# bibtab

bibtype: article
filename: elefunt.bib
label: Friedland:1967:AAV
author: Paul Friedland
title: Algorithm 312: Absolute Value and Square Root of a Complex Number
journal: j-CACM
volume: 10
number: 10
pages: 665--665
month: oct
monthnumber: 10
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363717.363780
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:15 MST 2005
bibtimestamp: 2005.11.25 18:20:15 MST
fjournal: Communications of the ACM
keywords: $abs (z)$; $sqrt (z)$; elementary functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Paul Friedland
rawtitle: {Algorithm 312}: {Absolute} Value and Square Root of a Complex Number
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Friedland:1967:AAV,
  author =       "Paul Friedland",
  title =        "{Algorithm 312}: {Absolute} Value and Square Root of a
                 Complex Number",
  journal =      j-CACM,
  volume =       "10",
  number =       "10",
  pages =        "665--665",
  month =        oct,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363717.363780",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\abs(z)$; $\sqrt(z)$; elementary functions",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1967:CAT
author: Walter Gautschi
title: Computational Aspects of Three-Term Recurrence Relations
journal: j-SIAM-REVIEW
volume: 9
number: 1
pages: 24--82
month: jan
monthnumber: 1
year: 1967
CODEN: SIREAD
DOI: https://doi.org/10.1137/1009002
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:05:42 MDT 2014
bibtimestamp: 2014.03.27 09:05:42 MDT
URL: http://link.aip.org/link/?SIR/9/24/1
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1967
rawauthor: Walter Gautschi
rawtitle: Computational Aspects of Three-Term Recurrence Relations
bibsource:
http://epubs.siam.org/toc/siread/9/1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

keywords:
Bessel functions; continued fractions; Coulomb wave functions; Fourier coefficients; incomplete beta functions; incomplete gamma functions; Legendre functions; Sturm--Liouville boundary value problems; three-term recurrence relations

remark:
This paper is frequently cited in later work on continued fractions, three-term recurrence relations, and special functions.

entry:
@Article{Gautschi:1967:CAT,
  author =       "Walter Gautschi",
  title =        "Computational Aspects of Three-Term Recurrence
                 Relations",
  journal =      j-SIAM-REVIEW,
  volume =       "9",
  number =       "1",
  pages =        "24--82",
  month =        jan,
  year =         "1967",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1009002",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:42 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/9/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://link.aip.org/link/?SIR/9/24/1",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "Bessel functions; continued fractions; Coulomb wave
                 functions; Fourier coefficients; incomplete beta
                 functions; incomplete gamma functions; Legendre
                 functions; Sturm--Liouville boundary value problems;
                 three-term recurrence relations",
  onlinedate =   "January 1967",
  remark =       "This paper is frequently cited in later work on
                 continued fractions, three-term recurrence relations,
                 and special functions.",
}


bibtype: article
filename: elefunt.bib
label: Goldstein:1967:CSB
author: Max Goldstein and C. W. Clenshaw and Susan M. Picken
title: Chebyshev Series for Bessel Functions of Fractional Order
journal: j-MATH-COMPUT
volume: 21
number: 99
pages: 509--??
month: jul
monthnumber: 7
year: 1967
CODEN: MCMPAF
DOI: https://doi.org/10.2307/2003271
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Sun Nov 12 09:25:35 2023
bibtimestamp: 2023.11.12 09:25:35 ???
fjournal: Mathematics of Computation
remark: TO DO: Why is this missing from journal bibliography file, mathcomp1970.bib?
acknowledgement: ack-nhfb
authordates: Charles William Clenshaw (15 March 1926--23 September 2004)
journalURL: http://www.ams.org/mcom/
rawauthor: Max Goldstein and C. W. Clenshaw and Susan M. Picken
rawtitle: {Chebyshev} Series for {Bessel} Functions of Fractional Order
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Goldstein:1967:CSB,
  author =       "Max Goldstein and C. W. Clenshaw and Susan M. Picken",
  title =        "{Chebyshev} Series for {Bessel} Functions of
                 Fractional Order",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "509--??",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2003271",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sun Nov 12 09:25:35 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "TO DO: Why is this missing from journal bibliography
                 file, mathcomp1970.bib?",
}


