year =         "1992",
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  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (11Y70 65D20)",
  MRnumber =     "92e:33001",
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  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
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bibtype: article
filename: elefunt.bib
label: Borwein:1992:FEG
author: J. M. Borwein and I. J. Zucker
journal: j-IMA-J-NUMER-ANAL
volume: 12
number: 4
pages: 519--526
year: 1992
CODEN: IJNADH
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65D20
MRnumber: 93g:65028
bibdate: Sat Dec 23 17:06:35 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; MathSciNet database
bibtimestamp: 2000.12.23 17:06:35 MST
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: J. M. Borwein and I. J. Zucker
title:
Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind

rawtitle:
Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind

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  author =       "J. M. Borwein and I. J. Zucker",
  title =        "Fast evaluation of the gamma function for small
                 rational fractions using complete elliptic integrals of
                 the first kind",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "12",
  number =       "4",
  pages =        "519--526",
  year =         "1992",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
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  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
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bibtype: article
filename: elefunt.bib
label: Buhring:1992:GHF
author: Wolfgang Buhring
title: Generalized hypergeometric functions at unit argument
journal: j-PROC-AM-MATH-SOC
volume: 114
number: 1
pages: 145--153
year: 1992
CODEN: PAMYAR
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 33C20
MRnumber: MR1068116 (92c:33004)
bibdate: Thu Dec 01 09:52:06 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:52:06 ???
fjournal: Proceedings of the American Mathematical Society
remark: The paper treats $_p + 1F_p$ (or equivalently, $_p F_p - 1$ ).
ZMnumber: Zbl 0754.33003
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/proc
rawauthor: Wolfgang B{\"u}hring
rawtitle: Generalized hypergeometric functions at unit argument
entry:
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  title =        "Generalized hypergeometric functions at unit
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  journal =      j-PROC-AM-MATH-SOC,
  volume =       "114",
  number =       "1",
  pages =        "145--153",
  month =        "????",
  year =         "1992",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
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  MRnumber =     "MR1068116 (92c:33004)",
  bibdate =      "Thu Dec 01 09:52:06 2011",
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  ZMnumber =     "Zbl 0754.33003",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  remark =       "The paper treats $_{p + 1F}_p$ (or equivalently, $_p
                 F_{p - 1}$ ).",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1992:TEI
author: B. C. Carlson
title: A Table of Elliptic Integrals: Two Quadratic Factors
journal: j-MATH-COMPUT
volume: 59
number: 199
pages: 165--180
month: jul
monthnumber: 7
year: 1992
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20 (33C75 33E05)
MRnumber: 92k:65027
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
journalURL: http://www.ams.org/mcom/
rawauthor: B. C. Carlson
rawtitle: A Table of Elliptic Integrals: Two Quadratic Factors
entry:
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  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals: Two Quadratic Factors",
  journal =      j-MATH-COMPUT,
  volume =       "59",
  number =       "199",
  pages =        "165--180",
  month =        jul,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33C75 33E05)",
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  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
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                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
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bibtype: article
filename: elefunt.bib
label: Corless:1992:NEAa
author: R. M. Corless and D. J. Jeffrey and H. Rasmussen
title: Numerical evaluation of Airy functions with complex arguments
journal: j-J-COMPUT-PHYS
volume: 98
number: 2
pages: 347--347
month: feb
monthnumber: 2
year: 1992
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(92)90150-W
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:53 MST 2012
bibtimestamp: 2012.01.02 07:55:53 MST
URL: http://www.sciencedirect.com/science/article/pii/002199919290150W
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. M. Corless and D. J. Jeffrey and H. Rasmussen
rawtitle: Numerical evaluation of {Airy} functions with complex arguments
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib

entry:
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  author =       "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
  title =        "Numerical evaluation of {Airy} functions with complex
                 arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "98",
  number =       "2",
  pages =        "347--347",
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  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(92)90150-W",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
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bibtype: article
filename: elefunt.bib
label: Corless:1992:NEAb
author: R. M. Corless and D. J. Jeffrey and H. Rasmussen
title: Numerical evaluation of Airy functions with complex arguments
journal: j-J-COMPUT-PHYS
volume: 99
number: 1
pages: 106--114
month: mar
monthnumber: 3
year: 1992
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(92)90279-8
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
MRclass: 65D20 (33E30)
MRnumber: 92k:65028
bibdate: Mon Jan 2 07:55:54 MST 2012
bibtimestamp: 2012.01.02 07:55:54 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999192902798
fjournal: Journal of Computational Physics
keywords: Maple
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: R. M. Corless and D. J. Jeffrey and H. Rasmussen
rawtitle: Numerical evaluation of {Airy} functions with complex arguments
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bibtype: article
filename: elefunt.bib
label: Croft:1992:ACA
author: A. Croft
journal: j-NUMER-ALGORITHMS
volume: 2
number: 3--4
pages: 307--320
month: sep
monthnumber: 9
year: 1992
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65L10 (65B99)
MRnumber: 93g:65097
bibdate: Fri Nov 6 18:06:29 MST 1998
bibsource: http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.06 18:06:29 MST
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Dept. of Math. Sci., Leicester Polytech., UK
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: A. Croft
title:
An application of convergence acceleration techniques to a class of two-point boundary value problems on a semi-infinite domain

keywords:
boundary condition; boundary-value problems; convergence acceleration; convergence acceleration algorithms; convergence of numerical methods; extrapolate; extrapolation; semi-infinite domain; two-point boundary value problems; unbounded domains

rawtitle:
An application of convergence acceleration techniques to a class of two-point boundary value problems on a semi-infinite domain

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@Article{Croft:1992:ACA,
  author =       "A. Croft",
  title =        "An application of convergence acceleration techniques
                 to a class of two-point boundary value problems on a
                 semi-infinite domain",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "2",
  number =       "3--4",
  pages =        "307--320",
  month =        sep,
  year =         "1992",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65L10 (65B99)",
  MRnumber =     "93g:65097",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
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  corpsource =   "Dept. of Math. Sci., Leicester Polytech., UK",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
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                 extrapolate; extrapolation; semi-infinite domain;
                 two-point boundary value problems; unbounded domains",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Dattoli:1992:GFM
author: G. Dattoli and C. Chiccoli and S. Lorenzutta and G. Maino and M. Richetta and A. Torre
title: Generating functions of multivariable generalized Bessel functions and Jacobi-elliptic functions
journal: j-J-MATH-PHYS
volume: 33
number: 1
pages: 25--36
month: jan
monthnumber: 1
year: 1992
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.529959
ISSNL: 0022-2488 OR 00222488
MRclass: 33E05 (33C10 34B30 42A16 42A85)
MRnumber: 92m:33037
MRreviewer: J. M. H. Peters
bibdate: Tue Nov 1 08:57:37 MDT 2011
bibtimestamp: 2011.11.01 08:57:37 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v33/i1/p25_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: G. Dattoli and C. Chiccoli and S. Lorenzutta and G. Maino and M. Richetta and A. Torre
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib

rawtitle:
Generating functions of multivariable generalized {Bessel} functions and {Jacobi}-elliptic functions

entry:
@Article{Dattoli:1992:GFM,
  author =       "G. Dattoli and C. Chiccoli and S. Lorenzutta and G.
                 Maino and M. Richetta and A. Torre",
  title =        "Generating functions of multivariable generalized
                 {Bessel} functions and {Jacobi}-elliptic functions",
  journal =      j-J-MATH-PHYS,
  volume =       "33",
  number =       "1",
  pages =        "25--36",
  month =        jan,
  year =         "1992",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.529959",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33E05 (33C10 34B30 42A16 42A85)",
  MRnumber =     "92m:33037",
  MRreviewer =   "J. M. H. Peters",
  bibdate =      "Tue Nov 1 08:57:37 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/jmathphys1990.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v33/i1/p25_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "12",
}


bibtype: article
filename: elefunt.bib
label: DiDonato:1992:ASD
author: Armido R. DiDonato and Alfred H. Morris, Jr.
title: Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios
journal: j-TOMS
volume: 18
number: 3
pages: 360--373
month: sep
monthnumber: 9
year: 1992
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 19 13:14:47 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.11.19 13:14:47 ???
note: See also cite Brown:1994:CAS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
subject: bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Armido R. {DiDonato} and Alfred H. {Morris, Jr.}
rawnote: See also \cite{Brown:1994:CAS}.
rawtitle: {Algorithm 708}: Significant Digit Computation of the Incomplete Beta Function Ratios
URL:
http://doi.acm.org/10.1145/131766.131776; http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p360-didonato/

abstract:
An algorithm is given for evaluating the incomplete beta function ratio $ I_x(a, b) $ and its complement $ 1 - I^x(a, b) $. A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is accurate to 14 significant digits when precision is not restricted by inherent error.

rawabstract:
An algorithm is given for evaluating the incomplete beta function ratio $ I_x(a, b) $ and its complement $ 1 - I^x(a, b) $. A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is accurate to 14 significant digits when precision is not restricted by inherent error.

entry:
@Article{DiDonato:1992:ASD,
  author =       "Armido R. {DiDonato} and Alfred H. {Morris, Jr.}",
  title =        "{Algorithm 708}: Significant Digit Computation of the
                 Incomplete Beta Function Ratios",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "360--373",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:14:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Brown:1994:CAS}.",
  URL =          "http://doi.acm.org/10.1145/131766.131776;
                 http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p360-didonato/",
  abstract =     "An algorithm is given for evaluating the incomplete
                 beta function ratio $ I_x(a, b) $ and its complement $
                 1 - I^x(a, b) $. A new continued fraction and a new
                 asymptotic series are used with classical results. A
                 transportable Fortran subroutine based on this
                 algorithm is currently in use. It is accurate to 14
                 significant digits when precision is not restricted by
                 inherent error.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Dubois:1992:CFQ
author: D. Dubois and H. Prade
title: Calculation with fuzzy quantities
crossref: EC2:1992:DJN
pages: 24--27
year: 1992
bibdate: Thu Dec 14 17:22:18 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.14 17:22:18 MST
language: French
acknowledgement: ack-nhfb
affiliation: IRIT, Paul Sabatier Univ., Toulouse, France
bookpages: 384
thesaurus: Fuzzy logic; Fuzzy set theory; Statistical analysis
rawauthor: D. Dubois and H. Prade
rawtitle: Calculation with fuzzy quantities
abstract:
In some instances where numerical data are either provisional, incomplete, or variable within a limited range, the classical calculation of confidence intervals can be extended in a fuzzy-set approach, distinguishing between more or less plausible values. The simultaneous use of relatively wide intervals containing all possible values, and generally much narrower intervals covering only the most likely ones, can give sufficiently informative results. Some precautions advisable in arithmetic operations on imprecisely known quantities are outlined. Examples of application include provisional budgeting, resource estimation, evaluation of candidates, and extension of PERT to projects involving precedence among elementary tasks with uncertain durations and/or starting times. Computer-aided engineering design can also benefit from fuzzy specifications for values eventually to be optimised.

keywords:
Arithmetic operations; Candidates; Confidence intervals; Engineering design; Fuzzy quantities; Fuzzy specifications; Fuzzy-set approach; Imprecisely known quantities; Numerical data; PERT; Provisional budgeting; Resource estimation

rawabstract:
In some instances where numerical data are either provisional, incomplete, or variable within a limited range, the classical calculation of confidence intervals can be extended in a fuzzy-set approach, distinguishing between more or less plausible values. The simultaneous use of relatively wide intervals containing all possible values, and generally much narrower intervals covering only the most likely ones, can give sufficiently informative results. Some precautions advisable in arithmetic operations on imprecisely known quantities are outlined. Examples of application include provisional budgeting, resource estimation, evaluation of candidates, and extension of PERT to projects involving precedence among elementary tasks with uncertain durations and/or starting times. Computer-aided engineering design can also benefit from fuzzy specifications for values eventually to be optimised.

entry:
@InProceedings{Dubois:1992:CFQ,
  author =       "D. Dubois and H. Prade",
  title =        "Calculation with fuzzy quantities",
  crossref =     "EC2:1992:DJN",
  bookpages =    "384",
  pages =        "24--27",
  year =         "1992",
  bibdate =      "Thu Dec 14 17:22:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In some instances where numerical data are either
                 provisional, incomplete, or variable within a limited
                 range, the classical calculation of confidence
                 intervals can be extended in a fuzzy-set approach,
                 distinguishing between more or less plausible values.
                 The simultaneous use of relatively wide intervals
                 containing all possible values, and generally much
                 narrower intervals covering only the most likely ones,
                 can give sufficiently informative results. Some
                 precautions advisable in arithmetic operations on
                 imprecisely known quantities are outlined. Examples of
                 application include provisional budgeting, resource
                 estimation, evaluation of candidates, and extension of
                 PERT to projects involving precedence among elementary
                 tasks with uncertain durations and/or starting times.
                 Computer-aided engineering design can also benefit from
                 fuzzy specifications for values eventually to be
                 optimised.",
  acknowledgement = ack-nhfb,
  affiliation =  "IRIT, Paul Sabatier Univ., Toulouse, France",
  classification = "C1160 (Combinatorial mathematics); C4210 (Formal
                 logic); C7310 (Mathematics)",
  confdate =     "2-3 Nov. 1992",
  conflocation = "Nimes, France",
  keywords =     "Arithmetic operations; Candidates; Confidence
                 intervals; Engineering design; Fuzzy quantities; Fuzzy
                 specifications; Fuzzy-set approach; Imprecisely known
                 quantities; Numerical data; PERT; Provisional
                 budgeting; Resource estimation",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Fuzzy logic; Fuzzy set theory; Statistical analysis",
}


bibtype: article
filename: elefunt.bib
label: Feinsilver:1992:BFR
author: P. Feinsilver and R. Schott
title: On Bessel functions and rate of convergence of zeros of Lommel polynomials
journal: j-MATH-COMPUT
volume: 59
number: 199
pages: 153--156
month: jul
monthnumber: 7
year: 1992
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33C10 (33C45)
MRnumber: 93a:33007
MRreviewer: Boro D{\"o}ring
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
affiliation: Southern Illinois Univ., Carbondale, IL, USA
corpsource: Southern Illinois Univ., Carbondale, IL, USA
journalURL: http://www.ams.org/mcom/
thesaurus: Bessel functions; Convergence of numerical methods; Differential equations; Polynomials
treatment: T Theoretical or Mathematical
rawauthor: P. Feinsilver and R. Schott
rawtitle: On {Bessel} functions and rate of convergence of zeros of {Lommel} polynomials
keywords:
average case analysis; Average case analysis; Bessel function; Bessel functions; convergence of numerical methods; convergence rate; Convergence rate; data structures; differential equations; dynamic; Dynamic data structures; Lommel; Lommel polynomials; Maple program; polynomials; rate of convergence; Rate of convergence; zeros; Zeros

classcodes:
B0220 (Analysis); B0290P (Differential equations); B0290F (Interpolation and function approximation); B0210 (Algebra); C1120 (Analysis); C4170 (Differential equations); C4130 (Interpolation and function approximation); C1110 (Algebra)

entry:
@Article{Feinsilver:1992:BFR,
  author =       "P. Feinsilver and R. Schott",
  title =        "On {Bessel} functions and rate of convergence of zeros
                 of {Lommel} polynomials",
  journal =      j-MATH-COMPUT,
  volume =       "59",
  number =       "199",
  pages =        "153--156",
  month =        jul,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33C10 (33C45)",
  MRnumber =     "93a:33007",
  MRreviewer =   "Boro D{\"o}ring",
  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,
  affiliation =  "Southern Illinois Univ., Carbondale, IL, USA",
  classcodes =   "B0220 (Analysis); B0290P (Differential equations);
                 B0290F (Interpolation and function approximation);
                 B0210 (Algebra); C1120 (Analysis); C4170 (Differential
                 equations); C4130 (Interpolation and function
                 approximation); C1110 (Algebra)",
  classification = "B0210 (Algebra); B0220 (Analysis); B0290F
                 (Interpolation and function approximation); B0290P
                 (Differential equations); C1110 (Algebra); C1120
                 (Analysis); C4130 (Interpolation and function
                 approximation); C4170 (Differential equations)",
  corpsource =   "Southern Illinois Univ., Carbondale, IL, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "average case analysis; Average case analysis; Bessel
                 function; Bessel functions; convergence of numerical
                 methods; convergence rate; Convergence rate; data
                 structures; differential equations; dynamic; Dynamic
                 data structures; Lommel; Lommel polynomials; Maple
                 program; polynomials; rate of convergence; Rate of
                 convergence; zeros; Zeros",
  thesaurus =    "Bessel functions; Convergence of numerical methods;
                 Differential equations; Polynomials",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Fillebrown:1992:FCB
author: Sandra Fillebrown
title: Faster computation of Bernoulli numbers
journal: j-J-ALG
volume: 13
number: 3
pages: 431--445
month: sep
monthnumber: 9
year: 1992
CODEN: JOALDV
DOI: https://doi.org/10.1016/0196-6774(92)90048-H
ISSN: 0196-6774 (print), 1090-2678 (electronic) OR 01966774 (print), 10902678 (electronic)
ISSNL: 0196-6774 OR 01966774
bibdate: Tue Dec 11 09:15:18 MST 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jalg.bib
bibtimestamp: 2012.12.11 09:15:18 MST
URL: http://www.sciencedirect.com/science/article/pii/019667749290048H
fjournal: Journal of Algorithms
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01966774
rawauthor: Sandra Fillebrown
rawtitle: Faster computation of {Bernoulli} numbers
remark:
The author gives algorithms for computing Bernoulli numbers of high order that require at most $ lfloor 2 n lg n rfloor $ bits. One algorithm requires $ O(n^2 log n) $ multiplications of numbers of $ O(n log n) $ bits, and the other need $ O(n) $ multiplications of numbers of $ O(n log n) $ bits.

entry:
@Article{Fillebrown:1992:FCB,
  author =       "Sandra Fillebrown",
  title =        "Faster computation of {Bernoulli} numbers",
  journal =      j-J-ALG,
  volume =       "13",
  number =       "3",
  pages =        "431--445",
  month =        sep,
  year =         "1992",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1016/0196-6774(92)90048-H",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:15:18 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/019667749290048H",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
  remark =       "The author gives algorithms for computing Bernoulli
                 numbers of high order that require at most $ \lfloor 2
                 n \lg n \rfloor $ bits. One algorithm requires $ O(n^2
                 \log n) $ multiplications of numbers of $ O(n \log n) $
                 bits, and the other need $ O(n) $ multiplications of
                 numbers of $ O(n \log n) $ bits.",
}


bibtype: article
filename: elefunt.bib
label: Giordano:1992:FMC
author: Carla Giordano and Lucia G. Rodono
title: Further monotonicity and convexity properties of the zeros of cylinder functions
journal: j-J-COMPUT-APPL-MATH
volume: 42
number: 2
pages: 245--251
day: 12
month: oct
monthnumber: 10
year: 1992
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:54 MST 2017
bibtimestamp: 2017.02.25 12:20:54 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279290078C
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Carla Giordano and Lucia G. Rodon{\`o}
rawtitle: Further monotonicity and convexity properties of the zeros of cylinder functions
entry:
@Article{Giordano:1992:FMC,
  author =       "Carla Giordano and Lucia G. Rodon{\`o}",
  title =        "Further monotonicity and convexity properties of the
                 zeros of cylinder functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "42",
  number =       "2",
  pages =        "245--251",
  day =          "12",
  month =        oct,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:54 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279290078C",
  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: Ifantis:1992:DIP
author: E. K. Ifantis and P. D. Siafarikas
title: A differential inequality for the positive zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 44
number: 1
pages: 115--120
day: 9
month: dec
monthnumber: 12
year: 1992
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:56 MST 2017
bibtimestamp: 2017.02.25 12:20:56 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042792900553
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: E. K. Ifantis and P. D. Siafarikas
rawtitle: A differential inequality for the positive zeros of {Bessel} functions
entry:
@Article{Ifantis:1992:DIP,
  author =       "E. K. Ifantis and P. D. Siafarikas",
  title =        "A differential inequality for the positive zeros of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "44",
  number =       "1",
  pages =        "115--120",
  day =          "9",
  month =        dec,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042792900553",
  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: Jiang:1992:CCM
author: Thomas J. Jiang and Joseph B. Kadane and James M. Dickey
title: Computation of Carlson's Multiple Hypergeometric Function $R$ for Bayesian Applications
journal: j-J-COMPUT-GRAPH-STAT
volume: 1
number: 3
pages: 231--251
month: sep
monthnumber: 9
year: 1992
DOI: https://doi.org/10.1080/10618600.1992.10474583
ISSN: 1061-8600 (print), 1537-2715 (electronic) OR 10618600 (print), 15372715 (electronic)
ISSNL: 1061-8600 OR 10618600
MRclass: 33C90 (62F15 65D20)
MRnumber: 95e:33021
MRreviewer: P. N. Rathie
bibdate: Thu Aug 13 10:27:39 MDT 2020
bibtimestamp: 2020.08.13 10:27:39 MDT
URL: http://www.tandfonline.com/doi/abs/10.1080/10618600.1992.10474583
fjournal: Journal of Computational and Graphical Statistics
acknowledgement: ack-nhfb
journalURL: http://www.amstat.org/publications/jcgs/; http://www.tandfonline.com/loi/ucgs20
onlinedate: 21 Feb 2012
rawauthor: Thomas J. Jiang and Joseph B. Kadane and James M. Dickey
rawtitle: Computation of {Carlson}'s Multiple Hypergeometric Function {$R$} for {Bayesian} Applications
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputgraphstat.bib

entry:
@Article{Jiang:1992:CCM,
  author =       "Thomas J. Jiang and Joseph B. Kadane and James M.
                 Dickey",
  title =        "Computation of {Carlson}'s Multiple Hypergeometric
                 Function {$R$} for {Bayesian} Applications",
  journal =      j-J-COMPUT-GRAPH-STAT,
  volume =       "1",
  number =       "3",
  pages =        "231--251",
  month =        sep,
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10618600.1992.10474583",
  ISSN =         "1061-8600 (print), 1537-2715 (electronic)",
  ISSN-L =       "1061-8600",
  MRclass =      "33C90 (62F15 65D20)",
  MRnumber =     "95e:33021",
  MRreviewer =   "P. N. Rathie",
  bibdate =      "Thu Aug 13 10:27:39 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputgraphstat.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/10618600.1992.10474583",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Graphical Statistics",
  journal-URL =  "http://www.amstat.org/publications/jcgs/;
                 http://www.tandfonline.com/loi/ucgs20",
  onlinedate =   "21 Feb 2012",
  xxtitle =      "Computation of {Carlson}'s multiple hypergeometric
                 function {$ {\cal R} $} for {Bayesian} applications",
}


bibtype: book
filename: elefunt.bib
label: Johnson:1992:UDD
author: Norman Lloyd Johnson and Samuel Kotz and Adrienne W. Kemp
title: Univariate Discrete Distributions
publisher: pub-WILEY
address: pub-WILEY:adr
edition: Second
pages: xx + 565
year: 1992
ISBN: 0-471-54897-9 (hardcover) OR 0471548979 (hardcover)
ISBN13: 978-0-471-54897-3 (hardcover) OR 9780471548973 (hardcover)
LCCN: QA273.6 .J64 1992
bibdate: Sat Feb 7 17:19:01 MST 2015
bibtimestamp: 2015.02.07 17:19:01 MST
series: Wiley series in probability and mathematical statistics. Applied probability and statistics
remark: Revised edition of booktitle Discrete distributions, Norman L. Johnson, Samuel Kotz. 1969.
subject: Distribution (Probability theory)
acknowledgement: ack-nhfb
rawauthor: Norman Lloyd Johnson and Samuel Kotz and Adrienne W. Kemp
rawtitle: Univariate Discrete Distributions
bibsource:
https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

URL:
http://www.loc.gov/catdir/description/wiley031/92011685.html; http://www.loc.gov/catdir/enhancements/fy0607/92011685-b.html; http://www.loc.gov/catdir/toc/onix01/92011685.html

TOC:
Preface / xv List of Tables / xix 1. Preliminary Information / 1 A. Mathematical Preliminaries B. Probability and Statistical Preliminaries C. Computer Generation of Univariate Discrete Random Variables 2. Families of Discrete Distributions / 69 1. Lattice Distributions 2. Power Series Distributions 3. Difference Equation Systems 4. Kemp Families 5. Distributions Based on Lagrangian Expansions 6. Factorial Series Distributions 3. Binomial Distribution / 105 1. Definition 2. Historical Remarks and Genesis 3. Moments 4. Properties 5. Order Statistics 6. Approximations, Bounds, and Transformations 7. Computation and Tables 8. Estimation 9. Characterizations 10. Applications 11. Truncated Binomial Distributions 12. Other Related Distributions 4. Poisson Distribution / 151 1. Definition 2. Historical Remarks and Genesis 3. Moments 4. Properties 5. Approximations, Bounds, and Transformations 6. Computation and Tables 7. Estimation 8. Characterizations 9. Applications 10. Truncated and Misrecorded Poisson Distributions 11. Poisson-Stopped-Sum Distributions 12. Other Related Distributions 5. Negative Binomial Distribution / 199 1. Definition 2. Geometric Distribution 3. Historical Remarks and Genesis 4. Moments 5. Properties 6. Approximations and Transformations 7. Computation and Tables 8. Estimation 9. Characterizations 10. Applications 11. Truncated Negative Binomial Distributions 12. Other Related Distributions 6. Hypergeometric Distributions / 237 1. Definition 2. Historical Remarks and Genesis 3. Moments 4. Properties 5. Approximations and Bounds 6. Tables and Computation 7. Estimation 8. Characterizations 9. Applications 10. Special Cases 11. Extended Hypergeometric Distributions 12. Other Related Distributions 7. Logarithmic Distribution / 285 1. Definition 2. Historical Remarks and Genesis 3. Moments 4. Properties 5. Approximations and Bounds 6. Computation and Tables 7. Estimation 8. Characterizations 9. Applications 10. Truncated and Modified Logarithmic Distributions 11. Other Related Distributions 8. Mixture Distributions / 305 1. Introduction 2. Finite Mixtures of Discrete Distributions 3. Continuous and Countable Mixtures of Discrete Distributions 9. Generalized (Stopped-Sum) Distributions / 343 1. Introduction 2. Damage Processes 3. Poisson-Stopped-Sum Distributions: Generalized Poisson Distributions 4. Hermite Distribution 5. Poisson-Binomial Distribution 6. Neyman Type A Distribution 7. Polya--Aeppli Distribution 8. Poisson--Pascal Distribution: Poisson-Negative Binomial Distribution, Generalized Polya--Aeppli Distribution 9. Generalizations of the Neyman Type A Distribution 10. Thomas Distribution 11. Lagrangian Poisson Distribution: Shifted Borel--Tanner Distribution 12. Other Families of Stopped-Sum Distributions 10. Matching, Occupancy, and Runs Distributions / 405 1. Introduction 2. Probabilities of Combined Events 3. Matching Distributions 4. Occupancy Distributions 5. Runs Distributions 6. Distributions of Order k 11. Miscellaneous Discrete Distributions / 433 1. Absorption Distribution 2. Dandekar's Modified Binomial and Poisson Distributions 3. Digammma and Trigamma Distributions 4. Discrete Ades Distribution 5. Discrete Student's $t$-Distribution 6. Geeta Distribution 7. Gegenbauer Distribution: Negative Binomial* Pseudo-Negative Binomial Convolution 8. Gram-Charlier Type B Distributions 9. ``Interrupted'' Distributions 10. Lost-Games Distributions 11. Naor's Distribution 12. Partial-Sums Distributions 13. Queueing Theory Distributions 14. Record-Value Distributions 15. Sichel Distribution: Poisson-Inverse Gaussian Distribution 16. Skellam's Gene Frequency Distribution 17. Steyn's Two-Parameter Power Series Distributions 18. Univariate Multinomial-Type Distributions 19. Urn Models with Stochastic Replacements 20. Zipf and Zeta Distributions Bibliography / 473 Abbreviations / 549 Index / 551

shortTOC:
Preface Preliminary Information Families of Discrete Distributions Binomial Distributions Poisson Distributions Neggative Binomial Distributions Hypergeometric Distributions Logarithmic and Lagrangian Distributions Mixture Distributions Stopped-Sum Distributions Matching, Occupancy, Runs, and q-Series Distributions Parametric Regression Models and Miscellanea Bibliography Abbreviations Index

rawshortTOC:
Preface \\ Preliminary Information \\ Families of Discrete Distributions \\ Binomial Distributions \\ Poisson Distributions \\ Neggative Binomial Distributions \\ Hypergeometric Distributions \\ Logarithmic and Lagrangian Distributions \\ Mixture Distributions \\ Stopped-Sum Distributions \\ Matching, Occupancy, Runs, and q-Series Distributions \\ Parametric Regression Models and Miscellanea \\ Bibliography \\ Abbreviations \\ Index

rawTOC:
Preface / xv \\ List of Tables / xix \\ 1. Preliminary Information / 1 \\ A. Mathematical Preliminaries \\ B. Probability and Statistical Preliminaries \\ C. Computer Generation of Univariate Discrete Random Variables \\ 2. Families of Discrete Distributions / 69 \\ 1. Lattice Distributions \\ 2. Power Series Distributions \\ 3. Difference Equation Systems \\ 4. Kemp Families \\ 5. Distributions Based on Lagrangian Expansions \\ 6. Factorial Series Distributions \\ 3. Binomial Distribution / 105 \\ 1. Definition \\ 2. Historical Remarks and Genesis \\ 3. Moments \\ 4. Properties \\ 5. Order Statistics \\ 6. Approximations, Bounds, and Transformations \\ 7. Computation and Tables \\ 8. Estimation \\ 9. Characterizations \\ 10. Applications \\ 11. Truncated Binomial Distributions \\ 12. Other Related Distributions \\ 4. Poisson Distribution / 151 \\ 1. Definition \\ 2. Historical Remarks and Genesis \\ 3. Moments \\ 4. Properties \\ 5. Approximations, Bounds, and Transformations \\ 6. Computation and Tables \\ 7. Estimation \\ 8. Characterizations \\ 9. Applications \\ 10. Truncated and Misrecorded Poisson Distributions \\ 11. Poisson-Stopped-Sum Distributions \\ 12. Other Related Distributions \\ 5. Negative Binomial Distribution / 199 \\ 1. Definition \\ 2. Geometric Distribution \\ 3. Historical Remarks and Genesis \\ 4. Moments \\ 5. Properties \\ 6. Approximations and Transformations \\ 7. Computation and Tables \\ 8. Estimation \\ 9. Characterizations \\ 10. Applications \\ 11. Truncated Negative Binomial Distributions \\ 12. Other Related Distributions \\ 6. Hypergeometric Distributions / 237 \\ 1. Definition \\ 2. Historical Remarks and Genesis \\ 3. Moments \\ 4. Properties \\ 5. Approximations and Bounds \\ 6. Tables and Computation \\ 7. Estimation \\ 8. Characterizations \\ 9. Applications \\ 10. Special Cases \\ 11. Extended Hypergeometric Distributions \\ 12. Other Related Distributions \\ 7. Logarithmic Distribution / 285 \\ 1. Definition \\ 2. Historical Remarks and Genesis \\ 3. Moments \\ 4. Properties \\ 5. Approximations and Bounds \\ 6. Computation and Tables \\ 7. Estimation \\ 8. Characterizations \\ 9. Applications \\ 10. Truncated and Modified Logarithmic Distributions \\ 11. Other Related Distributions \\ 8. Mixture Distributions / 305 \\ 1. Introduction \\ 2. Finite Mixtures of Discrete Distributions \\ 3. Continuous and Countable Mixtures of Discrete Distributions \\ 9. Generalized (Stopped-Sum) Distributions / 343 \\ 1. Introduction \\ 2. Damage Processes \\ 3. Poisson-Stopped-Sum Distributions: Generalized Poisson Distributions \\ 4. Hermite Distribution \\ 5. Poisson-Binomial Distribution \\ 6. Neyman Type A Distribution \\ 7. Polya--Aeppli Distribution \\ 8. Poisson--Pascal Distribution: Poisson-Negative Binomial Distribution, Generalized Polya--Aeppli Distribution \\ 9. Generalizations of the Neyman Type A Distribution \\ 10. Thomas Distribution \\ 11. Lagrangian Poisson Distribution: Shifted Borel--Tanner Distribution \\ 12. Other Families of Stopped-Sum Distributions \\ 10. Matching, Occupancy, and Runs Distributions / 405 \\ 1. Introduction \\ 2. Probabilities of Combined Events \\ 3. Matching Distributions \\ 4. Occupancy Distributions \\ 5. Runs Distributions \\ 6. Distributions of Order k \\ 11. Miscellaneous Discrete Distributions / 433 \\ 1. Absorption Distribution \\ 2. Dandekar's Modified Binomial and Poisson Distributions \\ 3. Digammma and Trigamma Distributions \\ 4. Discrete Ad{\`e}s Distribution \\ 5. Discrete Student's $t$-Distribution \\ 6. Geeta Distribution \\ 7. Gegenbauer Distribution: Negative Binomial* Pseudo-Negative Binomial Convolution \\ 8. Gram-Charlier Type B Distributions \\ 9. ``Interrupted'' Distributions \\ 10. Lost-Games Distributions \\ 11. Naor's Distribution \\ 12. Partial-Sums Distributions \\ 13. Queueing Theory Distributions \\ 14. Record-Value Distributions \\ 15. Sichel Distribution: Poisson-Inverse Gaussian Distribution \\ 16. Skellam's Gene Frequency Distribution \\ 17. Steyn's Two-Parameter Power Series Distributions \\ 18. Univariate Multinomial-Type Distributions \\ 19. Urn Models with Stochastic Replacements \\ 20. Zipf and Zeta Distributions \\ Bibliography / 473 \\ Abbreviations / 549 \\ Index / 551

entry:
@Book{Johnson:1992:UDD,
  author =       "Norman Lloyd Johnson and Samuel Kotz and Adrienne W.
                 Kemp",
  title =        "Univariate Discrete Distributions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xx + 565",
  year =         "1992",
  ISBN =         "0-471-54897-9 (hardcover)",
  ISBN-13 =      "978-0-471-54897-3 (hardcover)",
  LCCN =         "QA273.6 .J64 1992",
  bibdate =      "Sat Feb 7 17:19:01 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in probability and mathematical
                 statistics. Applied probability and statistics",
  URL =          "http://www.loc.gov/catdir/description/wiley031/92011685.html;
                 http://www.loc.gov/catdir/enhancements/fy0607/92011685-b.html;
                 http://www.loc.gov/catdir/toc/onix01/92011685.html",
  acknowledgement = ack-nhfb,
  remark =       "Revised edition of \booktitle{Discrete distributions},
                 Norman L. Johnson, Samuel Kotz. 1969.",
  shorttableofcontents = "Preface \\
                 Preliminary Information \\
                 Families of Discrete Distributions \\
                 Binomial Distributions \\
                 Poisson Distributions \\
                 Neggative Binomial Distributions \\
                 Hypergeometric Distributions \\
                 Logarithmic and Lagrangian Distributions \\
                 Mixture Distributions \\
                 Stopped-Sum Distributions \\
                 Matching, Occupancy, Runs, and q-Series Distributions
                 \\
                 Parametric Regression Models and Miscellanea \\
                 Bibliography \\
                 Abbreviations \\
                 Index",
  subject =      "Distribution (Probability theory)",
  tableofcontents = "Preface / xv \\
                 List of Tables / xix \\
                 1. Preliminary Information / 1 \\
                 A. Mathematical Preliminaries \\
                 B. Probability and Statistical Preliminaries \\
                 C. Computer Generation of Univariate Discrete Random
                 Variables \\
                 2. Families of Discrete Distributions / 69 \\
                 1. Lattice Distributions \\
                 2. Power Series Distributions \\
                 3. Difference Equation Systems \\
                 4. Kemp Families \\
                 5. Distributions Based on Lagrangian Expansions \\
                 6. Factorial Series Distributions \\
                 3. Binomial Distribution / 105 \\
                 1. Definition \\
                 2. Historical Remarks and Genesis \\
                 3. Moments \\
                 4. Properties \\
                 5. Order Statistics \\
                 6. Approximations, Bounds, and Transformations \\
                 7. Computation and Tables \\
                 8. Estimation \\
                 9. Characterizations \\
                 10. Applications \\
                 11. Truncated Binomial Distributions \\
                 12. Other Related Distributions \\
                 4. Poisson Distribution / 151 \\
                 1. Definition \\
                 2. Historical Remarks and Genesis \\
                 3. Moments \\
                 4. Properties \\
                 5. Approximations, Bounds, and Transformations \\
                 6. Computation and Tables \\
                 7. Estimation \\
                 8. Characterizations \\
                 9. Applications \\
                 10. Truncated and Misrecorded Poisson Distributions \\
                 11. Poisson-Stopped-Sum Distributions \\
                 12. Other Related Distributions \\
                 5. Negative Binomial Distribution / 199 \\
                 1. Definition \\
                 2. Geometric Distribution \\
                 3. Historical Remarks and Genesis \\
                 4. Moments \\
                 5. Properties \\
                 6. Approximations and Transformations \\
                 7. Computation and Tables \\
                 8. Estimation \\
                 9. Characterizations \\
                 10. Applications \\
                 11. Truncated Negative Binomial Distributions \\
                 12. Other Related Distributions \\
                 6. Hypergeometric Distributions / 237 \\
                 1. Definition \\
                 2. Historical Remarks and Genesis \\
                 3. Moments \\
                 4. Properties \\
                 5. Approximations and Bounds \\
                 6. Tables and Computation \\
                 7. Estimation \\
                 8. Characterizations \\
                 9. Applications \\
                 10. Special Cases \\
                 11. Extended Hypergeometric Distributions \\
                 12. Other Related Distributions \\
                 7. Logarithmic Distribution / 285 \\
                 1. Definition \\
                 2. Historical Remarks and Genesis \\
                 3. Moments \\
                 4. Properties \\
                 5. Approximations and Bounds \\
                 6. Computation and Tables \\
                 7. Estimation \\
                 8. Characterizations \\
                 9. Applications \\
                 10. Truncated and Modified Logarithmic Distributions
                 \\
                 11. Other Related Distributions \\
                 8. Mixture Distributions / 305 \\
                 1. Introduction \\
                 2. Finite Mixtures of Discrete Distributions \\
                 3. Continuous and Countable Mixtures of Discrete
                 Distributions \\
                 9. Generalized (Stopped-Sum) Distributions / 343 \\
                 1. Introduction \\
                 2. Damage Processes \\
                 3. Poisson-Stopped-Sum Distributions: Generalized
                 Poisson Distributions \\
                 4. Hermite Distribution \\
                 5. Poisson-Binomial Distribution \\
                 6. Neyman Type A Distribution \\
                 7. Polya--Aeppli Distribution \\
                 8. Poisson--Pascal Distribution: Poisson-Negative
                 Binomial Distribution, Generalized Polya--Aeppli
                 Distribution \\
                 9. Generalizations of the Neyman Type A Distribution
                 \\
                 10. Thomas Distribution \\
                 11. Lagrangian Poisson Distribution: Shifted
                 Borel--Tanner Distribution \\
                 12. Other Families of Stopped-Sum Distributions \\
                 10. Matching, Occupancy, and Runs Distributions / 405
                 \\
                 1. Introduction \\
                 2. Probabilities of Combined Events \\
                 3. Matching Distributions \\
                 4. Occupancy Distributions \\
                 5. Runs Distributions \\
                 6. Distributions of Order k \\
                 11. Miscellaneous Discrete Distributions / 433 \\
                 1. Absorption Distribution \\
                 2. Dandekar's Modified Binomial and Poisson
                 Distributions \\
                 3. Digammma and Trigamma Distributions \\
                 4. Discrete Ad{\`e}s Distribution \\
                 5. Discrete Student's $t$-Distribution \\
                 6. Geeta Distribution \\
                 7. Gegenbauer Distribution: Negative Binomial*
                 Pseudo-Negative Binomial Convolution \\
                 8. Gram-Charlier Type B Distributions \\
                 9. ``Interrupted'' Distributions \\
                 10. Lost-Games Distributions \\
                 11. Naor's Distribution \\
                 12. Partial-Sums Distributions \\
                 13. Queueing Theory Distributions \\
                 14. Record-Value Distributions \\
                 15. Sichel Distribution: Poisson-Inverse Gaussian
                 Distribution \\
                 16. Skellam's Gene Frequency Distribution \\
                 17. Steyn's Two-Parameter Power Series Distributions
                 \\
                 18. Univariate Multinomial-Type Distributions \\
                 19. Urn Models with Stochastic Replacements \\
                 20. Zipf and Zeta Distributions \\
                 Bibliography / 473 \\
                 Abbreviations / 549 \\
                 Index / 551",
}