bibtype: article
filename: elefunt.bib
label: Gunn:1967:ACW
author: J. H. Gunn
title: Algorithm 300: Coulomb Wave Functions
journal: j-CACM
volume: 10
number: 4
pages: 244--245
month: apr
monthnumber: 4
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:12 MST 2005
bibtimestamp: 2005.11.25 18:20:12 MST
note: See remark cite Vos:1973:RAC.
fjournal: Communications of the ACM
keywords: Coulomb wave functions; special functions
remark: Fullerton: 150-line Algol procedure that is superseded by other routines in the physics literature.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. H. Gunn
rawnote: See remark \cite{Vos:1973:RAC}.
rawtitle: {Algorithm 300}: {Coulomb} Wave Functions
entry:
@Article{Gunn:1967:ACW,
  author =       "J. H. Gunn",
  title =        "{Algorithm 300}: {Coulomb} Wave Functions",
  journal =      j-CACM,
  volume =       "10",
  number =       "4",
  pages =        "244--245",
  month =        apr,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:12 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Vos:1973:RAC}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: 150-line Algol procedure that is superseded
                 by other routines in the physics literature.",
}


bibtype: article
filename: elefunt.bib
label: Hill:1967:ACS
author: I. D. Hill and M. C. Pike
title: Algorithm 299: Chi-Squared Integral
journal: j-CACM
volume: 10
number: 4
pages: 243--244
month: apr
monthnumber: 4
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:12 MST 2005
bibtimestamp: 2005.11.25 18:20:12 MST
note: See also cite Hill:1985:RCS,elLozy:1976:RAC.
fjournal: Communications of the ACM
keywords: chi-squared; probability functions
remark: Fullerton: Short Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: I. D. Hill and M. C. Pike
rawnote: See also \cite{Hill:1985:RCS,elLozy:1976:RAC}.
rawtitle: {Algorithm 299}: {Chi}-Squared Integral
entry:
@Article{Hill:1967:ACS,
  author =       "I. D. Hill and M. C. Pike",
  title =        "{Algorithm 299}: {Chi}-Squared Integral",
  journal =      j-CACM,
  volume =       "10",
  number =       "4",
  pages =        "243--244",
  month =        apr,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:12 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Hill:1985:RCS,elLozy:1976:RAC}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "chi-squared; probability functions",
  remark =       "Fullerton: Short Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Hill:1967:ANCa
author: I. D. Hill and S. A. Joyce
title: Algorithm 304: Normal Curve Integral
journal: j-CACM
volume: 10
number: 6
pages: 374--375
month: jun
monthnumber: 6
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363332.363411
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:13 MST 2005
bibtimestamp: 2005.11.25 18:20:13 MST
note: See remarks cite Hill:1967:RAS,Bergson:1968:ACR.
fjournal: Communications of the ACM
keywords: probability functions
remark: Fullerton: 75-line Algol procedure that is superseded by numerous $ erf $ routines.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: I. D. Hill and S. A. Joyce
rawnote: See remarks \cite{Hill:1967:RAS,Bergson:1968:ACR}.
rawtitle: {Algorithm 304}: {Normal} Curve Integral
abstract:
tt normal(x,upper) calculates the curve, i.e., tail area of the standardized normal curve, i.e., $ (1 / sqrt 2 pi ) int exp ( - t^2 / 2) d t $. If tt upper is tt true, the limits of integration are $x$ and $ infty $. If tt upper is tt false, the limits of integration are $ - infty $ and $x$.

rawabstract:
{\tt normal(x,upper)} calculates the curve, i.e., tail area of the standardized normal curve, i.e., $ (1 / \sqrt {2 \pi }) \int \exp ( - t^2 / 2) \, d t $. If {\tt upper} is {\tt true}, the limits of integration are $x$ and $ \infty $. If {\tt upper} is {\tt false}, the limits of integration are $ - \infty $ and $x$.

entry:
@Article{Hill:1967:ANCa,
  author =       "I. D. Hill and S. A. Joyce",
  title =        "{Algorithm 304}: {Normal} Curve Integral",
  journal =      j-CACM,
  volume =       "10",
  number =       "6",
  pages =        "374--375",
  month =        jun,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363332.363411",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remarks \cite{Hill:1967:RAS,Bergson:1968:ACR}.",
  abstract =     "{\tt normal(x,upper)} calculates the curve, i.e., tail
                 area of the standardized normal curve, i.e., $ (1 /
                 \sqrt {2 \pi }) \int \exp ( - t^2 / 2) \, d t $. If
                 {\tt upper} is {\tt true}, the limits of integration
                 are $x$ and $ \infty $. If {\tt upper} is {\tt false},
                 the limits of integration are $ - \infty $ and $x$.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
  remark =       "Fullerton: 75-line Algol procedure that is superseded
                 by numerous $ \erf $ routines.",
}