bibtype: article
filename: elefunt.bib
label: Kearfott:1992:IPF
author: Baker Kearfott and Milind Dawande and Kaisheng Du and Chen-Yi Hu
title: INTLIB: a Portable FORTRAN 77 Elementary Function Library
journal: j-INTERVAL-COMP
volume: 3
number: 5
pages: 96--105
year: 1992
ISSN: 0135-4868 OR 01354868
MRclass: 65G10
MRnumber: 1 253 132
bibdate: Sat Jan 11 17:44:01 MST 1997
bibtimestamp: 1997.01.11 17:44:01 MST
note: Interval '92 (Moscow, 1992).
fjournal: Interval Computations = Interval'nye vychisleniia
acknowledgement: ack-nhfb
rawauthor: Baker Kearfott and Milind Dawande and Kaisheng Du and Chen-Yi Hu
rawnote: Interval '92 (Moscow, 1992).
rawtitle: {INTLIB}: a Portable {FORTRAN} 77 Elementary Function Library
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Kearfott:1992:IPF,
  author =       "Baker Kearfott and Milind Dawande and Kaisheng Du and
                 Chen-Yi Hu",
  title =        "{INTLIB}: a Portable {FORTRAN} 77 Elementary Function
                 Library",
  journal =      j-INTERVAL-COMP,
  volume =       "3",
  number =       "5",
  pages =        "96--105",
  year =         "1992",
  ISSN =         "0135-4868",
  MRclass =      "65G10",
  MRnumber =     "1 253 132",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Interval '92 (Moscow, 1992).",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
}


bibtype: article
filename: elefunt.bib
label: Kzaz:1992:CAS
author: M. Kzaz
title: Convergence acceleration of some Gaussian quadrature formulas for analytic functions
journal: j-APPL-NUM-MATH
volume: 10
number: 6
pages: 481--496
month: nov
monthnumber: 11
year: 1992
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65B10 (65D32)
MRnumber: 93j:65004
MRreviewer: J. Kofro{\v{n}}
bibdate: Sat Feb 8 10:09:54 MST 1997
bibtimestamp: 1997.02.08 10:09:54 MST
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: M. Kzaz
rawtitle: Convergence acceleration of some {Gaussian} quadrature formulas for analytic functions
entry:
@Article{Kzaz:1992:CAS,
  author =       "M. Kzaz",
  title =        "Convergence acceleration of some {Gaussian} quadrature
                 formulas for analytic functions",
  journal =      j-APPL-NUM-MATH,
  volume =       "10",
  number =       "6",
  pages =        "481--496",
  month =        nov,
  year =         "1992",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B10 (65D32)",
  MRnumber =     "93j:65004",
  MRreviewer =   "J. Kofro{\v{n}}",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Lang:1992:HRS
author: T. Lang and P. Montuschi
title: Higher radix square root with prescaling
journal: j-IEEE-TRANS-COMPUT
volume: 41
number: 8
pages: 996--1009
month: aug
monthnumber: 8
year: 1992
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.156542
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Lang and P. Montuschi
rawtitle: Higher radix square root with prescaling
entry:
@Article{Lang:1992:HRS,
  author =       "T. Lang and P. Montuschi",
  title =        "Higher radix square root with prescaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "996--1009",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156542",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A scheme for performing higher radix square root based
                 on prescaling of the radicand is presented to reduce
                 the complexity of the result-digit selection. The
                 scheme requires several steps, namely multiplication
                 for prescaling the radicand, square \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lee:1992:LCF
author: Chu-In Charles Lee
title: On Laplace continued fraction for the normal integral
journal: j-ANN-INST-STAT-MATH-TOKYO
volume: 44
number: 1
pages: 107--120
month: mar
monthnumber: 3
year: 1992
CODEN: AISXAD
DOI: https://doi.org/10.1007/BF00048673
ISSN: 0020-3157 (print), 1572-9052 (electronic) OR 00203157 (print), 15729052 (electronic)
ISSNL: 0020-3157 OR 00203157
bibdate: Sat Jan 31 16:59:48 MST 2015
bibtimestamp: 2015.01.31 16:59:48 MST
URL: http://link.springer.com/article/10.1007/BF00048673
fjournal: Annals of the Institute of Statistical Mathematics
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10463
rawauthor: Chu-In Charles Lee
rawtitle: On {Laplace} continued fraction for the normal integral
bibsource:
https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Lee:1992:LCF,
  author =       "Chu-In Charles Lee",
  title =        "On {Laplace} continued fraction for the normal
                 integral",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "44",
  number =       "1",
  pages =        "107--120",
  month =        mar,
  year =         "1992",
  CODEN =        "AISXAD",
  DOI =          "https://doi.org/10.1007/BF00048673",
  ISSN =         "0020-3157 (print), 1572-9052 (electronic)",
  ISSN-L =       "0020-3157",
  bibdate =      "Sat Jan 31 16:59:48 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00048673",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the Institute of Statistical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10463",
}


bibtype: inproceedings
filename: elefunt.bib
label: Liu:1992:QBS
author: K. J. R. Liu and E. Frantzeskakis
booktitle: Workshop on VLSI Signal Processing, V, 1992
title: Qrd-based Square Root Free and Division Free Algorithms and Architectures
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 459--468
year: 1992
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: K. J. R. Liu and E. Frantzeskakis
rawbooktitle: Workshop on {VLSI} Signal Processing, V, 1992
rawtitle: Qrd-based Square Root Free and Division Free Algorithms and Architectures
entry:
@InProceedings{Liu:1992:QBS,
  author =       "K. J. R. Liu and E. Frantzeskakis",
  booktitle =    "Workshop on {VLSI} Signal Processing, V, 1992",
  title =        "Qrd-based Square Root Free and Division Free
                 Algorithms and Architectures",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "459--468",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Not \ldots{}",
}


bibtype: misc
filename: elefunt.bib
label: Lynch:1992:HSD
author: T. Lynch and S. McIntyre and K. Tseng and S. Shaw and T. Hurson
title: High speed divider with square root capability
pages: 459--468
year: 1992
bibdate: Thu Apr 2 08:38:35 1998
bibtimestamp: 1998.04.02 08:38:35 ???
note: U.S. Patent No. 5,128,891.
acknowledgement: ack-sfo
rawauthor: T. Lynch and S. McIntyre and K. Tseng and S. Shaw and T. Hurson
rawnote: U.S. Patent No. 5,128,891.
rawtitle: High speed divider with square root capability
entry:
@Misc{Lynch:1992:HSD,
  author =       "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
                 T. Hurson",
  title =        "High speed divider with square root capability",
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,128,891.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Martin:1992:TPQa
author: Pablo Martin and Ricardo Perez and Antonio L. Guerrero
title: Two-point quasi-fractional approximations to the Airy function $ rm Ai(x) $
journal: j-J-COMPUT-PHYS
volume: 98
number: 2
pages: 349--349
month: feb
monthnumber: 2
year: 1992
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(92)90165-U
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:53 MST 2012
bibtimestamp: 2012.01.02 07:55:53 MST
URL: http://www.sciencedirect.com/science/article/pii/002199919290165U
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Pablo Martin and Ricardo P{\'e}rez and Antonio L. Guerrero
rawtitle: Two-point quasi-fractional approximations to the {Airy} function {$ {\rm Ai}(x) $}
entry:
@Article{Martin:1992:TPQa,
  author =       "Pablo Martin and Ricardo P{\'e}rez and Antonio L.
                 Guerrero",
  title =        "Two-point quasi-fractional approximations to the
                 {Airy} function {$ {\rm Ai}(x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "98",
  number =       "2",
  pages =        "349--349",
  month =        feb,
  year =         "1992",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(92)90165-U",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:53 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199919290165U",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Martin:1992:TPQb
author: Pablo Martin and Ricardo Perez and Antonio L. Guerrero
title: Two-point quasi-fractional approximations to the Airy function $ rm Ai(x) $
journal: j-J-COMPUT-PHYS
volume: 99
number: 2
pages: 337--340
month: apr
monthnumber: 4
year: 1992
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(92)90212-H
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:55 MST 2012
bibtimestamp: 2012.01.02 07:55:55 MST
URL: http://www.sciencedirect.com/science/article/pii/002199919290212H
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Pablo Mart{\'\i}n and Ricardo P{\'e}rez and Antonio L. Guerrero
rawtitle: Two-point quasi-fractional approximations to the {Airy} function {$ {\rm Ai}(x) $}
entry:
@Article{Martin:1992:TPQb,
  author =       "Pablo Mart{\'\i}n and Ricardo P{\'e}rez and Antonio L.
                 Guerrero",
  title =        "Two-point quasi-fractional approximations to the
                 {Airy} function {$ {\rm Ai}(x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "99",
  number =       "2",
  pages =        "337--340",
  month =        apr,
  year =         "1992",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(92)90212-H",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:55 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199919290212H",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Matos:1992:CAP
author: Ana C. Matos
title: Convergence and acceleration properties for the vector $ epsilon $-algorithm
journal: j-NUMER-ALGORITHMS
volume: 3
number: 1--4
pages: 313--319
month: dec
monthnumber: 12
year: 1992
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65B99
MRnumber: 93h:65006
bibdate: Fri Nov 6 18:06:29 MST 1998
bibsource: http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.06 18:06:29 MST
note: Extrapolation and rational approximation (Puerto de la Cruz, 1992).
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Fac. de Ciencias, Porto Univ., Portugal
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: Ana C. Matos
rawnote: Extrapolation and rational approximation (Puerto de la Cruz, 1992).
rawtitle: Convergence and acceleration properties for the vector $ \epsilon $-algorithm
keywords:
acceleration; convergence acceleration; convergence of numerical methods; convergence speed; exactness; extrapolation; extrapolation algorithm; speed of convergence; vector $epsilon $-algorithm; vector sequences

entry:
@Article{Matos:1992:CAP,
  author =       "Ana C. Matos",
  title =        "Convergence and acceleration properties for the vector
                 $ \epsilon $-algorithm",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "3",
  number =       "1--4",
  pages =        "313--319",
  month =        dec,
  year =         "1992",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B99",
  MRnumber =     "93h:65006",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Extrapolation and rational approximation (Puerto de la
                 Cruz, 1992).",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  conflocation = "Puerto de la Cruz, Spain; 13-17 Jan. 1992",
  conftitle =    "International Mathematical Congress on Extrapolation
                 and Rational Approximation",
  corpsource =   "Fac. de Ciencias, Porto Univ., Portugal",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "acceleration; convergence acceleration; convergence of
                 numerical methods; convergence speed; exactness;
                 extrapolation; extrapolation algorithm; speed of
                 convergence; vector $\epsilon$-algorithm; vector
                 sequences",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: McQuillan:1992:VMH
author: S. E. McQuillan and J. V. McCanny
title: VLSI module for high-performance multiply, square root and divide
journal: j-IEE-PROC-COMPUT-DIGIT-TECH
volume: 139
number: 6
pages: 505--510
month: nov
monthnumber: 11
year: 1992
CODEN: ICDTEA
ISSN: 1350-2387 (print), 1359-7027 (electronic) OR 13502387 (print), 13597027 (electronic)
ISSNL: 1350-2387 OR 13502387
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEE Proceedings. Computers and Digital Techniques
acknowledgement: ack-nhfb
rawauthor: S. E. McQuillan and J. V. McCanny
rawtitle: {VLSI} module for high-performance multiply, square root and divide
entry:
@Article{McQuillan:1992:VMH,
  author =       "S. E. McQuillan and J. V. McCanny",
  title =        "{VLSI} module for high-performance multiply, square
                 root and divide",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "139",
  number =       "6",
  pages =        "505--510",
  month =        nov,
  year =         "1992",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  summary =      "A high-performance VLSI architecture to perform
                 multiply-accumulate, division and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control and ean be pipelined
                 right down to the bit level. The system can also
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Mikami:1992:NDO
author: N. Mikami and M. Kobayashi and Y. Yokoyama
title: A New DSP-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter
journal: j-IEEE-TRANS-SIG-PROC
volume: 40
number: 7
pages: 1663--1669
month: jul
monthnumber: 7
year: 1992
CODEN: ITPRED
DOI: https://doi.org/10.1109/78.143438
ISSN: 1053-587X (print), 1941-0476 (electronic) OR 1053587X (print), 19410476 (electronic)
ISSNL: 1053-587X OR 1053587X
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Signal Processing
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
rawauthor: N. Mikami and M. Kobayashi and Y. Yokoyama
rawtitle: A New {DSP}-Oriented Algorithm for Calculation of the Square Root Using a Nonlinear Digital Filter
entry:
@Article{Mikami:1992:NDO,
  author =       "N. Mikami and M. Kobayashi and Y. Yokoyama",
  title =        "A New {DSP}-Oriented Algorithm for Calculation of the
                 Square Root Using a Nonlinear Digital Filter",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "7",
  pages =        "1663--1669",
  month =        jul,
  year =         "1992",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.143438",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "A high-speed algorithm for calculating the square root
                 is proposed. This algorithm, which can be regarded as
                 calculation of the step response of a kind of nonlinear
                 IIR filter, requires no divisions. Therefore, it is
                 suitable for a VLSI digital \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Mitchell:1992:VFA
author: H. B. Mitchell
title: Very fast accurate square-root algorithm for use with gradient edge operators
journal: j-ELECT-LETTERS
volume: 28
number: 10
pages: 922--923
day: 7
month: may
monthnumber: 5
year: 1992
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: H. B. Mitchell
rawtitle: Very fast accurate square-root algorithm for use with gradient edge operators
entry:
@Article{Mitchell:1992:VFA,
  author =       "H. B. Mitchell",
  title =        "Very fast accurate square-root algorithm for use with
                 gradient edge operators",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "10",
  pages =        "922--923",
  day =          "7",
  month =        may,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Commonly used gradient edge operators such as the
                 Sobel, Prewitt and Roberts operators all required a
                 square root operation; this is, however,
                 computationally intensive and, consequently, simple but
                 very inaccurate approximations are often used
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Paris:1992:EIA
author: R. B. Paris and A. D. Wood
title: Exponentially-improved asymptotics for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 41
number: 1--2
pages: 135--143
day: 20
month: aug
monthnumber: 8
year: 1992
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:53 MST 2017
bibtimestamp: 2017.02.25 12:20:53 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279290243Q
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris and A. D. Wood
rawtitle: Exponentially-improved asymptotics for the gamma function
entry:
@Article{Paris:1992:EIA,
  author =       "R. B. Paris and A. D. Wood",
  title =        "Exponentially-improved asymptotics for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "41",
  number =       "1--2",
  pages =        "135--143",
  day =          "20",
  month =        aug,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:53 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279290243Q",
  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: Paszkowski:1992:CAC
author: Stefan Paszkowski
title: Convergence acceleration of continued fractions of Poincare's type $1$
journal: j-NUMER-ALGORITHMS
volume: 2
number: 2
pages: 155--170
year: 1992
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65B05 (40A15)
MRnumber: 93c:65006
MRreviewer: A. Bultheel
bibdate: Fri Nov 6 18:06:29 MST 1998
bibsource: http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.06 18:06:29 MST
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Instytut Niskich Temp. i Badan Strukturalnych PAN, Wroclaw, Poland
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: Stefan Paszkowski
rawtitle: Convergence acceleration of continued fractions of {Poincar{\'e}}'s type $1$
keywords:
asymptotic behaviour; continued fractions; convergence acceleration; convergence of numerical methods; function approximation

entry:
@Article{Paszkowski:1992:CAC,
  author =       "Stefan Paszkowski",
  title =        "Convergence acceleration of continued fractions of
                 {Poincar{\'e}}'s type $1$",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "2",
  number =       "2",
  pages =        "155--170",
  month =        "????",
  year =         "1992",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B05 (40A15)",
  MRnumber =     "93c:65006",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Instytut Niskich Temp. i Badan Strukturalnych PAN,
                 Wroclaw, Poland",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "asymptotic behaviour; continued fractions; convergence
                 acceleration; convergence of numerical methods;
                 function approximation",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: elefunt.bib
label: Prudnikov:1992:IS
author: Anatolij P. Prudnikov and Jurij A. Bryckov and Oleg I. Maricev
title: Integrals and series. More special functions
volume: 3
publisher: Gordon and Breach Science Publishers
address: New York, NY, USA
pages: xx + 618
year: 1992
ISBN: 2-88124-097-6 OR 2881240976
ISBN13: 978-2-88124-097-3 OR 9782881240973
LCCN: QA308 P68 1986
bibdate: Thu Nov 2 15:54:36 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.11.02 15:54:36 MDT
remark: Translated from the Russian by N. M. Queen.
subject: Mathematics
acknowledgement: ack-nhfb
rawauthor: Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and Oleg I. Mari{\v{c}}ev
rawtitle: Integrals and series. {More} special functions
entry:
@Book{Prudnikov:1992:IS,
  author =       "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
                 Oleg I. Mari{\v{c}}ev",
  title =        "Integrals and series. {More} special functions",
  volume =       "3",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "New York, NY, USA",
  pages =        "xx + 618",
  year =         "1992",
  ISBN =         "2-88124-097-6",
  ISBN-13 =      "978-2-88124-097-3",
  LCCN =         "QA308 P68 1986",
  bibdate =      "Thu Nov 2 15:54:36 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Translated from the Russian by N. M. Queen.",
  seriestableofcontents = "v. 1. Elementary functions \\
                 v. 2. Special functions \\
                 v. 3. More special functions \\
                 v. 4. Direct Laplace transforms \\
                 v. 5. Inverse Laplace transforms",
  subject =      "Mathematics",
}


bibtype: article
filename: elefunt.bib
label: Salwin:1992:UPE
author: Arthur E. Salwin
title: Using the Proposed Elementary Functions Standard to Build a Strongly Typed Trig Package
journal: j-SIGADA-LETTERS
volume: 12
number: 5
pages: 59--63
month: sep
monthnumber: 9
year: 1992
CODEN: AALEE5
ISSN: 1094-3641 (print), 1557-9476 (electronic) OR 10943641 (print), 15579476 (electronic)
ISSNL: 1094-3641 OR 10943641
bibdate: Sat Aug 9 09:05:46 MDT 2003
bibtimestamp: 2003.08.09 09:05:46 MDT
fjournal: ACM SIGAda Ada Letters
acknowledgement: ack-nhfb
classcodes: C6140D (High level languages)
corpsource: Mitre Corp., McLean, VA, USA
journalURL: http://portal.acm.org/citation.cfm?id=J32
treatment: P Practical
rawauthor: Arthur E. Salwin
rawtitle: Using the Proposed Elementary Functions Standard to Build a Strongly Typed Trig Package
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigada.bib

keywords:
Ada; compiler; elementary functions standard; standards; strong typing; strongly typed trig package; trigonometric functions

entry:
@Article{Salwin:1992:UPE,
  author =       "Arthur E. Salwin",
  title =        "Using the Proposed Elementary Functions Standard to
                 Build a Strongly Typed Trig Package",
  journal =      j-SIGADA-LETTERS,
  volume =       "12",
  number =       "5",
  pages =        "59--63",
  month =        sep # "\slash " # oct,
  year =         "1992",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:46 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages)",
  corpsource =   "Mitre Corp., McLean, VA, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; compiler; elementary functions standard;
                 standards; strong typing; strongly typed trig package;
                 trigonometric functions",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Saunders:1992:EFS
author: L. R. Saunders
journal: j-AUST-J-STAT
volume: 34
number: 2
pages: 261--264
month: jun
monthnumber: 6
year: 1992
CODEN: AUJSA3
DOI: https://doi.org/10.1111/j.1467-842X.1992.tb01358.x
ISSN: 0004-9581 OR 00049581
ISSNL: 0004-9581 OR 00049581
bibdate: Fri Jul 15 14:28:59 MDT 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/anzjs.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2016.07.15 14:28:59 MDT
fjournal: Australian Journal of Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-842X/issues
rawauthor: L. R. Saunders
title:
An Exact Formula for the Symmetrical Incomplete Beta Function Where the Parameter Is an Integer or Half-Integer

rawtitle:
An Exact Formula for the Symmetrical Incomplete Beta Function Where the Parameter Is an Integer or Half-Integer

entry:
@Article{Saunders:1992:EFS,
  author =       "L. R. Saunders",
  title =        "An Exact Formula for the Symmetrical Incomplete Beta
                 Function Where the Parameter Is an Integer or
                 Half-Integer",
  journal =      j-AUST-J-STAT,
  volume =       "34",
  number =       "2",
  pages =        "261--264",
  month =        jun,
  year =         "1992",
  CODEN =        "AUJSA3",
  DOI =          "https://doi.org/10.1111/j.1467-842X.1992.tb01358.x",
  ISSN =         "0004-9581",
  ISSN-L =       "0004-9581",
  bibdate =      "Fri Jul 15 14:28:59 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anzjs.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Journal of Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-842X/issues",
}


bibtype: mastersthesis
filename: elefunt.bib
label: Schulte:1992:AHD
author: Michael Joseph Schulte and Function generation
title: Algorithms and hardware designs for parallel elementary function generation
type: Thesis (M.S. in Engin.)
school: University of Texas at Austin
address: Austin, TX, USA
pages: ix + 73
year: 1992
bibdate: Sat Jan 11 10:14:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 10:14:06 MST
acknowledgement: ack-nhfb
rawauthor: Michael Joseph Schulte and Function generation
rawtitle: Algorithms and hardware designs for parallel elementary function generation
keywords:
Computer input-output equipment -- Design and construction.; Computer science -- Mathematics.; Numerical analysis.; Parallel processing (Electronic computers)

entry:
@MastersThesis{Schulte:1992:AHD,
  author =       "Michael Joseph Schulte and Function generation",
  title =        "Algorithms and hardware designs for parallel
                 elementary function generation",
  type =         "Thesis ({M.S.} in Engin.)",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "ix + 73",
  year =         "1992",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer input-output equipment -- Design and
                 construction.; Computer science -- Mathematics.;
                 Numerical analysis.; Parallel processing (Electronic
                 computers)",
  searchkey =    "ti:elementary n1 function",
}


bibtype: article
filename: elefunt.bib
label: Tang:1992:TDI
author: Ping Tak Peter Tang
title: Table-Driven Implementation of the tt Expm1 Function in IEEE Floating-Point Arithmetic
journal: j-TOMS
volume: 18
number: 2
pages: 211--222
month: jun
monthnumber: 6
year: 1992
CODEN: ACMSCU
DOI: https://doi.org/10.1145/146847.146928
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D15
MRnumber: 1 167 891
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: See independent analysis and accuracy confirmation of this algorithm in cite Kramer:1998:PWC.
URL: http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ping Tak Peter Tang
rawnote: See independent analysis and accuracy confirmation of this algorithm in \cite{Kramer:1998:PWC}.
rawtitle: Table-Driven Implementation of the {{\tt Expm1}} Function in {IEEE} Floating-Point Arithmetic
abstract:
Algorithms and implementation details for the function $ e^x - 1 $ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
Algorithms and implementation details for the function $ e^x - 1 $ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.

entry:
@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the {{\tt Expm1}}
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146928",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "1 167 891",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See independent analysis and accuracy confirmation of
                 this algorithm in \cite{Kramer:1998:PWC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
  abstract =     "Algorithms and implementation details for the function
                 $ e^x - 1 $ in both single and double precision of IEEE
                 754 arithmetic are presented here. With a table of
                 moderate size, the implementations need only
                 working-precision arithmetic and are provably accurate
                 to within 0.58 ulp.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}


bibtype: article
filename: elefunt.bib
label: Temme:1992:AII
author: N. M. Temme
title: Asymptotic Inversion of Incomplete Gamma Functions
journal: j-MATH-COMPUT
volume: 58
number: 198
pages: 755--764
month: apr
monthnumber: 4
year: 1992
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B20
MRnumber: 93a:33003
MRreviewer: F. W. J. Olver
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
journalURL: http://www.ams.org/mcom/
rawauthor: N. M. Temme
rawtitle: Asymptotic Inversion of Incomplete Gamma Functions
entry:
@Article{Temme:1992:AII,
  author =       "N. M. Temme",
  title =        "Asymptotic Inversion of Incomplete Gamma Functions",
  journal =      j-MATH-COMPUT,
  volume =       "58",
  number =       "198",
  pages =        "755--764",
  month =        apr,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B20",
  MRnumber =     "93a:33003",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Wong:1992:DSR
author: W. F. Wong and E. Goto
title: Division and square-rooting using a split multiplier
journal: j-ELECT-LETTERS
volume: 28
number: 18
pages: 1758--1759
day: 27
month: aug
monthnumber: 8
year: 1992
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: W. F. Wong and E. Goto
rawtitle: Division and square-rooting using a split multiplier
entry:
@Article{Wong:1992:DSR,
  author =       "W. F. Wong and E. Goto",
  title =        "Division and square-rooting using a split multiplier",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "18",
  pages =        "1758--1759",
  day =          "27",
  month =        aug,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A modification is proposed to the traditional design
                 of a fast floating point multiplication circuit such
                 that instead of just performing A$\times$B where A and
                 B are m bits long, it is also capable of \ldots{}",
}


bibtype: techreport
filename: elefunt.bib
label: Wood:1992:CP
author: David C. Wood
title: The Computation of Polylogarithms
type: Report
institution: University of Kent
address: Canterbury, Kent CT2 7NZ, UK
pages: 1758--1759
year: 1992
bibdate: Fri Jun 30 10:12:54 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.06.30 10:12:54 ???
URL: https://www.cs.kent.ac.uk/pubs/1992/110/content.pdf
keywords: polylogarithm
acknowledgement: ack-nhfb
rawauthor: David C. Wood
rawtitle: The Computation of Polylogarithms
abstract:
The polylogarithm function, $ Li _p(z) $, is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter $p$ and complex argument $z$.

remark:
Undated, but its URL suggests the year. The PDF file was created 20-Mar-2014. The latest reference is to a 1992 journal article.

rawabstract:
The polylogarithm function, $ \Li_p(z) $, is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter $p$ and complex argument $z$.

entry:
@TechReport{Wood:1992:CP,
  author =       "David C. Wood",
  title =        "The Computation of Polylogarithms",
  type =         "Report",
  institution =  "University of Kent",
  address =      "Canterbury, Kent CT2 7NZ, UK",
  year =         "1992",
  bibdate =      "Fri Jun 30 10:12:54 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cs.kent.ac.uk/pubs/1992/110/content.pdf",
  abstract =     "The polylogarithm function, $ \Li_p(z) $, is defined,
                 and a number of algorithms are derived for its
                 computation, valid in different ranges of its real
                 parameter $p$ and complex argument $z$.",
  acknowledgement = ack-nhfb,
  keywords =     "polylogarithm",
  remark =       "Undated, but its URL suggests the year. The PDF file
                 was created 20-Mar-2014. The latest reference is to a
                 1992 journal article.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Woods:1992:HPD
author: R. F. Woods and S. E. McQuillan and J. Dowling and J. V. McCanny
booktitle: Proceedings of Fifth Annual IEEE International ASIC Conference and Exhibit, 1992
title: High performance DSP ASIC for multiply, divide and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 209--213
year: 1992
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: R. F. Woods and S. E. McQuillan and J. Dowling and J. V. McCanny
rawbooktitle: Proceedings of Fifth Annual {IEEE} International {ASIC} Conference and Exhibit, 1992
rawtitle: High performance {DSP} {ASIC} for multiply, divide and square root
entry:
@InProceedings{Woods:1992:HPD,
  author =       "R. F. Woods and S. E. McQuillan and J. Dowling and J.
                 V. McCanny",
  booktitle =    "Proceedings of Fifth Annual {IEEE} International
                 {ASIC} Conference and Exhibit, 1992",
  title =        "High performance {DSP} {ASIC} for multiply, divide and
                 square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "209--213",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The design of a high-speed ASIC that combines the
                 operations of multiplication, division and square root
                 is described. The chip is based on a systolic array
                 architecture that uses a redundant number system and
                 allows multiplication, division, and \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Yeyios:1992:TSA
author: A. K. Yeyios
title: On two sequences of algorithms for approximating square roots
journal: j-J-COMPUT-APPL-MATH
volume: 40
number: 1
pages: 63--72
month: jun
monthnumber: 6
year: 1992
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Thu Sep 1 10:15:56 1994
bibtimestamp: 1994.09.01 10:15:56 ???
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. K. Yeyios
rawtitle: On two sequences of algorithms for approximating square roots
entry:
@Article{Yeyios:1992:TSA,
  author =       "A. K. Yeyios",
  title =        "On two sequences of algorithms for approximating
                 square roots",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "40",
  number =       "1",
  pages =        "63--72",
  month =        jun,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Sep 1 10:15:56 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 =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1993:SGF
author: Horst Alzer
title: Some gamma function inequalities
journal: j-MATH-COMPUT
volume: 60
number: 201
pages: 337--346
month: jan
monthnumber: 1
year: 1993
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B15 (26D20)
MRnumber: 93f:33001
MRreviewer: Aurelio Cannizzo
bibdate: Sat Jan 11 13:29:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 13:29:06 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Horst Alzer
rawtitle: Some gamma function inequalities
entry:
@Article{Alzer:1993:SGF,
  author =       "Horst Alzer",
  title =        "Some gamma function inequalities",
  journal =      j-MATH-COMPUT,
  volume =       "60",
  number =       "201",
  pages =        "337--346",
  month =        jan,
  year =         "1993",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (26D20)",
  MRnumber =     "93f:33001",
  MRreviewer =   "Aurelio Cannizzo",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: periodical
filename: elefunt.bib
label: Anonymous:1993:ITS
author: Anonymous
title: Integral transforms and special functions
publisher: Gordon and Breach Science Publishers
address: Yverdon, Switzerland
pages: 337--346
year: 1993
ISSN: 1065-2469, 1476-8291 OR 10652469, 14768291
ISSNL: 1065-2469 OR 10652469
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 ???
note: Appears with variable frequency from 1993--2001, and six times yearly from 2002--date.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawnote: Appears with variable frequency from 1993--2001, and six times yearly from 2002--date.
rawtitle: Integral transforms and special functions
entry:
@Periodical{Anonymous:1993:ITS,
  author =       "Anonymous",
  title =        "Integral transforms and special functions",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Yverdon, Switzerland",
  year =         "1993",
  ISSN =         "1065-2469, 1476-8291",
  ISSN-L =       "1065-2469",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Appears with variable frequency from 1993--2001, and
                 six times yearly from 2002--date.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Arenstorf:1993:SMZ
author: R. F. Arenstorf and L. L. Brewer
journal: j-COMPUT-MATH-APPL
volume: 26
number: 5
pages: 57--69
month: sep
monthnumber: 9
year: 1993
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(93)90074-6
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:16 MST 2017
bibtimestamp: 2017.03.01 19:11:16 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122193900746
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: R. F. Arenstorf and L. L. Brewer
title:
A study of the motion of zeros of the Epstein zeta function associated to $ m^2 + y^2 n^2 $ as $y$ varies from $1$ to $ sqrt 6$

bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
A study of the motion of zeros of the {Epstein} zeta function associated to $ m^2 + y^2 n^2 $ as $y$ varies from $1$ to $ \sqrt {6}$

entry:
@Article{Arenstorf:1993:SMZ,
  author =       "R. F. Arenstorf and L. L. Brewer",
  title =        "A study of the motion of zeros of the {Epstein} zeta
                 function associated to $ m^2 + y^2 n^2 $ as $y$ varies
                 from $1$ to $ \sqrt {6}$",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "26",
  number =       "5",
  pages =        "57--69",
  month =        sep,
  year =         "1993",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(93)90074-6",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122193900746",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Bailey:1993:AMT
author: D. H. Bailey
title: Algorithm 719: Multiprecision Translation and Execution of FORTRAN Programs
journal: j-TOMS
volume: 19
number: 3
pages: 288--319
month: sep
monthnumber: 9
year: 1993
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Dec 13 18:37:31 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.13 18:37:31 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: NASA Ames Res. Center, Moffett Field, CA, USA
journalURL: https://dl.acm.org/loi/toms
rawauthor: D. H. Bailey
rawtitle: Algorithm 719: Multiprecision Translation and Execution of {FORTRAN} Programs
abstract:
The author describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose. The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls. This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.

keywords:
Algorithm 719; Arithmetic operations; Array space; Complex data types; Computational expressions; Floating point numbers; Fortran programs; Fortran subroutines; Fortran utilities; Fortran-77 intrinsics; Mixed mode operations; Multiprecision computation; Multiprecision data types; Multiprecision subroutine calls; Multiprecision translation; Operator precedence; Source directives; Transcendental functions; Translator program

thesaurus:
Data structures; Digital arithmetic; FORTRAN; Mathematics computing; Program interpreters; Subroutines

rawabstract:
The author describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose. The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls. This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.

entry:
@Article{Bailey:1993:AMT,
  author =       "D. H. Bailey",
  title =        "Algorithm 719: Multiprecision Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:37:31 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The author describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose. The second utility is a
                 translator program, which facilitates the conversion of
                 ordinary Fortran programs to use this package. By means
                 of source directives (special comments) in the original
                 Fortran program, the user declares the precision level
                 and specifies which variables in each subprogram are to
                 be treated as multiprecision. The translator program
                 reads this source program and outputs a program with
                 the appropriate multiprecision subroutine calls. This
                 translator supports multiprecision integer, real, and
                 complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NASA Ames Res. Center, Moffett Field, CA, USA",
  classification = "C5230 (Digital arithmetic methods); C6120 (File
                 organisation); C6140D (High level languages); C6150C
                 (Compilers, interpreters and other processors); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithm 719; Arithmetic operations; Array space;
                 Complex data types; Computational expressions; Floating
                 point numbers; Fortran programs; Fortran subroutines;
                 Fortran utilities; Fortran-77 intrinsics; Mixed mode
                 operations; Multiprecision computation; Multiprecision
                 data types; Multiprecision subroutine calls;
                 Multiprecision translation; Operator precedence; Source
                 directives; Transcendental functions; Translator
                 program",
  pubcountry =   "USA",
  thesaurus =    "Data structures; Digital arithmetic; FORTRAN;
                 Mathematics computing; Program interpreters;
                 Subroutines",
}


bibtype: article
filename: elefunt.bib
label: Barrera:1993:IBS
author: Tony Barrera and Pelle Olsson
title: An Integer Based Square Root Algorithm
journal: j-BIT
volume: 33
number: 2
pages: 253--261
month: jun
monthnumber: 6
year: 1993
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01989748
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 68M07
MRnumber: 1 326 017
bibdate: Wed Jan 4 18:52:23 MST 2006
bibtimestamp: 2006.01.04 18:52:23 MST
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
affiliation: AB Consonant, Uppsala, Sweden
journalURL: http://link.springer.com/journal/10543
thesaurus: Digital arithmetic
rawauthor: Tony Barrera and Pelle Olsson
rawtitle: An Integer Based Square Root Algorithm
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=33&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit33.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253

abstract:
The authors propose a fast integer based method for computing square roots of floating point numbers. This implies high accuracy and robustness, since no precision will be lost during the computation. Only integer addition and shifts are necessary to obtain the square root. Comparisons made with the modified Newton method indicate that the suggested method is twice as fast for computing floating point square roots. (5 Refs.)

keywords:
Floating point numbers; floating-point arithmetic; Integer based square root algorithm; Modified Newton method; Robustness

rawabstract:
The authors propose a fast integer based method for computing square roots of floating point numbers. This implies high accuracy and robustness, since no precision will be lost during the computation. Only integer addition and shifts are necessary to obtain the square root. Comparisons made with the modified Newton method indicate that the suggested method is twice as fast for computing floating point square roots. (5 Refs.)

entry:
@Article{Barrera:1993:IBS,
  author =       "Tony Barrera and Pelle Olsson",
  title =        "An Integer Based Square Root Algorithm",
  journal =      j-BIT,
  volume =       "33",
  number =       "2",
  pages =        "253--261",
  month =        jun,
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01989748",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68M07",
  MRnumber =     "1 326 017",
  bibdate =      "Wed Jan 4 18:52:23 MST 2006",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=33&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit33.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
  abstract =     "The authors propose a fast integer based method for
                 computing square roots of floating point numbers. This
                 implies high accuracy and robustness, since no
                 precision will be lost during the computation. Only
                 integer addition and shifts are necessary to obtain the
                 square root. Comparisons made with the modified Newton
                 method indicate that the suggested method is twice as
                 fast for computing floating point square roots. (5
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "AB Consonant, Uppsala, Sweden",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Floating point numbers; floating-point arithmetic;
                 Integer based square root algorithm; Modified Newton
                 method; Robustness",
  pubcountry =   "Denmark",
  thesaurus =    "Digital arithmetic",
  xxpages =      "254--261??",
}


bibtype: incollection
filename: elefunt.bib
label: Bohlender:1993:PAF
author: G. Bohlender and D. Cordes and A. Knofel and U. Kulisch and R. Lohner and W. V. Walter
title: Proposal for accurate floating-point vector arithmetic
crossref: Adams:1993:ACA
pages: 87--102
year: 1993
bibdate: Tue Dec 12 09:27:13 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:27:13 MST
acknowledgement: ack-nhfb
affiliation: Inst. fur Angewandte Math., Karlsruhe Univ., Germany
bookpages: x + 612
thesaurus: Digital arithmetic; Mathematics computing; Roundoff errors; Standards
rawauthor: G. Bohlender and D. Cordes and A. Knofel and U. Kulisch and R. Lohner and W. V. Walter
rawtitle: Proposal for accurate floating-point vector arithmetic
abstract:
Many computers provide accurate and reliable scalar arithmetic for floating point numbers. An accurate definition of the four elementary floating-point operations +, -, *, / is given in the IEEE standards for floating-point arithmetic and was well established long before. An increasing number of computers (especially PC's and workstations) feature IEEE arithmetic. In many numerical algorithms, however, compound operations such as the summation of a sequence of numbers or the dot product of two vectors are highly common. A simulation of these compound operations by means of elementary floating-point operations leads to accumulation of rounding errors and may suffer from catastrophic cancellation of leading digits. Existing standards for floating-point arithmetic do not improve this situation. The goal of the proposal is to define vector operations in a manner consistent with the elementary scalar arithmetic operations. The rounding modes and accuracy requirements as well as the data formats of the operands and results of the vector operations described in the proposal are chosen to be fully consistent with the existing scalar floating-point arithmetic.