bibtype: article
filename: elefunt.bib
label: Hill:1967:RAS
author: I. D. Hill and S. A. Joyce
journal: j-CACM
volume: 10
number: 6
pages: 377--378
month: jun
monthnumber: 6
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363332.365433
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:13 MST 2005
bibtimestamp: 2005.11.25 18:20:13 MST
note: See cite Cyvin:1964:AND,MacLaren:1965:APN,Hill:1967:ANCa.
fjournal: Communications of the ACM
keywords: $erf (x)$; $erfc (x)$; probability functions; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: I. D. Hill and S. A. Joyce
rawnote: See \cite{Cyvin:1964:AND,MacLaren:1965:APN,Hill:1967:ANCa}.
title:
Remarks on Algorithm 123 [S15]: Real error function, tt ERF(x); Algorithm 180 [S15]: Error Function --- Large $ X $; Algorithm 181 [S15]: Complementary Error Function --- Large $ X $; Algorithm 209 [S15]: Gauss; Algorithm 226 [S15]: Normal Distribution Function; Algorithm 272 [S15]: Procedure for the Normal Distribution Functions; Algorithm 304 [S15]: Normal Curve Integral

rawtitle:
Remarks on {Algorithm 123} [{S15}]: {Real} error function, {{\tt ERF(x)}}; {Algorithm 180} [{S15}]: {Error} Function --- Large $ {X} $; {Algorithm 181} [{S15}]: {Complementary} Error Function --- Large $ {X} $; {Algorithm 209} [{S15}]: {Gauss}; {Algorithm 226} [{S15}]: {Normal} Distribution Function; {Algorithm 272} [{S15}]: {Procedure} for the Normal Distribution Functions; {Algorithm 304} [{S15}]: {Normal} Curve Integral

entry:
@Article{Hill:1967:RAS,
  author =       "I. D. Hill and S. A. Joyce",
  title =        "Remarks on {Algorithm 123} [{S15}]: {Real} error
                 function, {{\tt ERF(x)}}; {Algorithm 180} [{S15}]:
                 {Error} Function --- Large $ {X} $; {Algorithm 181}
                 [{S15}]: {Complementary} Error Function --- Large $ {X}
                 $; {Algorithm 209} [{S15}]: {Gauss}; {Algorithm 226}
                 [{S15}]: {Normal} Distribution Function; {Algorithm
                 272} [{S15}]: {Procedure} for the Normal Distribution
                 Functions; {Algorithm 304} [{S15}]: {Normal} Curve
                 Integral",
  journal =      j-CACM,
  volume =       "10",
  number =       "6",
  pages =        "377--378",
  month =        jun,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363332.365433",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Cyvin:1964:AND,MacLaren:1965:APN,Hill:1967:ANCa}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\erf(x)$; $\erfc(x)$; probability functions; special
                 functions",
}


bibtype: article
filename: elefunt.bib
label: Kilpatrick:1967:CIP
author: J. E. Kilpatrick and Shigetoshi Katsura and Yuji Inoue
title: Calculations of Integrals of Products of Bessel Functions
journal: j-MATH-COMPUT
volume: 21
number: 99
pages: 407--412
month: jul
monthnumber: 7
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: J. E. Kilpatrick and Shigetoshi Katsura and Yuji Inoue
rawtitle: Calculations of Integrals of Products of {Bessel} Functions
entry:
@Article{Kilpatrick:1967:CIP,
  author =       "J. E. Kilpatrick and Shigetoshi Katsura and Yuji
                 Inoue",
  title =        "Calculations of Integrals of Products of {Bessel}
                 Functions",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "407--412",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Knuth:1967:CTE
author: Donald E. Knuth and Thomas J. Buckholtz
title: Computation of Tangent, Euler, and Bernoulli Numbers
journal: j-MATH-COMPUT
volume: 21
number: 100
pages: 663--688
month: oct
monthnumber: 10
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.25
MRnumber: 36 #4787
bibdate: Fri Mar 22 18:03:29 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database; MathSciNet database
bibtimestamp: 2002.03.22 18:03:29 MST
fjournal: Mathematics of Computation
remark: Fullerton: The first 119. 120 and 250 tangent, Euler and Bernoulli numbers, respectively.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Donald E. Knuth and Thomas J. Buckholtz
rawtitle: Computation of Tangent, {Euler}, and {Bernoulli} Numbers
entry:
@Article{Knuth:1967:CTE,
  author =       "Donald E. Knuth and Thomas J. Buckholtz",
  title =        "Computation of Tangent, {Euler}, and {Bernoulli}
                 Numbers",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "100",
  pages =        "663--688",
  month =        oct,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "36 #4787",
  bibdate =      "Fri Mar 22 18:03:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database; MathSciNet database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: The first 119. 120 and 250 tangent, Euler
                 and Bernoulli numbers, respectively.",
}