keywords:
Accuracy requirements; Catastrophic cancellation; Compound operations; Data formats; Dot product; Elementary floating-point operations; Elementary scalar arithmetic operations; Floating point numbers; IEEE arithmetic; IEEE standards; Leading digits; Numerical algorithms; Operands; Rounding errors; Rounding modes; Scalar floating-point arithmetic; Sequence; Standards; Summation; Vector operations

rawabstract:
Many computers provide accurate and reliable scalar arithmetic for floating point numbers. An accurate definition of the four elementary floating-point operations +, -, *, / is given in the IEEE standards for floating-point arithmetic and was well established long before. An increasing number of computers (especially PC's and workstations) feature IEEE arithmetic. In many numerical algorithms, however, compound operations such as the summation of a sequence of numbers or the dot product of two vectors are highly common. A simulation of these compound operations by means of elementary floating-point operations leads to accumulation of rounding errors and may suffer from catastrophic cancellation of leading digits. Existing standards for floating-point arithmetic do not improve this situation. The goal of the proposal is to define vector operations in a manner consistent with the elementary scalar arithmetic operations. The rounding modes and accuracy requirements as well as the data formats of the operands and results of the vector operations described in the proposal are chosen to be fully consistent with the existing scalar floating-point arithmetic.

entry:
@InCollection{Bohlender:1993:PAF,
  author =       "G. Bohlender and D. Cordes and A. Knofel and U.
                 Kulisch and R. Lohner and W. V. Walter",
  title =        "Proposal for accurate floating-point vector
                 arithmetic",
  crossref =     "Adams:1993:ACA",
  bookpages =    "x + 612",
  pages =        "87--102",
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Many computers provide accurate and reliable scalar
                 arithmetic for floating point numbers. An accurate
                 definition of the four elementary floating-point
                 operations +, -, *, / is given in the IEEE standards
                 for floating-point arithmetic and was well established
                 long before. An increasing number of computers
                 (especially PC's and workstations) feature IEEE
                 arithmetic. In many numerical algorithms, however,
                 compound operations such as the summation of a sequence
                 of numbers or the dot product of two vectors are highly
                 common. A simulation of these compound operations by
                 means of elementary floating-point operations leads to
                 accumulation of rounding errors and may suffer from
                 catastrophic cancellation of leading digits. Existing
                 standards for floating-point arithmetic do not improve
                 this situation. The goal of the proposal is to define
                 vector operations in a manner consistent with the
                 elementary scalar arithmetic operations. The rounding
                 modes and accuracy requirements as well as the data
                 formats of the operands and results of the vector
                 operations described in the proposal are chosen to be
                 fully consistent with the existing scalar
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C7310 (Mathematics)",
  keywords =     "Accuracy requirements; Catastrophic cancellation;
                 Compound operations; Data formats; Dot product;
                 Elementary floating-point operations; Elementary scalar
                 arithmetic operations; Floating point numbers; IEEE
                 arithmetic; IEEE standards; Leading digits; Numerical
                 algorithms; Operands; Rounding errors; Rounding modes;
                 Scalar floating-point arithmetic; Sequence; Standards;
                 Summation; Vector operations",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Mathematics computing; Roundoff
                 errors; Standards",
}


bibtype: article
filename: elefunt.bib
label: Cody:1993:ACP
author: W. J. Cody
title: Algorithm 714: CELEFUNT: a Portable Test Package for Complex Elementary Functions
journal: j-TOMS
volume: 19
number: 1
pages: 1--21
month: mar
monthnumber: 3
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/151271.151272
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Sep 20 18:24:35 1994
bibtimestamp: 1994.09.20 18:24:35 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody
rawtitle: {Algorithm 714}: {CELEFUNT}: a Portable Test Package for Complex Elementary Functions
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

URL:
http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/; http://www.acm.org/pubs/toc/Abstracts/toms/151272.html

abstract:
This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.

keywords:
algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex elementary functions; Complex power function; CSIN/CCOS; CSQRT; Floating-point elementary functions; Fortran programs; measurement; performance; Portable test package

subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

thesaurus:
Conformance testing; Digital arithmetic; FORTRAN; Mathematics computing; Numerical analysis; Program testing; Software packages

rawabstract:
This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.

entry:
@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "1--21",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:35 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",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/151272.html",
  abstract =     "This paper discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.",
  abstract-2 =   "The author discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.
                 CELEFUNT is a collection of test programs for the
                 complex floating-point elementary functions required by
                 the 1978 ANSI Fortran Standard (CABS), CSQRT, CLOG,
                 CEXP, CSIN/CCOS, and the complex power function.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  classification = "C4100 (Numerical analysis); C5230 (Digital
                 arithmetic methods); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex
                 elementary functions; Complex power function;
                 CSIN/CCOS; CSQRT; Floating-point elementary functions;
                 Fortran programs; measurement; performance; Portable
                 test package",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
  thesaurus =    "Conformance testing; Digital arithmetic; FORTRAN;
                 Mathematics computing; Numerical analysis; Program
                 testing; Software packages",
}


bibtype: article
filename: elefunt.bib
label: Cody:1993:ASP
author: W. J. Cody, Jr.
title: Algorithm 715: SPECFUN: a Portable FORTRAN Package of Special Function Routines and Test Drivers
journal: j-TOMS
volume: 19
number: 1
pages: 22--32
month: mar
monthnumber: 3
year: 1993
CODEN: ACMSCU
DOI: https://doi.org/10.1145/151271.151273
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Sep 20 18:24:38 1994
bibtimestamp: 1994.09.20 18:24:38 ???
URL: http://www.acm.org/pubs/toc/Abstracts/0098-3500/151273.html
fjournal: ACM Transactions on Mathematical Software
acknowledgement: ack-nhfb
affiliation: Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL, USA
journalURL: http://portal.acm.org/toc.cfm?idx=J782
thesaurus: FORTRAN; Mathematics computing; Numerical analysis; Software packages; Software portability
rawauthor: W. J. {Cody, Jr.}
abstract:
SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.

keywords:
algorithms; Bessel functions; Error functions; Exponential integrals; Gamma functions; Portable FORTRAN package; Real arguments; SPECFUN; Special function routines; Test drivers

subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.

rawtitle:
Algorithm 715: {SPECFUN}: a Portable {FORTRAN} Package of Special Function Routines and Test Drivers

entry:
@Article{Cody:1993:ASP,
  author =       "W. J. {Cody, Jr.}",
  title =        "Algorithm 715: {SPECFUN}: a Portable {FORTRAN} Package
                 of Special Function Routines and Test Drivers",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "22--32",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:38 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",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0098-3500/151273.html",
  abstract =     "SPECFUN is a package containing transportable FORTRAN
                 special function programs for real arguments and
                 accompanying test drivers. Components include Bessel
                 functions, exponential integrals, error functions and
                 related functions, and gamma functions and related
                 functions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  classification = "C4100 (Numerical analysis); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://portal.acm.org/toc.cfm?idx=J782",
  keywords =     "algorithms; Bessel functions; Error functions;
                 Exponential integrals; Gamma functions; Portable
                 FORTRAN package; Real arguments; SPECFUN; Special
                 function routines; Test drivers",
  pubcountry =   "USA",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
  thesaurus =    "FORTRAN; Mathematics computing; Numerical analysis;
                 Software packages; Software portability",
}


bibtype: article
filename: elefunt.bib
label: duToit:1993:BFI
author: C. F. du Toit
title: Bessel functions $ J_n(z) $ and $ Y_n(z) $ of integer order and complex argument
journal: j-COMP-PHYS-COMM
volume: 78
number: 1--2
pages: 181--189
month: dec
monthnumber: 12
year: 1993
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(93)90153-4
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:29:41 MST 2012
bibtimestamp: 2012.02.13 21:29:41 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465593901534
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: C. F. du Toit
rawtitle: {Bessel} functions {$ J_n(z) $} and {$ Y_n(z) $} of integer order and complex argument
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
This paper describes computer subroutines which were developed to compute Bessel functions of the first and second kind ($ J_n(z) $ and $ Y_n(z) $, respectively) for a complex argument $z$ and a range of integer orders. A novel way of determining the starting point of backward recurrence is used, and the algorithm for $ Y_n(z) $ improves on previous algorithms in terms of accuracy and restrictions on the range of orders.

rawabstract:
This paper describes computer subroutines which were developed to compute Bessel functions of the first and second kind ($ J_n(z) $ and $ Y_n(z) $, respectively) for a complex argument $z$ and a range of integer orders. A novel way of determining the starting point of backward recurrence is used, and the algorithm for $ Y_n(z) $ improves on previous algorithms in terms of accuracy and restrictions on the range of orders.

entry:
@Article{duToit:1993:BFI,
  author =       "C. F. du Toit",
  title =        "{Bessel} functions {$ J_n(z) $} and {$ Y_n(z) $} of
                 integer order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "78",
  number =       "1--2",
  pages =        "181--189",
  month =        dec,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90153-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:29:41 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465593901534",
  abstract =     "This paper describes computer subroutines which were
                 developed to compute Bessel functions of the first and
                 second kind ($ J_n(z) $ and $ Y_n(z) $, respectively)
                 for a complex argument $z$ and a range of integer
                 orders. A novel way of determining the starting point
                 of backward recurrence is used, and the algorithm for $
                 Y_n(z) $ improves on previous algorithms in terms of
                 accuracy and restrictions on the range of orders.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Feinsilver:1993:ASO
author: Philip J. (Philip Joel) Feinsilver and Rene Schott
title: Algebraic Structures and Operator Calculus
volume: 241, 292, 347
publisher: pub-KLUWER
address: pub-KLUWER:adr
year: 1993, 1994, 1996
LCCN: QA432 .F45 1993
bibdate: Sat Oct 30 17:31:34 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:31:34 MDT
series: Mathematics and its applications
subject: Calculus, Operational; Probabilities; Representations of groups
acknowledgement: ack-nhfb
rawauthor: Philip J. (Philip Joel) Feinsilver and Ren{\'e} Schott
rawtitle: Algebraic Structures and Operator Calculus
ISBN:
0-7923-2116-2 (v. 1), 0-7923-2921-X (v. 2), 0-7923-3834-0 (v. 3) OR 0792321162 (v. 1), 079232921X (v. 2), 0792338340 (v. 3)

ISBN13:
978-0-7923-2116-3 (v. 1), 978-0-7923-2921-3 (v. 2), 978-0-7923-3834-5 (v. 3) OR 9780792321163 (v. 1), 9780792329213 (v. 2), 9780792338345 (v. 3)

note:
Volume 1: Representations and probability theory. Volume 2: Special functions and computer science. Volume 3: Representations of Lie groups

rawnote:
Volume 1: Representations and probability theory. Volume 2: Special functions and computer science. Volume 3: Representations of Lie groups

entry:
@Book{Feinsilver:1993:ASO,
  author =       "Philip J. (Philip Joel) Feinsilver and Ren{\'e}
                 Schott",
  title =        "Algebraic Structures and Operator Calculus",
  volume =       "241, 292, 347",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "?????",
  year =         "1993, 1994, 1996",
  ISBN =         "0-7923-2116-2 (v. 1), 0-7923-2921-X (v. 2),
                 0-7923-3834-0 (v. 3)",
  ISBN-13 =      "978-0-7923-2116-3 (v. 1), 978-0-7923-2921-3 (v. 2),
                 978-0-7923-3834-5 (v. 3)",
  LCCN =         "QA432 .F45 1993",
  bibdate =      "Sat Oct 30 17:31:34 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Volume 1: Representations and probability theory.
                 Volume 2: Special functions and computer science.
                 Volume 3: Representations of Lie groups",
  series =       "Mathematics and its applications",
  acknowledgement = ack-nhfb,
  subject =      "Calculus, Operational; Probabilities; Representations
                 of groups",
}


bibtype: article
filename: elefunt.bib
label: Fowkes:1993:HEA
author: R. E. Fowkes
title: Hardware Efficient Algorithms for Trigonometric Functions
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 2
pages: 235--239
month: feb
monthnumber: 2
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.204796
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:47 MDT 2011
bibtimestamp: 2011.07.07 07:58:47 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204796
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: R. E. Fowkes
rawtitle: Hardware Efficient Algorithms for Trigonometric Functions
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/ieeetranscomput1990.bib

entry:
@Article{Fowkes:1993:HEA,
  author =       "R. E. Fowkes",
  title =        "Hardware Efficient Algorithms for Trigonometric
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "235--239",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204796",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 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/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204796",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Frappier:1993:QFI
author: Clement Frappier and Patrick Olivier
title: A quadrature formula involving zeros of Bessel functions
journal: j-MATH-COMPUT
volume: 60
number: 201
pages: 303--316
month: jan
monthnumber: 1
year: 1993
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 41A55 (65D32)
MRnumber: 93d:41025
MRreviewer: Hans Strauss
bibdate: Tue Mar 25 15:38:13 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.25 15:38:13 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Dept. de Math. Appliquees, Montreal, Que., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Cl{\'e}ment Frappier and Patrick Olivier
rawtitle: A quadrature formula involving zeros of {Bessel} functions
keywords:
Bessel functions; integration; interpolation; poles and; polynomials; quadrature formula; sampling theorem; zeros

classcodes:
B0290F (Interpolation and function approximation); B0290M (Numerical integration and differentiation); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)

entry:
@Article{Frappier:1993:QFI,
  author =       "Cl{\'e}ment Frappier and Patrick Olivier",
  title =        "A quadrature formula involving zeros of {Bessel}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "60",
  number =       "201",
  pages =        "303--316",
  month =        jan,
  year =         "1993",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A55 (65D32)",
  MRnumber =     "93d:41025",
  MRreviewer =   "Hans Strauss",
  bibdate =      "Tue Mar 25 15:38:13 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 C4130 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Dept. de Math. Appliqu{\'e}es, Montreal, Que.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; integration; interpolation; poles
                 and; polynomials; quadrature formula; sampling theorem;
                 zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Han:1993:CAS
author: Weimin Han and Florian A. Potra
title: Convergence acceleration for some rootfinding methods
crossref: Albrecht:1993:VNT
volume: 9
pages: 67--78
year: 1993
CODEN: COSPDM
ISSN: 0344-8029 OR 03448029
bibdate: Sun Oct 17 11:55:48 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.17 11:55:48 MDT
series: j-COMPUTING-SUPPLEMENTUM
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: Weimin Han and Florian A. Potra
rawtitle: Convergence acceleration for some rootfinding methods
entry:
@InProceedings{Han:1993:CAS,
  author =       "Weimin Han and Florian A. Potra",
  title =        "Convergence acceleration for some rootfinding
                 methods",
  crossref =     "Albrecht:1993:VNT",
  volume =       "9",
  pages =        "67--78",
  year =         "1993",
  CODEN =        "COSPDM",
  ISSN =         "0344-8029",
  bibdate =      "Sun Oct 17 11:55:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       j-COMPUTING-SUPPLEMENTUM,
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Higginbotham:1993:ISR
author: T. F. Higginbotham
title: The integer square root of $N$ via a binary search
journal: j-SIGCSE
volume: 25
number: 4
pages: 41--45
month: dec
monthnumber: 12
year: 1993
CODEN: SIGSD3
DOI: https://doi.org/10.1145/164205.164229
ISSN: 0097-8418 (print), 2331-3927 (electronic) OR 00978418 (print), 23313927 (electronic)
ISSNL: 0097-8418 OR 00978418
bibdate: Sat Nov 17 18:57:24 MST 2012
bibtimestamp: 2012.11.17 18:57:24 MST
fjournal: SIGCSE Bulletin (ACM Special Interest Group on Computer Science Education)
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J688
rawauthor: T. F. Higginbotham
rawtitle: The integer square root of {$N$} via a binary search
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib

abstract:
An algorithm is presented which may be used to find the integer square root of N. The method is intended for use on a binary computer, where only addition, subtraction, multiplication, or division by 2 is required. The problem arose when the author was working on factoring large numbers, where the machine, the Honeywell DPS 8, had double precision integer addition and subtraction, and the simulation of multiplication was easy. The actual factoring of the large number was to be Fermat's Method, requiring only addition and subtraction, but the integer square root is required in order to test for termination. The algorithm is implemented in FORTRAN for ease of reading. Students enjoy the unconventional approach to solving this problem. It isn't long before some of them think of other unusual solutions.

rawabstract:
An algorithm is presented which may be used to find the integer square root of N. The method is intended for use on a binary computer, where only addition, subtraction, multiplication, or division by 2 is required. The problem arose when the author was working on factoring large numbers, where the machine, the Honeywell DPS 8, had double precision integer addition and subtraction, and the simulation of multiplication was easy. The actual factoring of the large number was to be Fermat's Method, requiring only addition and subtraction, but the integer square root is required in order to test for termination. The algorithm is implemented in FORTRAN for ease of reading. Students enjoy the unconventional approach to solving this problem. It isn't long before some of them think of other unusual solutions.