bibtype: book
filename: elefunt.bib
label: MacRobert:1967:SHE
author: Thomas Murray MacRobert and Ian Naismith Sneddon
title: Spherical harmonics; an elementary treatise on harmonic functions, with applications
volume: 98
publisher: pub-PERGAMON
address: pub-PERGAMON:adr
edition: Third
pages: xviii + 349
year: 1967
LCCN: QA406 .M3 1967
bibdate: Sat Oct 30 21:22:03 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:22:03 MDT
series: International series of monographs in pure and applied mathematics
subject: Spherical harmonics
acknowledgement: ack-nhfb
authordates: 1884--1962
rawauthor: Thomas Murray MacRobert and Ian Naismith Sneddon
rawtitle: Spherical harmonics; an elementary treatise on harmonic functions, with applications
entry:
@Book{MacRobert:1967:SHE,
  author =       "Thomas Murray MacRobert and Ian Naismith Sneddon",
  title =        "Spherical harmonics; an elementary treatise on
                 harmonic functions, with applications",
  volume =       "98",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  edition =      "Third",
  pages =        "xviii + 349",
  year =         "1967",
  LCCN =         "QA406 .M3 1967",
  bibdate =      "Sat Oct 30 21:22:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series of monographs in pure and applied
                 mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1884--1962",
  subject =      "Spherical harmonics",
}


bibtype: book
filename: elefunt.bib
label: Meinardus:1967:AFT
author: Gunter Meinardus
title: Approximation of functions: Theory and numerical methods
volume: 13
publisher: pub-SV
address: pub-SV:adr
pages: viii + 198
year: 1967
ISBN: 0-387-03985-6, 3-540-03985-6 OR 0387039856, 3540039856
ISBN13: 978-0-387-03985-5, 978-3-540-03985-3 OR 9780387039855, 9783540039853
ISSN: 0081-3877 OR 00813877
LCCN: QA221 .M3813
bibdate: Thu Oct 19 17:07:54 MDT 2023
bibtimestamp: 2023.10.19 17:07:54 MDT
series: Springer Tracts in Natural Philosophy
URL: http://catalogue.bnf.fr/ark:/12148/cb37378349d
remark: Translation by Larry L. Schumaker of cite Meinardus:1964:AFI.
acknowledgement: ack-nhfb
authordates: (1926--2007)
rawauthor: G{\"u}nter Meinardus
rawtitle: Approximation of functions: Theory and numerical methods
bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

subject:
Approximation theory; Numerical analysis; Theorie de l'approximation; Analyse numerique; Fonctions (mathematiques); Approximation, Theorie de l'; Analyse numerique; Approximation theory; Numerical analysis; Approximation; Funktion; Mathematik