entry:
@Article{Higginbotham:1993:ISR,
  author =       "T. F. Higginbotham",
  title =        "The integer square root of {$N$} via a binary search",
  journal =      j-SIGCSE,
  volume =       "25",
  number =       "4",
  pages =        "41--45",
  month =        dec,
  year =         "1993",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/164205.164229",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 18:57:24 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
  abstract =     "An algorithm is presented which may be used to find
                 the integer square root of N. The method is intended
                 for use on a binary computer, where only addition,
                 subtraction, multiplication, or division by 2 is
                 required. The problem arose when the author was working
                 on factoring large numbers, where the machine, the
                 Honeywell DPS 8, had double precision integer addition
                 and subtraction, and the simulation of multiplication
                 was easy. The actual factoring of the large number was
                 to be Fermat's Method, requiring only addition and
                 subtraction, but the integer square root is required in
                 order to test for termination. The algorithm is
                 implemented in FORTRAN for ease of reading. Students
                 enjoy the unconventional approach to solving this
                 problem. It isn't long before some of them think of
                 other unusual solutions.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}


bibtype: article
filename: elefunt.bib
label: Hu:1993:BRS
author: Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad
title: On Bounding the Range of Some Elementary Functions in FORTRAN 77
journal: j-INTERVAL-COMP
volume: 1993
number: 3
pages: 29--39
year: 1993
ISSN: 0135-4868 OR 01354868
MRclass: 65G10
MRnumber: 1 305 844
bibdate: Wed Dec 4 11:13:33 1996
bibtimestamp: 1996.12.04 11:13:33 ???
fjournal: Interval Computations = Interval'nye vychisleniia
acknowledgement: ack-nhfb
rawauthor: Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad
rawtitle: On Bounding the Range of Some Elementary Functions in {FORTRAN} 77
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

note:
Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993)

rawnote:
Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993)

entry:
@Article{Hu:1993:BRS,
  author =       "Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad",
  title =        "On Bounding the Range of Some Elementary Functions in
                 {FORTRAN} 77",
  journal =      j-INTERVAL-COMP,
  volume =       "1993",
  number =       "3",
  pages =        "29--39",
  year =         "1993",
  ISSN =         "0135-4868",
  MRclass =      "65G10",
  MRnumber =     "1 305 844",
  bibdate =      "Wed Dec 4 11:13:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the International Conference on
                 Numerical Analysis with Automatic Result Verification
                 (Lafayette, LA, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
}


bibtype: techreport
filename: elefunt.bib
label: Karp:1993:HPD
author: A. H. Karp and P. Markstein
title: High precision division and square root
number: HPL-93-42
institution: Hewlett--Packard Lab.
address: Palo Alto, CA, USA
pages: 20
month: jun
monthnumber: 6
year: 1993
bibdate: Tue Dec 12 09:27:13 MST 1995
bibtimestamp: 1995.12.12 09:27:13 MST
keywords: Division; Floating point hardware; Square root algorithms
acknowledgement: ack-nhfb
thesaurus: Digital arithmetic
rawauthor: A. H. Karp and P. Markstein
rawtitle: High precision division and square root
abstract:
The authors present division and square root algorithms for calculations with more bits than are handled by the floating point hardware. These algorithms avoid the need to multiply two high precision numbers, speeding up the last iteration by as much as a factor of ten.

rawabstract:
The authors present division and square root algorithms for calculations with more bits than are handled by the floating point hardware. These algorithms avoid the need to multiply two high precision numbers, speeding up the last iteration by as much as a factor of ten.

entry:
@TechReport{Karp:1993:HPD,
  author =       "A. H. Karp and P. Markstein",
  title =        "High precision division and square root",
  number =       "HPL-93-42",
  institution =  "Hewlett--Packard Lab.",
  address =      "Palo Alto, CA, USA",
  pages =        "20",
  month =        jun,
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present division and square root
                 algorithms for calculations with more bits than are
                 handled by the floating point hardware. These
                 algorithms avoid the need to multiply two high
                 precision numbers, speeding up the last iteration by as
                 much as a factor of ten.",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Division; Floating point hardware; Square root
                 algorithms",
  thesaurus =    "Digital arithmetic",
}


bibtype: incollection
filename: elefunt.bib
label: Kramer:1993:MPC
author: Walter Kramer
booktitle: Mathematics in Science and Engineering: Scientific Computing with Automatic Result Verification
title: Multiple-Precision Computations with Result Verification
volume: 189
publisher: Elsevier BV
address: Amsterdam, The Netherlands
pages: 325--356
year: 1993
DOI: https://doi.org/10.1016/s0076-5392(08)62851-9
bibdate: Tue Mar 14 19:20:47 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.14 19:20:47 ???
acknowledgement: ack-nhfb
rawauthor: Walter Kr{\"a}mer
rawbooktitle: Mathematics in Science and Engineering: Scientific Computing with Automatic Result Verification
rawtitle: Multiple-Precision Computations with Result Verification
keywords:
arithmetic-geometric mean iteration; computation of $ e^pi $; computation of a large number of digits of $pi $; computation of elliptic integrals; computation of guaranteed bounds for the natural logarithm; interval arithmetic; PASCAL-XSC

entry:
@InCollection{Kramer:1993:MPC,
  author =       "Walter Kr{\"a}mer",
  booktitle =    "Mathematics in Science and Engineering: Scientific
                 Computing with Automatic Result Verification",
  title =        "Multiple-Precision Computations with Result
                 Verification",
  volume =       "189",
  publisher =    "Elsevier BV",
  address =      "Amsterdam, The Netherlands",
  pages =        "325--356",
  year =         "1993",
  DOI =          "https://doi.org/10.1016/s0076-5392(08)62851-9",
  bibdate =      "Tue Mar 14 19:20:47 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic-geometric mean iteration; computation of $
                 e^\pi $; computation of a large number of digits of
                 $\pi$; computation of elliptic integrals; computation
                 of guaranteed bounds for the natural logarithm;
                 interval arithmetic; PASCAL-XSC",
}


bibtype: article
filename: elefunt.bib
label: Laforgia:1993:AMR
author: Andrea Laforgia and Maria Luisa Mathis
title: Additional monotonicity results for the zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 47
number: 1
pages: 135--139
day: 28
month: jun
monthnumber: 6
year: 1993
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:58 MST 2017
bibtimestamp: 2017.02.25 12:20:58 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279390095S
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Andrea Laforgia and Maria Luisa Mathis
rawtitle: Additional monotonicity results for the zeros of {Bessel} functions
entry:
@Article{Laforgia:1993:AMR,
  author =       "Andrea Laforgia and Maria Luisa Mathis",
  title =        "Additional monotonicity results for the zeros of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "47",
  number =       "1",
  pages =        "135--139",
  day =          "28",
  month =        jun,
  year =         "1993",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279390095S",
  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: Lee:1993:DAE
author: Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han
title: Design of an area efficient unit for floating-point division and square root
journal: j-J-KOREA-INFO-SCI-SOCIETY
volume: 20
number: 7
pages: 1060--1071
month: jul
monthnumber: 7
year: 1993
CODEN: HJKHDC
ISSN: 0258-9125 OR 02589125
bibdate: Tue Dec 12 09:27:13 MST 1995
bibtimestamp: 1995.12.12 09:27:13 MST
fjournal: Journal of the Korea Information Science Society = Chongbo Kwahakhoe nonmunji
language: Korean
acknowledgement: ack-nhfb
thesaurus: Adders; Digital arithmetic; Parallel algorithms
rawauthor: Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han
rawtitle: Design of an area efficient unit for floating-point division and square root
abstract:
The authors propose an algorithm for a high performance floating point division and square root unit that uses a parallel multiplier. The basic algorithm used in the design is the continued-product normalization method. In this method, an arbitrary number is constantly multiplied to the divisor and dividend and dividend/divisor ends up with quotient/1 and the desired result attained. However this method requires computation of x*(2-x) and x*(3-x)/2 and this is quite an overhead. Therefore they propose a new algorithm to compute (2-x) and (3-x)/2 by using the modified Booth algorithm. When applied to the continued-product normalization method, this algorithm can maximize the inherent parallelism of the continued-product normalization method, and reduce computation time by effectively applying pipelining, and also achieve area efficient design by eliminating one register and one carry propagate adder needed for computing (2-x) and (3-x)/2. When the designed unit is used with the seed generator which has the accuracy of 2/sup -7/, division can be executed in eight cycles and the square root operation in 13 cycles.

keywords:
Area efficient unit; Continued-product normalization method; Floating-point division; Modified Booth algorithm; Parallel multiplier; Pipelining; Seed generator; Square root

rawabstract:
The authors propose an algorithm for a high performance floating point division and square root unit that uses a parallel multiplier. The basic algorithm used in the design is the continued-product normalization method. In this method, an arbitrary number is constantly multiplied to the divisor and dividend and dividend/divisor ends up with quotient/1 and the desired result attained. However this method requires computation of x*(2-x) and x*(3-x)/2 and this is quite an overhead. Therefore they propose a new algorithm to compute (2-x) and (3-x)/2 by using the modified Booth algorithm. When applied to the continued-product normalization method, this algorithm can maximize the inherent parallelism of the continued-product normalization method, and reduce computation time by effectively applying pipelining, and also achieve area efficient design by eliminating one register and one carry propagate adder needed for computing (2-x) and (3-x)/2. When the designed unit is used with the seed generator which has the accuracy of 2/sup -7/, division can be executed in eight cycles and the square root operation in 13 cycles.

entry:
@Article{Lee:1993:DAE,
  author =       "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
  title =        "Design of an area efficient unit for floating-point
                 division and square root",
  journal =      j-J-KOREA-INFO-SCI-SOCIETY,
  volume =       "20",
  number =       "7",
  pages =        "1060--1071",
  month =        jul,
  year =         "1993",
  CODEN =        "HJKHDC",
  ISSN =         "0258-9125",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors propose an algorithm for a high
                 performance floating point division and square root
                 unit that uses a parallel multiplier. The basic
                 algorithm used in the design is the continued-product
                 normalization method. In this method, an arbitrary
                 number is constantly multiplied to the divisor and
                 dividend and dividend/divisor ends up with quotient/1
                 and the desired result attained. However this method
                 requires computation of x*(2-x) and x*(3-x)/2 and this
                 is quite an overhead. Therefore they propose a new
                 algorithm to compute (2-x) and (3-x)/2 by using the
                 modified Booth algorithm. When applied to the
                 continued-product normalization method, this algorithm
                 can maximize the inherent parallelism of the
                 continued-product normalization method, and reduce
                 computation time by effectively applying pipelining,
                 and also achieve area efficient design by eliminating
                 one register and one carry propagate adder needed for
                 computing (2-x) and (3-x)/2. When the designed unit is
                 used with the seed generator which has the accuracy of
                 2/sup -7/, division can be executed in eight cycles and
                 the square root operation in 13 cycles.",
  acknowledgement = ack-nhfb,
  classification = "B1265B (Logic circuits); C4240P (Parallel
                 programming and algorithm theory); C5120 (Logic and
                 switching circuits); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "Journal of the Korea Information Science Society =
                 Chongbo Kwahakhoe nonmunji",
  keywords =     "Area efficient unit; Continued-product normalization
                 method; Floating-point division; Modified Booth
                 algorithm; Parallel multiplier; Pipelining; Seed
                 generator; Square root",
  language =     "Korean",
  pubcountry =   "South Korea",
  thesaurus =    "Adders; Digital arithmetic; Parallel algorithms",
}


bibtype: article
filename: elefunt.bib
label: Li:1993:CAF
author: Y. Li and X. Dong and S. Pan
journal: j-IJQC
volume: 45
number: 1
pages: 3--??
year: 1993
CODEN: IJQCB2
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Wed Jan 3 14:24:13 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ijqc.bib
bibtimestamp: 1996.01.03 14:24:13 MST
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
rawauthor: Y. Li and X. Dong and S. Pan
title:
Computation of Auxiliary Functions in STO Molecular Integrals up to Arbitrary Accuracy. I. Evaluation of Incomplete Gamma Function E$_n$ (X) by Forward Recursion

rawtitle:
Computation of Auxiliary Functions in {STO} Molecular Integrals up to Arbitrary Accuracy. {I}. {Evaluation} of Incomplete Gamma Function {E$_n$ (X)} by Forward Recursion

entry:
@Article{Li:1993:CAF,
  author =       "Y. Li and X. Dong and S. Pan",
  title =        "Computation of Auxiliary Functions in {STO} Molecular
                 Integrals up to Arbitrary Accuracy. {I}. {Evaluation}
                 of Incomplete Gamma Function {E$_n$ (X)} by Forward
                 Recursion",
  journal =      j-IJQC,
  volume =       "45",
  number =       "1",
  pages =        "3--??",
  year =         "1993",
  CODEN =        "IJQCB2",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Wed Jan 3 14:24:13 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
}


bibtype: techreport
filename: elefunt.bib
label: Litvinov:1993:ACR
author: Grigori L. Litvinov
title: Approximate construction of rational approximations and the effect of error autocorrection
type: Technical report
number: 8
institution: Institute of Mathematics, University of Oslo
address: Oslo, Norway
pages: 3--??
month: may
monthnumber: 5
year: 1993
bibdate: Tue Mar 24 20:51:52 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.03.24 20:51:52 ???
note: See cite Litvinov:1994:ACR.
acknowledgement: ack-nhfb
rawauthor: Grigori L. Litvinov
rawnote: See \cite{Litvinov:1994:ACR}.
rawtitle: Approximate construction of rational approximations and the effect of error autocorrection
entry:
@TechReport{Litvinov:1993:ACR,
  author =       "Grigori L. Litvinov",
  title =        "Approximate construction of rational approximations
                 and the effect of error autocorrection",
  type =         "Technical report",
  number =       "8",
  institution =  "Institute of Mathematics, University of Oslo",
  address =      "Oslo, Norway",
  month =        may,
  year =         "1993",
  bibdate =      "Tue Mar 24 20:51:52 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Litvinov:1994:ACR}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Liu:1993:DSC
author: Hui Min Liu
title: Determination of several classes of elementary functions by functional inequalities. (Chinese)
journal: Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)
volume: 11
number: 2
pages: 30--35, 12
year: 1993
ISSN: 1001-6074 OR 10016074
MRclass: 26A09 (39B72)
MRnumber: 94g:26003
MRreviewer: Ling Yau Chan
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: Hui Min Liu
rawtitle: Determination of several classes of elementary functions by functional inequalities. ({Chinese})
entry:
@Article{Liu:1993:DSC,
  author =       "Hui Min Liu",
  title =        "Determination of several classes of elementary
                 functions by functional inequalities. ({Chinese})",
  journal =      "Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)",
  volume =       "11",
  number =       "2",
  pages =        "30--35, 12",
  year =         "1993",
  ISSN =         "1001-6074",
  MRclass =      "26A09 (39B72)",
  MRnumber =     "94g:26003",
  MRreviewer =   "Ling Yau Chan",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Louie:1993:DRS
author: M. E. Louie and M. D. Ercegovac
booktitle: Proceedings of the IEEE Workshop on FPGAs for Custom Computing Machines, 5--7 April 1993
title: A digit-recurrence square root implementation for field programmable gate arrays
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 178--183
year: 1993
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. E. Louie and M. D. Ercegovac
rawbooktitle: Proceedings of the {IEEE} Workshop on {FPGAs} for Custom Computing Machines, 5--7 April 1993
rawtitle: A digit-recurrence square root implementation for field programmable gate arrays
entry:
@InProceedings{Louie:1993:DRS,
  author =       "M. E. Louie and M. D. Ercegovac",
  booktitle =    "Proceedings of the {IEEE} Workshop on {FPGAs} for
                 Custom Computing Machines, 5--7 April 1993",
  title =        "A digit-recurrence square root implementation for
                 field programmable gate arrays",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "178--183",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Creating efficient arithmetic processors requires a
                 pairing of high speed arithmetic algorithms with
                 optimal mapping strategies for a given technology. The
                 authors propose bit reduction as key to an efficient
                 pairing process for lookup table based \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lozier:1993:ABF
author: Daniel W. Lozier and F. W. J. Olver
title: Airy and Bessel Functions by Parallel Integration of ODEs
crossref: Sincovec:1993:PSS
pages: 530--538
year: 1993
bibdate: Fri Jul 09 06:36:27 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:36:27 ???
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier and F. W. J. Olver
rawtitle: {Airy} and {Bessel} Functions by Parallel Integration of {ODEs}
entry:
@InProceedings{Lozier:1993:ABF,
  author =       "Daniel W. Lozier and F. W. J. Olver",
  title =        "{Airy} and {Bessel} Functions by Parallel Integration
                 of {ODEs}",
  crossref =     "Sincovec:1993:PSS",
  pages =        "530--538",
  year =         "1993",
  bibdate =      "Fri Jul 09 06:36:27 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Mathai:1993:HGS
author: A. M. Mathai
title: A handbook of generalized special functions for statistical and physical sciences
publisher: pub-CLARENDON
address: pub-CLARENDON:adr
pages: xi + 235
year: 1993
ISBN: 0-19-853595-3 OR 0198535953
ISBN13: 978-0-19-853595-9 OR 9780198535959
LCCN: QA351 .M35 1993
bibdate: Sat Oct 30 18:57:40 MDT 2010
bibtimestamp: 2010.10.30 18:57:40 MDT
series: Oxford science publications
subject: Functions, Special; Handbooks, manuals, etc
acknowledgement: ack-nhfb
rawauthor: A. M. Mathai
rawtitle: A handbook of generalized special functions for statistical and physical sciences
bibsource:
http://cat.cisti-icist.nrc-cnrc.gc.ca/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

URL:
http://www.loc.gov/catdir/enhancements/fy0635/92036065-d.html; http://www.loc.gov/catdir/enhancements/fy0635/92036065-t.html

TOC:
I Mathematical preliminaries 1.1 The gamma function 1 1.2 Bernoulli polynomials 6 1.3 Asymptotic expansions of gamma functions 9 1.4 The psi function 11 1.5 The generalized zeta functions 12 1.6 The beta function 15 1.7 Calculation of residues for gamma functions 16 1.8 The Mellin transform 23 1.9 Density functions 24 1.10 Methods of deriving distributions 49 2 The G-function 2.1 The G-function 60 2.2 Some basic properties of the G-function 69 2.3 The Mellin transform of a G-function 78 2.4 Properties connected with the derivatives of a G-function 94 2.5 Series representations for a G-function 96 2.6 G-functions as multiple integrals or as solutions of integral equations 106 2.7 Differential equation for a G-function 111 2.8 Asymptotic expansions for a G-function 112 3 Elementary special functions and the G-function 3.1 Gamma and related functions: notations and definitions 117 3.2 Hypergeometric functions: notations and special cases 118 3.3 Confluent hypergeometric function and related functions 119 3.4 Exponential integral and related functions 121 3.5 Bessel functions and associated functions 121 3.6 Other special functions 122 3.7 Orthogonal polynomials 124 3.8 Elementary special functions expressed in terms of G-functions 127 3.9 G-functions expressed in terms of elementary special functions 129 3.10 Some integrals involving G-functions 132 3.11 The H-function 140 3.12 Computational aspects of G- and H-functions 144 3.13 Orders of the special functions for small and large values of the argument 145 4 Generalizations to matrix variables 4.1 Scalar functions of a symmetric positive definite matrix 152 4.2 Scalar functions of matrix arguments 158 4.3 Laplace transform 160 4.4 Hypergeometric functions of matrix arguments 171 4.5 Generalized matrix transform or M-transform 177 4.6 Zonal polynomial 194 4.7 Matrix variate Dirichlet distribution 197 4.8 Hypergeometric functions of many scalar variables 205 4.9 Hypergeometric functions of many matrix arguments 215 4.10 G- and H-functions of two variables 217 Bibliography 227 Glossary of symbols 231 Author index 233 Subject index 234

rawTOC:
I Mathematical preliminaries \\ 1.1 The gamma function 1 \\ 1.2 Bernoulli polynomials 6 \\ 1.3 Asymptotic expansions of gamma functions 9 \\ 1.4 The psi function 11 \\ 1.5 The generalized zeta functions 12 \\ 1.6 The beta function 15 \\ 1.7 Calculation of residues for gamma functions 16 \\ 1.8 The Mellin transform 23 \\ 1.9 Density functions 24 \\ 1.10 Methods of deriving distributions 49 \\ 2 The G-function \\ 2.1 The G-function 60 \\ 2.2 Some basic properties of the G-function 69 \\ 2.3 The Mellin transform of a G-function 78 \\ 2.4 Properties connected with the derivatives of a G-function 94 \\ 2.5 Series representations for a G-function 96 \\ 2.6 G-functions as multiple integrals or as solutions of integral equations 106 \\ 2.7 Differential equation for a G-function 111 \\ 2.8 Asymptotic expansions for a G-function 112 \\ 3 Elementary special functions and the G-function \\ 3.1 Gamma and related functions: notations and definitions 117 \\ 3.2 Hypergeometric functions: notations and special cases 118 \\ 3.3 Confluent hypergeometric function and related functions 119 \\ 3.4 Exponential integral and related functions 121 \\ 3.5 Bessel functions and associated functions 121 \\ 3.6 Other special functions 122 \\ 3.7 Orthogonal polynomials 124 \\ 3.8 Elementary special functions expressed in terms of G-functions 127 \\ 3.9 G-functions expressed in terms of elementary special functions 129 \\ 3.10 Some integrals involving G-functions 132 \\ 3.11 The H-function 140 \\ 3.12 Computational aspects of G- and H-functions 144 \\ 3.13 Orders of the special functions for small and large values of the argument 145 \\ 4 Generalizations to matrix variables \\ 4.1 Scalar functions of a symmetric positive definite matrix 152 \\ 4.2 Scalar functions of matrix arguments 158 \\ 4.3 Laplace transform 160 \\ 4.4 Hypergeometric functions of matrix arguments 171 \\ 4.5 Generalized matrix transform or M-transform 177 \\ 4.6 Zonal polynomial 194 \\ 4.7 Matrix variate Dirichlet distribution 197 \\ 4.8 Hypergeometric functions of many scalar variables 205 \\ 4.9 Hypergeometric functions of many matrix arguments 215 \\ 4.10 G- and H-functions of two variables 217 \\ Bibliography 227 \\ Glossary of symbols 231 \\ Author index 233 \\ Subject index 234

entry:
@Book{Mathai:1993:HGS,
  author =       "A. M. Mathai",
  title =        "A handbook of generalized special functions for
                 statistical and physical sciences",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xi + 235",
  year =         "1993",
  ISBN =         "0-19-853595-3",
  ISBN-13 =      "978-0-19-853595-9",
  LCCN =         "QA351 .M35 1993",
  bibdate =      "Sat Oct 30 18:57:40 MDT 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Oxford science publications",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0635/92036065-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0635/92036065-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Handbooks, manuals, etc",
  tableofcontents = "I Mathematical preliminaries \\
                 1.1 The gamma function 1 \\
                 1.2 Bernoulli polynomials 6 \\
                 1.3 Asymptotic expansions of gamma functions 9 \\
                 1.4 The psi function 11 \\
                 1.5 The generalized zeta functions 12 \\
                 1.6 The beta function 15 \\
                 1.7 Calculation of residues for gamma functions 16 \\
                 1.8 The Mellin transform 23 \\
                 1.9 Density functions 24 \\
                 1.10 Methods of deriving distributions 49 \\
                 2 The G-function \\
                 2.1 The G-function 60 \\
                 2.2 Some basic properties of the G-function 69 \\
                 2.3 The Mellin transform of a G-function 78 \\
                 2.4 Properties connected with the derivatives of a
                 G-function 94 \\
                 2.5 Series representations for a G-function 96 \\
                 2.6 G-functions as multiple integrals or as solutions
                 of integral equations 106 \\
                 2.7 Differential equation for a G-function 111 \\
                 2.8 Asymptotic expansions for a G-function 112 \\
                 3 Elementary special functions and the G-function \\
                 3.1 Gamma and related functions: notations and
                 definitions 117 \\
                 3.2 Hypergeometric functions: notations and special
                 cases 118 \\
                 3.3 Confluent hypergeometric function and related
                 functions 119 \\
                 3.4 Exponential integral and related functions 121 \\
                 3.5 Bessel functions and associated functions 121 \\
                 3.6 Other special functions 122 \\
                 3.7 Orthogonal polynomials 124 \\
                 3.8 Elementary special functions expressed in terms of
                 G-functions 127 \\
                 3.9 G-functions expressed in terms of elementary
                 special functions 129 \\
                 3.10 Some integrals involving G-functions 132 \\
                 3.11 The H-function 140 \\
                 3.12 Computational aspects of G- and H-functions 144
                 \\
                 3.13 Orders of the special functions for small and
                 large values of the argument 145 \\
                 4 Generalizations to matrix variables \\
                 4.1 Scalar functions of a symmetric positive definite
                 matrix 152 \\
                 4.2 Scalar functions of matrix arguments 158 \\
                 4.3 Laplace transform 160 \\
                 4.4 Hypergeometric functions of matrix arguments 171
                 \\
                 4.5 Generalized matrix transform or M-transform 177 \\
                 4.6 Zonal polynomial 194 \\
                 4.7 Matrix variate Dirichlet distribution 197 \\
                 4.8 Hypergeometric functions of many scalar variables
                 205 \\
                 4.9 Hypergeometric functions of many matrix arguments
                 215 \\
                 4.10 G- and H-functions of two variables 217 \\
                 Bibliography 227 \\
                 Glossary of symbols 231 \\
                 Author index 233 \\
                 Subject index 234",
}


bibtype: article
filename: elefunt.bib
label: Mazenc:1993:CFU
author: Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
title: Computing functions $ cos ^-1 $ and $ sin ^-1 $ using Cordic
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 1
pages: 118--122
month: jan
monthnumber: 1
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.192222
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:58:47 MDT 2011
bibtimestamp: 2011.07.07 07:58:47 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
rawtitle: Computing functions $ \cos^{-1} $ and $ \sin^{-1} $ using {Cordic}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Mazenc:1993:CFU,
  author =       "Christophe Mazenc and Xavier Merrheim and Jean-Michel
                 Muller",
  title =        "Computing functions $ \cos^{-1} $ and $ \sin^{-1} $
                 using {Cordic}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "1",
  pages =        "118--122",
  month =        jan,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.192222",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: elefunt.bib
label: McQuillan:1993:NAV
author: S. E. McQuillan and J. V. McCanny and R. Hamill
booktitle: Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993
title: New algorithms and VLSI architectures for SRT division and square root
crossref: Swartzlander:1993:SCA
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 80--86
year: 1993
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
URL: http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf
keywords: ARITH-11
acknowledgement: ack-sfo
rawauthor: S. E. McQuillan and J. V. McCanny and R. Hamill
rawbooktitle: Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993
rawtitle: New algorithms and {VLSI} architectures for {SRT} division and square root
entry:
@InProceedings{McQuillan:1993:NAV,
  author =       "S. E. McQuillan and J. V. McCanny and R. Hamill",
  booktitle =    "Proceedings of the 11th Symposium on Computer
                 Arithmetic, 2 July 1993",
  title =        "New algorithms and {VLSI} architectures for {SRT}
                 division and square root",
  crossref =     "Swartzlander:1993:SCA",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "80--86",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "Radix two algorithms for SRT division and
                 square-rooting are developed. For these schemes, the
                 result digits and the residuals are computed
                 concurrently and the computations in adjacent rows are
                 overlapped. Consequently, their performance should
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Montuschi:1993:RIT
author: P. Montuschi and L. Ciminiera
journal: j-IEEE-TRANS-COMPUT
volume: 42
number: 2
pages: 239--246
month: feb
monthnumber: 2
year: 1993
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.204797
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
note: See remark cite Montuschi:1995:RRI.
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Montuschi and L. Ciminiera
rawnote: See remark \cite{Montuschi:1995:RRI}.
title:
Reducing iteration time when result digit is zero for radix $2$ SRT division and square root with redundant remainders

rawtitle:
Reducing iteration time when result digit is zero for radix $2$ {SRT} division and square root with redundant remainders

entry:
@Article{Montuschi:1993:RIT,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "Reducing iteration time when result digit is zero for
                 radix $2$ {SRT} division and square root with redundant
                 remainders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "239--246",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204797",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Montuschi:1995:RRI}.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A new architecture is presented for shared radix 2
                 division and square root whose main characteristic is
                 the ability to avoid any addition/subtraction, when the
                 digit 0 has been selected. The solution presented uses
                 a redundant representation of the \ldots{}",
}


bibtype: techreport
filename: elefunt.bib
label: Morris:1993:NLM
author: Alfred H. Morris, Jr.
title: NSWC Library of Mathematics Subroutines
type: Report
number: NSWCDD/TR-92/425
institution: Naval Surface Warfare Center
address: Dahlgren, VA 22448-5000, USA; Silver Spring, MD 20903-5000, USA
pages: 464
month: jan
monthnumber: 1
year: 1993
bibdate: Tue Jun 13 08:47:19 2023
bibtimestamp: 2023.06.13 08:47:19 ???
note: See also earlier edition cite Morris:1990:NLM.
URL: https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA261511.xhtml
acknowledgement: ack-nhfb
rawauthor: Alfred H. {Morris, Jr.}
rawnote: See also earlier edition \cite{Morris:1990:NLM}.
rawtitle: {NSWC} Library of Mathematics Subroutines
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib

abstract:
The NSWC library is a library of general purpose Fortran subroutines that provide a basic computational capability for a variety of mathematical activities. Emphasis has been placed on the transportability of the codes. Subroutines are available in the following areas: elementary operations, geometry, special functions, polynomials, vectors, matrices, large dense systems of linear equations, banded matrices, sparse matrices, eigenvalues and eigenvectors, l1 solution of linear equations, least-squares solution of linear equations, optimization, transforms, approximation of functions, curve fitting, surface fitting, manifold fitting, numerical integration, integral equations, ordinary differential equations, partial differential equations, and random number generation.

remark:
[13-Jun-2023] Despite several Web searches, a machine-readable freely downloadable copy of this report, and its associated software, has not yet been located. The entry for the earlier edition [Morris:1993:NLM] has links to a PDF file and the Fortran 90 source code. Another entry [Miller:2004:AMF] has links to some of the source code, without indication of software version dates.

rawabstract:
The NSWC library is a library of general purpose Fortran subroutines that provide a basic computational capability for a variety of mathematical activities. Emphasis has been placed on the transportability of the codes. Subroutines are available in the following areas: elementary operations, geometry, special functions, polynomials, vectors, matrices, large dense systems of linear equations, banded matrices, sparse matrices, eigenvalues and eigenvectors, l1 solution of linear equations, least-squares solution of linear equations, optimization, transforms, approximation of functions, curve fitting, surface fitting, manifold fitting, numerical integration, integral equations, ordinary differential equations, partial differential equations, and random number generation.

entry:
@TechReport{Morris:1993:NLM,
  author =       "Alfred H. {Morris, Jr.}",
  title =        "{NSWC} Library of Mathematics Subroutines",
  type =         "Report",
  number =       "NSWCDD/TR-92/425",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
                 20903-5000, USA",
  pages =        "464",
  month =        jan,
  year =         "1993",
  bibdate =      "Tue Jun 13 08:47:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
  note =         "See also earlier edition \cite{Morris:1990:NLM}.",
  URL =          "https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA261511.xhtml",
  abstract =     "The NSWC library is a library of general purpose
                 Fortran subroutines that provide a basic computational
                 capability for a variety of mathematical activities.
                 Emphasis has been placed on the transportability of the
                 codes. Subroutines are available in the following
                 areas: elementary operations, geometry, special
                 functions, polynomials, vectors, matrices, large dense
                 systems of linear equations, banded matrices, sparse
                 matrices, eigenvalues and eigenvectors, l1 solution of
                 linear equations, least-squares solution of linear
                 equations, optimization, transforms, approximation of
                 functions, curve fitting, surface fitting, manifold
                 fitting, numerical integration, integral equations,
                 ordinary differential equations, partial differential
                 equations, and random number generation.",
  acknowledgement = ack-nhfb,
  remark =       "[13-Jun-2023] Despite several Web searches, a
                 machine-readable freely downloadable copy of this
                 report, and its associated software, has not yet been
                 located. The entry for the earlier edition
                 [Morris:1993:NLM] has links to a PDF file and the
                 Fortran 90 source code. Another entry [Miller:2004:AMF]
                 has links to some of the source code, without
                 indication of software version dates.",
}


bibtype: article
filename: elefunt.bib
label: Muller:1993:NAC
author: Jurgen Muller
title: On numerical analytic continuation and convergence acceleration by summability methods
journal: Analysis
volume: 13
number: 3
pages: 279--291
year: 1993
ISSN: 0174-4747 OR 01744747
MRclass: 40G10 (40A30 41A25 65B10)
MRnumber: 1245757 (94j:40013)
MRreviewer: S. Sridhar
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: Analysis. International Mathematical Journal of Analysis and its Applications
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: J{\"u}rgen M{\"u}ller
rawtitle: On numerical analytic continuation and convergence acceleration by summability methods
entry:
@Article{Muller:1993:NAC,
  author =       "J{\"u}rgen M{\"u}ller",
  title =        "On numerical analytic continuation and convergence
                 acceleration by summability methods",
  journal =      "Analysis",
  volume =       "13",
  number =       "3",
  pages =        "279--291",
  year =         "1993",
  ISSN =         "0174-4747",
  MRclass =      "40G10 (40A30 41A25 65B10)",
  MRnumber =     "1245757 (94j:40013)",
  MRreviewer =   "S. Sridhar",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Analysis. International Mathematical Journal of
                 Analysis and its Applications",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Perger:1993:NEG
author: Warren F. Perger and Atul Bhalla and Mark Nardin
title: A numerical evaluator for the generalized hypergeometric series
journal: j-COMP-PHYS-COMM
volume: 77
number: 2
pages: 249--254
month: oct
monthnumber: 10
year: 1993
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(93)90008-Z
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Dec 01 09:22:29 2011
bibtimestamp: 2011.12.01 09:22:29 ???
fjournal: Computer Physics Communications
remark: Uses extended precision complex arithmetic.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Warren F. Perger and Atul Bhalla and Mark Nardin
rawtitle: A numerical evaluator for the generalized hypergeometric series
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Perger:1993:NEG,
  author =       "Warren F. Perger and Atul Bhalla and Mark Nardin",
  title =        "A numerical evaluator for the generalized
                 hypergeometric series",
  journal =      j-COMP-PHYS-COMM,
  volume =       "77",
  number =       "2",
  pages =        "249--254",
  month =        oct,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90008-Z",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 01 09:22:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Uses extended precision complex arithmetic.",
}


bibtype: article
filename: elefunt.bib
label: Petkovic:1993:SII
author: Miodrag S. Petkovic and Carsten Carstensen
title: Some improved inclusion methods for polynomial roots with Weierstrass' corrections
journal: j-COMPUT-MATH-APPL
volume: 25
number: 3
pages: 59--67
month: feb
monthnumber: 2
year: 1993
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:11:11 MST 2017
bibtimestamp: 2017.03.01 19:11:11 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219390143J
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Miodrag S. Petkovi{\'c} and Carsten Carstensen
rawtitle: Some improved inclusion methods for polynomial roots with {Weierstrass}' corrections
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Petkovic:1993:SII,
  author =       "Miodrag S. Petkovi{\'c} and Carsten Carstensen",
  title =        "Some improved inclusion methods for polynomial roots
                 with {Weierstrass}' corrections",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "25",
  number =       "3",
  pages =        "59--67",
  month =        feb,
  year =         "1993",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:11 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219390143J",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: book
filename: elefunt.bib
label: Povolotskii:1993:OFR
author: A. I. Povolotskiui and G. A. Sviridyuk
publisher: Chelyabinsk. Gos. Univ.
address: Chelyabinsk, USSR
pages: 92
year: 1993
ISBN: 5-230-17764-0 OR 5230177640
ISBN13: 978-5-230-17764-7 OR 9785230177647
MRclass: 26-01 (00A05)
MRnumber: 94e:26001
MRreviewer: J{\'o}zef Kalinowski
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: A. I. Povolotski{\u\i} and G. A. Sviridyuk
title:
cyr Odnomernyui matematicheskiui analiz elementarnykh funktsiui . (Russian) [One-dimensional mathematical analysis of elementary functions] cyr Nepreryvnye funktsii. Differentsiruemye funktsii. Integriruemye funktsii. [Continuous functions. Differentiable functions. Integrable functions]

rawtitle:
{{\cyr Odnomerny{\u\i} matematicheski{\u\i} analiz {\`e}lementarnykh funktsi{\u\i}}}. ({Russian}) [One-dimensional mathematical analysis of elementary functions] {{\cyr Nepreryvnye funktsii. Differentsiruemye funktsii. Integriruemye funktsii}}. [Continuous functions. Differentiable functions. Integrable functions]

entry:
@Book{Povolotskii:1993:OFR,
  author =       "A. I. Povolotski{\u\i} and G. A. Sviridyuk",
  title =        "{{\cyr Odnomerny{\u\i} matematicheski{\u\i} analiz
                 {\`e}lementarnykh funktsi{\u\i}}}. ({Russian})
                 [One-dimensional mathematical analysis of elementary
                 functions] {{\cyr Nepreryvnye funktsii.
                 Differentsiruemye funktsii. Integriruemye funktsii}}.
                 [Continuous functions. Differentiable functions.
                 Integrable functions]",
  publisher =    "Chelyabinsk. Gos. Univ.",
  address =      "Chelyabinsk, USSR",
  pages =        "92",
  year =         "1993",
  ISBN =         "5-230-17764-0",
  ISBN-13 =      "978-5-230-17764-7",
  MRclass =      "26-01 (00A05)",
  MRnumber =     "94e:26001",
  MRreviewer =   "J{\'o}zef Kalinowski",
  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: Ratis:1993:CCH
author: Yu. L. Ratis and P. Fernandez de Cordoba
title: A code to calculate (high order) Bessel functions based on the continued fractions method
journal: j-COMP-PHYS-COMM
volume: 76
number: 3
pages: 381--388
month: aug
monthnumber: 8
year: 1993
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(93)90062-H
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:29:39 MST 2012
bibtimestamp: 2012.02.13 21:29:39 MST
URL: http://www.sciencedirect.com/science/article/pii/001046559390062H
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Yu. L. Ratis and P. Fern{\'a}ndez de C{\'o}rdoba
rawtitle: A code to calculate (high order) {Bessel} functions based on the continued fractions method
abstract:
We have developed a fast code to calculate Bessel functions of integer and fractional order based on the continued fractions method. This algorithm is specially useful in the case of Bessel functions of high order because it does not require any recalculation using normalization relations.

rawabstract:
We have developed a fast code to calculate Bessel functions of integer and fractional order based on the continued fractions method. This algorithm is specially useful in the case of Bessel functions of high order because it does not require any recalculation using normalization relations.

entry:
@Article{Ratis:1993:CCH,
  author =       "Yu. L. Ratis and P. Fern{\'a}ndez de C{\'o}rdoba",
  title =        "A code to calculate (high order) {Bessel} functions
                 based on the continued fractions method",
  journal =      j-COMP-PHYS-COMM,
  volume =       "76",
  number =       "3",
  pages =        "381--388",
  month =        aug,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90062-H",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:29:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001046559390062H",
  abstract =     "We have developed a fast code to calculate Bessel
                 functions of integer and fractional order based on the
                 continued fractions method. This algorithm is specially
                 useful in the case of Bessel functions of high order
                 because it does not require any recalculation using
                 normalization relations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Saurer:1993:BSF
author: Josef Saurer
title: Bases of special functions and their domains of convergence
volume: 73
publisher: Akademie Verlag GmbH
address: Berlin, Germany
pages: 158
year: 1993
ISBN: 3-05-501613-0 OR 3055016130
ISBN13: 978-3-05-501613-4 OR 9783055016134
ISSN: 0138-3019 OR 01383019
LCCN: QA351 .S28 1993
bibdate: Sat Oct 30 18:53:24 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 18:53:24 MDT
series: Mathematical research
remark: Revised version of the author's thesis--Universitat Essen, 1992.
subject: Functions, Special; Analytic functions; Eigenfunction expansions; Convergence; Mathematical physics
acknowledgement: ack-nhfb
rawauthor: Josef Saurer
rawtitle: Bases of special functions and their domains of convergence
TOC:
Introduction 9 1 Foundations of the theory 15 1.1 Holomorphic operator functions in Frechet spaces 15 1.2 Floquet eigenvalue problems (with a regular singular point) 22 1.3 Relationships between differential operators corresponding to Floquet eigenvalue problems for systems of differential equations and scalar differential equations 26 1.4 Biholomorphic images of functions 30 1.5 An expansion theorem 37 2 First order differential systems with a regular singular point 43 2.1 Fundamental properties 44 2.2 Construction of fundamental systems depending holomorphically on parameters 46 2.3 A family of second order differential equations 55 2.4 Differential equations and special functions of mathematical physics 57 2.4.1 Bessel equation, Bessel function 57 2.4.2 Whittaker equation, Whittaker function 58 2.4.3 Hypergeometric equation, hypergeometric function 60 2.4.4 Generalised spherical function 61 3 Floquet eigenvalue problems for first order differential systems with a regular singular point 63 3.1 Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions $T$ and $T^*$ 67 3.2 A general expansion theorem 73 3.3 Floquet eigenvalue problems and expansion theorems for a family of second order differential equations 75 4 Domains of convergence of the eigenfunction expansions 83 4.1 The Bessel and Whittaker case 85 4.2 The hypergeometric case 95 4.3 Typical domains of convergence 105 5 Examples of expansions in series of special functions 109 5.1 Expansions in series of Bessel functions 109 5.2 Expansions in series of Whittaker functions 115 5.3 Expansions in series of hypergeometric functions 119 6 First order differential systems for products of vector-valued functions 127 6.1 Products of vectors and sums of matrices of different dimensions 128 6.2 Construction of the first order differential system 132 7 Floquet eigenvalue problems and expansions in series, of m - fold products of special functions 135 7.1 Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions $T$ and $T^*$ 142 7.2 Application 145 References 151 Notation index 154 Index 157

rawTOC:
Introduction 9 \\ 1 Foundations of the theory 15 \\ 1.1 Holomorphic operator functions in Frechet spaces 15 \\ 1.2 Floquet eigenvalue problems (with a regular singular point) 22 \\ 1.3 Relationships between differential operators corresponding to Floquet eigenvalue problems for systems of differential equations and scalar differential equations 26 \\ 1.4 Biholomorphic images of functions 30 \\ 1.5 An expansion theorem 37 \\ 2 First order differential systems with a regular singular point 43 \\ 2.1 Fundamental properties 44 \\ 2.2 Construction of fundamental systems depending holomorphically on parameters 46 \\ 2.3 A family of second order differential equations 55 \\ 2.4 Differential equations and special functions of mathematical physics 57 \\ 2.4.1 Bessel equation, Bessel function 57 \\ 2.4.2 Whittaker equation, Whittaker function 58 \\ 2.4.3 Hypergeometric equation, hypergeometric function 60 \\ 2.4.4 Generalised spherical function 61 \\ 3 Floquet eigenvalue problems for first order differential systems with a regular singular point 63 \\ 3.1 Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions $T$ and $T^*$ 67 \\ 3.2 A general expansion theorem 73 \\ 3.3 Floquet eigenvalue problems and expansion theorems for a family of second order differential equations 75 \\ 4 Domains of convergence of the eigenfunction expansions 83 \\ 4.1 The Bessel and Whittaker case 85 \\ 4.2 The hypergeometric case 95 \\ 4.3 Typical domains of convergence 105 \\ 5 Examples of expansions in series of special functions 109 \\ 5.1 Expansions in series of Bessel functions 109 \\ 5.2 Expansions in series of Whittaker functions 115 \\ 5.3 Expansions in series of hypergeometric functions 119 \\ 6 First order differential systems for products of vector-valued functions 127 \\ 6.1 Products of vectors and sums of matrices of different dimensions 128 \\ 6.2 Construction of the first order differential system 132 \\ 7 Floquet eigenvalue problems and expansions in series, of m - fold products of special functions 135 \\ 7.1 Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions $T$ and $T^*$ 142 \\ 7.2 Application 145 \\ References 151 \\ Notation index 154 \\ Index 157

entry:
@Book{Saurer:1993:BSF,
  author =       "Josef Saurer",
  title =        "Bases of special functions and their domains of
                 convergence",
  volume =       "73",
  publisher =    "Akademie Verlag GmbH",
  address =      "Berlin, Germany",
  pages =        "158",
  year =         "1993",
  ISBN =         "3-05-501613-0",
  ISBN-13 =      "978-3-05-501613-4",
  ISSN =         "0138-3019",
  LCCN =         "QA351 .S28 1993",
  bibdate =      "Sat Oct 30 18:53:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematical research",
  acknowledgement = ack-nhfb,
  remark =       "Revised version of the author's
                 thesis--Universit{\"a}t Essen, 1992.",
  subject =      "Functions, Special; Analytic functions; Eigenfunction
                 expansions; Convergence; Mathematical physics",
  tableofcontents = "Introduction 9 \\
                 1 Foundations of the theory 15 \\
                 1.1 Holomorphic operator functions in Frechet spaces 15
                 \\
                 1.2 Floquet eigenvalue problems (with a regular
                 singular point) 22 \\
                 1.3 Relationships between differential operators
                 corresponding to Floquet eigenvalue problems for
                 systems of differential equations and scalar
                 differential equations 26 \\
                 1.4 Biholomorphic images of functions 30 \\
                 1.5 An expansion theorem 37 \\
                 2 First order differential systems with a regular
                 singular point 43 \\
                 2.1 Fundamental properties 44 \\
                 2.2 Construction of fundamental systems depending
                 holomorphically on parameters 46 \\
                 2.3 A family of second order differential equations 55
                 \\
                 2.4 Differential equations and special functions of
                 mathematical physics 57 \\
                 2.4.1 Bessel equation, Bessel function 57 \\
                 2.4.2 Whittaker equation, Whittaker function 58 \\
                 2.4.3 Hypergeometric equation, hypergeometric function
                 60 \\
                 2.4.4 Generalised spherical function 61 \\
                 3 Floquet eigenvalue problems for first order
                 differential systems with a regular singular point 63
                 \\
                 3.1 Construction of biorthogonal canonical systems of
                 eigen- and associated vectors of the operator functions
                 $T$ and $T^*$ 67 \\
                 3.2 A general expansion theorem 73 \\
                 3.3 Floquet eigenvalue problems and expansion theorems
                 for a family of second order differential equations 75
                 \\
                 4 Domains of convergence of the eigenfunction
                 expansions 83 \\
                 4.1 The Bessel and Whittaker case 85 \\
                 4.2 The hypergeometric case 95 \\
                 4.3 Typical domains of convergence 105 \\
                 5 Examples of expansions in series of special functions
                 109 \\
                 5.1 Expansions in series of Bessel functions 109 \\
                 5.2 Expansions in series of Whittaker functions 115 \\
                 5.3 Expansions in series of hypergeometric functions
                 119 \\
                 6 First order differential systems for products of
                 vector-valued functions 127 \\
                 6.1 Products of vectors and sums of matrices of
                 different dimensions 128 \\
                 6.2 Construction of the first order differential system
                 132 \\
                 7 Floquet eigenvalue problems and expansions in series,
                 of m - fold products of special functions 135 \\
                 7.1 Construction of biorthogonal canonical systems of
                 eigen- and associated vectors of the operator functions
                 $T$ and $T^*$ 142 \\
                 7.2 Application 145 \\
                 References 151 \\
                 Notation index 154 \\
                 Index 157",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schulte:1993:ERC
author: M. Schulte and E. Swartzlander
title: Exact rounding of certain elementary functions
crossref: Swartzlander:1993:SCA
pages: 138--145
year: 1993
bibdate: Thu Dec 14 11:25:18 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.14 11:25:18 MST
URL: http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf
acknowledgement: ack-nhfb
affiliation: Dept. of Electr. and Comput. Eng., Texas Univ., Austin, TX, USA
bookpages: xii + 284
thesaurus: Floating point arithmetic; Function evaluation
rawauthor: M. Schulte and E. Swartzlander
rawtitle: Exact rounding of certain elementary functions
abstract:
An algorithm is described which produces exactly rounded results for the functions of reciprocal, square root, 2/sup x/, and log 2/sup x/. Hardware designs based on this algorithm are presented for floating point numbers with 16- and 24-b significands. These designs use a polynomial approximation in which coefficients are originally selected based on the Chebyshev series approximation and are then adjusted to ensure exactly rounded results for all inputs. To reduce the number of terms in the approximation, the input interval is divided into subintervals of equal size and different coefficients are used for each subinterval. For floating point numbers with 16-b significands, the exactly rounded value of the function can be computed in 51 ns on a 20-mm/sup 2/ chip. For floating point numbers with 24-b significands, the functions can be computed in 80 ns on a 98-mm/sup 2/ chip.

keywords:
Elementary functions; Exact rounding; Floating point numbers; Polynomial approximation; Reciprocal; Rounded results; Square root

rawabstract:
An algorithm is described which produces exactly rounded results for the functions of reciprocal, square root, 2/sup x/, and log 2/sup x/. Hardware designs based on this algorithm are presented for floating point numbers with 16- and 24-b significands. These designs use a polynomial approximation in which coefficients are originally selected based on the Chebyshev series approximation and are then adjusted to ensure exactly rounded results for all inputs. To reduce the number of terms in the approximation, the input interval is divided into subintervals of equal size and different coefficients are used for each subinterval. For floating point numbers with 16-b significands, the exactly rounded value of the function can be computed in 51 ns on a 20-mm/sup 2/ chip. For floating point numbers with 24-b significands, the functions can be computed in 80 ns on a 98-mm/sup 2/ chip.

entry:
@InProceedings{Schulte:1993:ERC,
  author =       "M. Schulte and E. Swartzlander",
  title =        "Exact rounding of certain elementary functions",
  crossref =     "Swartzlander:1993:SCA",
  bookpages =    "xii + 284",
  pages =        "138--145",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf",
  abstract =     "An algorithm is described which produces exactly
                 rounded results for the functions of reciprocal, square
                 root, 2/sup x/, and log 2/sup x/. Hardware designs
                 based on this algorithm are presented for floating
                 point numbers with 16- and 24-b significands. These
                 designs use a polynomial approximation in which
                 coefficients are originally selected based on the
                 Chebyshev series approximation and are then adjusted to
                 ensure exactly rounded results for all inputs. To
                 reduce the number of terms in the approximation, the
                 input interval is divided into subintervals of equal
                 size and different coefficients are used for each
                 subinterval. For floating point numbers with 16-b
                 significands, the exactly rounded value of the function
                 can be computed in 51 ns on a 20-mm/sup 2/ chip. For
                 floating point numbers with 24-b significands, the
                 functions can be computed in 80 ns on a 98-mm/sup 2/
                 chip.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Electr. and Comput. Eng., Texas Univ.,
                 Austin, TX, USA",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods)",
  confdate =     "29 June--2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "Elementary functions; Exact rounding; Floating point
                 numbers; Polynomial approximation; Reciprocal; Rounded
                 results; Square root",
  thesaurus =    "Floating point arithmetic; Function evaluation",
}


bibtype: article
filename: elefunt.bib
label: Schulte:1993:PHD
author: Michael J. Schulte and Earl E. Swartzlander, Jr.
title: Parallel hardware designs for correctly rounded elementary functions
journal: j-INTERVAL-COMP
volume: 4
pages: 65--88
year: 1993
ISSN: 0135-4868 OR 01354868
MRclass: 65G10 (65C20)
MRnumber: 1 305 859
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: Interval Computations = Interval'nye vychisleniia
acknowledgement: ack-nhfb
rawauthor: Michael J. Schulte and Earl E. {Swartzlander, Jr.}
rawtitle: Parallel hardware designs for correctly rounded elementary functions
note:
Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993)

entry:
@Article{Schulte:1993:PHD,
  author =       "Michael J. Schulte and Earl E. {Swartzlander, Jr.}",
  title =        "Parallel hardware designs for correctly rounded
                 elementary functions",
  journal =      j-INTERVAL-COMP,
  volume =       "4",
  pages =        "65--88",
  year =         "1993",
  ISSN =         "0135-4868",
  MRclass =      "65G10 (65C20)",
  MRnumber =     "1 305 859",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the International Conference on
                 Numerical Analysis with Automatic Result Verification
                 (Lafayette, LA, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
}


bibtype: techreport
filename: elefunt.bib
label: Schwarz:1993:HRAa
author: E. Schwarz
title: High-radix algorithms for high-order arithmetic operations
type: Technical Report
number: CSL-TR-93-559
institution: Computer Systems Laboratory, Stanford University
address: Stanford, CA, USA
pages: 65--88
month: jan
monthnumber: 1
year: 1993
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.04.02 08:38:35 ???
acknowledgement: ack-sfo
rawauthor: E. Schwarz
rawtitle: High-radix algorithms for high-order arithmetic operations
entry:
@TechReport{Schwarz:1993:HRAa,
  author =       "E. Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Technical Report",
  number =       "CSL-TR-93-559",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jan,
  year =         "1993",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: phdthesis
filename: elefunt.bib
label: Schwarz:1993:HRAb
author: Eric Mark Schwarz
title: High-radix algorithms for high-order arithmetic operations
type: Thesis (Ph.D.)
school: Department of Electrical Engineering, Stanford University
address: Stanford, CA, USA
pages: 224
month: apr
monthnumber: 4
year: 1993
bibdate: Mon Jan 07 22:38:06 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2008.01.07 22:38:06 ???
remark: AAT 9317816. ProQuest document ID 746798521.
acknowledgement: ack-nhfb
rawauthor: Eric Mark Schwarz
rawtitle: High-radix algorithms for high-order arithmetic operations
abstract:
Many common algorithms for high-order arithmetic operations require an initial approximation. The Newton--Raphson algorithm starts with an approximation and then quadratically converges on the solution. The initial approximation determines the number of iterations of the algorithm and is typically implemented as a look-up table in the form of a ROM or PLA. A novel method is suggested which describes high-order arithmetic operations with a partial product array. This method applies to the operations of division, reciprocal, square root, natural logarithm, exponential, and trigonometric functions. The partial product array of Boolean elements which describes the operation can be summed on an existing floating-point multiplier. The hardware needed is only the logic gates to create the Boolean elements in the array and a multiplexor, and the latency is that of the multiplier. Thus, by reusing a floating-point multiplier, a high-precision approximation to a high-order arithmetic operation can be implemented with a low marginal cost.par This dissertation describes the implementation and shows a method for deriving partial product arrays to approximate arithmetic operations. Then the proposed method is applied and evaluated for several operations. The proposed method yields a minimum approximation of twelve bits correct for the reciprocal operation and sixteen bits for the square root operation. The proposed method is shown to be as small as 0.05% the size (in gates) of an equivalent precision look-up table and has up to four times the accuracy (in bits) as an equivalent latency polynomial approximation. Also, three new iterative algorithms to increase the precision of the approximations and a theoretical analysis of the partial product array representation are detailed. Thus, high-radix algorithms of many arithmetic operations are possible at low cost.

keywords:
division; elementary functions; exponential; logarithm; PPA (partial product array); reciprocal square root; square root

rawabstract:
Many common algorithms for high-order arithmetic operations require an initial approximation. The Newton--Raphson algorithm starts with an approximation and then quadratically converges on the solution. The initial approximation determines the number of iterations of the algorithm and is typically implemented as a look-up table in the form of a ROM or PLA. A novel method is suggested which describes high-order arithmetic operations with a partial product array. This method applies to the operations of division, reciprocal, square root, natural logarithm, exponential, and trigonometric functions. The partial product array of Boolean elements which describes the operation can be summed on an existing floating-point multiplier. The hardware needed is only the logic gates to create the Boolean elements in the array and a multiplexor, and the latency is that of the multiplier. Thus, by reusing a floating-point multiplier, a high-precision approximation to a high-order arithmetic operation can be implemented with a low marginal cost.\par This dissertation describes the implementation and shows a method for deriving partial product arrays to approximate arithmetic operations. Then the proposed method is applied and evaluated for several operations. The proposed method yields a minimum approximation of twelve bits correct for the reciprocal operation and sixteen bits for the square root operation. The proposed method is shown to be as small as 0.05\% the size (in gates) of an equivalent precision look-up table and has up to four times the accuracy (in bits) as an equivalent latency polynomial approximation. Also, three new iterative algorithms to increase the precision of the approximations and a theoretical analysis of the partial product array representation are detailed. Thus, high-radix algorithms of many arithmetic operations are possible at low cost.

entry:
@PhdThesis{Schwarz:1993:HRAb,
  author =       "Eric Mark Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "224",
  month =        apr,
  year =         "1993",
  bibdate =      "Mon Jan 07 22:38:06 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Many common algorithms for high-order arithmetic
                 operations require an initial approximation. The
                 Newton--Raphson algorithm starts with an approximation
                 and then quadratically converges on the solution. The
                 initial approximation determines the number of
                 iterations of the algorithm and is typically
                 implemented as a look-up table in the form of a ROM or
                 PLA. A novel method is suggested which describes
                 high-order arithmetic operations with a partial product
                 array. This method applies to the operations of
                 division, reciprocal, square root, natural logarithm,
                 exponential, and trigonometric functions. The partial
                 product array of Boolean elements which describes the
                 operation can be summed on an existing floating-point
                 multiplier. The hardware needed is only the logic gates
                 to create the Boolean elements in the array and a
                 multiplexor, and the latency is that of the multiplier.
                 Thus, by reusing a floating-point multiplier, a
                 high-precision approximation to a high-order arithmetic
                 operation can be implemented with a low marginal
                 cost.\par

                 This dissertation describes the implementation and
                 shows a method for deriving partial product arrays to
                 approximate arithmetic operations. Then the proposed
                 method is applied and evaluated for several operations.
                 The proposed method yields a minimum approximation of
                 twelve bits correct for the reciprocal operation and
                 sixteen bits for the square root operation. The
                 proposed method is shown to be as small as 0.05\% the
                 size (in gates) of an equivalent precision look-up
                 table and has up to four times the accuracy (in bits)
                 as an equivalent latency polynomial approximation.
                 Also, three new iterative algorithms to increase the
                 precision of the approximations and a theoretical
                 analysis of the partial product array representation
                 are detailed. Thus, high-radix algorithms of many
                 arithmetic operations are possible at low cost.",
  acknowledgement = ack-nhfb,
  keywords =     "division; elementary functions; exponential;
                 logarithm; PPA (partial product array); reciprocal
                 square root; square root",
  remark =       "AAT 9317816. ProQuest document ID 746798521.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schwarz:1993:HSA
author: E. M. Schwarz and M. J. Flynn
booktitle: Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993
title: Hardware starting approximation for the square root operation
crossref: Swartzlander:1993:SCA
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 103--111
year: 1993
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-sfo
rawauthor: E. M. Schwarz and M. J. Flynn
rawbooktitle: Proceedings of the 11th Symposium on Computer Arithmetic, 2 July 1993
rawtitle: Hardware starting approximation for the square root operation
entry:
@InProceedings{Schwarz:1993:HSA,
  author =       "E. M. Schwarz and M. J. Flynn",
  booktitle =    "Proceedings of the 11th Symposium on Computer
                 Arithmetic, 2 July 1993",
  title =        "Hardware starting approximation for the square root
                 operation",
  crossref =     "Swartzlander:1993:SCA",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "103--111",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "A method for obtaining high-precision approximations
                 of high-order arithmetic operations is presented. These
                 approximations provide an accurate starting
                 approximation for high-precision iterative algorithms,
                 which translates into few iterations and \ldots{}",
}