TOC:
Part I. Linear Approximation 1. The General Linear Approximation Problem / 1 1.1. Statement of the Problem. Existence Theorem / 1 1.2. Strictly Convex Spaces. Hilbert Space / 2 1.3. Maximal Linear Functionals / 4 2. Dense Systems / 5 2.1. A General Criterion of Banach / 5 2.2. Approximation Theorems of Weierstrass and Muntz / 6 2.3. Approximation Theorems in the Complex Plane / 10 3. General Theory of Linear Tchebycheff Approximation / 13 3.1. Fundamentals. The Theorem of Kolmogoroff / 13 3.2. The Haar Uniqueness Theorem. Linear Functionals and Alternants / 16 3.3. Further Uniqueness Results / 24 3.4. Invariants / 26 3.5. Vector-valued Functions / 28 4. Special Tchebycheff Approximations / 28 4.1. Tchebycheff Systems / 28 4.2. Tchebycheff Polynomials / 31 4.3. The Function ?? / 33 4.4. A Problem of Bernstein and Achieser / 36 4.5 Zolotareff's Problem / 41 5. Estimating the Magnitude of Error in Trigonometric and Polynomial Approximation / 45 5.1. Projection Operators. Linear Polynomial Operators / 45 5.2. The Connection between Trigonometric and Polynomial Approximation / 45 5.3. The Fejer Operator / 47 5.4. The Korovkin Operators / 50 5.5. The Theorems of D. Jackson / 52 5.6. The Theorems of Bernstein and Zygmund / 57 5.7. Supplements / 65 6. Approximation by Polynomials and Related Functions / 72 6.1. Foundations / 72 6.2. Upper Bounds for En (??) / 77 6.3. Lower Bounds for En (??) / 82 6.4. Dependence of the Approximation on the Interval / 85 6.5. Regular Haar Systems / 87 6.6. Asymptotic Results / 90 6.7. Results for tho Alternants / 101 7. Numerical Methods for Linear Tchebycheff Approximation / 105 7.1. The Iterative Methods of Remez / 105 7.2. Initial Approximations / 116 7.3. Direct Methods / 122 7.4. Discretization. Other Methods / 124 Part II. Non-linear Approximation 8. General Theory of Non-linear Tchebycheff Approximation / 131 8.1. Survey of the Problem. A Generalization of the Kolmogoroff Theorem / 131 8.2. The Haar Uniqueness Theorem. Alternants / 141 8.3. The Investigations of Rice / 148 8.4. The Newton Iteration Method / 149 8.5. H-Sets / 153 9. Rational Approximation / 154 9.1. Existence. Invariants. A Theorem of Walsh / 154 9.2. Theorems on Alternants. Anomalies. Continuity. Examples / 160 9.3. Asymptotic Results. Small Intervals / 167 9.4. Numerical Methods / 170 10. Exponential Approximation / 176 10.1. The Results of Rice / 176 10.2. An Anomaly Theorem. Constructive Methods / 179 11. Segment Approximation / 183 11.1. Statement of the Problem. Hypotheses / 183 11.2. The principle of Lawson / 184 H.3. Equidegree Polynomial Approximation / 188 Bibliography / 189 Subject Index / 197

rawTOC:
Part I. Linear Approximation \\ 1. The General Linear Approximation Problem / 1 \\ 1.1. Statement of the Problem. Existence Theorem / 1 \\ 1.2. Strictly Convex Spaces. Hilbert Space / 2 \\ 1.3. Maximal Linear Functionals / 4 \\ 2. Dense Systems / 5 \\ 2.1. A General Criterion of Banach / 5 \\ 2.2. Approximation Theorems of Weierstrass and Muntz / 6 \\ 2.3. Approximation Theorems in the Complex Plane / 10 \\ 3. General Theory of Linear Tchebycheff Approximation / 13 \\ 3.1. Fundamentals. The Theorem of Kolmogoroff / 13 \\ 3.2. The Haar Uniqueness Theorem. Linear Functionals and Alternants / 16 \\ 3.3. Further Uniqueness Results / 24 \\ 3.4. Invariants / 26 \\ 3.5. Vector-valued Functions / 28 \\ 4. Special Tchebycheff Approximations / 28 \\ 4.1. Tchebycheff Systems / 28 \\ 4.2. Tchebycheff Polynomials / 31 \\ 4.3. The Function ?? / 33 \\ 4.4. A Problem of Bernstein and Achieser / 36 \\ 4.5 Zolotareff's Problem / 41 \\ 5. Estimating the Magnitude of Error in Trigonometric and Polynomial Approximation / 45 \\ 5.1. Projection Operators. Linear Polynomial Operators / 45 \\ 5.2. The Connection between Trigonometric and Polynomial Approximation / 45 \\ 5.3. The Fej{\'e}r Operator / 47 \\ 5.4. The Korovkin Operators / 50 \\ 5.5. The Theorems of D. Jackson / 52 \\ 5.6. The Theorems of Bernstein and Zygmund / 57 \\ 5.7. Supplements / 65 \\ 6. Approximation by Polynomials and Related Functions / 72 \\ 6.1. Foundations / 72 \\ 6.2. Upper Bounds for En (??) / 77 \\ 6.3. Lower Bounds for En (??) / 82 \\ 6.4. Dependence of the Approximation on the Interval / 85 \\ 6.5. Regular Haar Systems / 87 \\ 6.6. Asymptotic Results / 90 \\ 6.7. Results for tho Alternants / 101 \\ 7. Numerical Methods for Linear Tchebycheff Approximation / 105 \\ 7.1. The Iterative Methods of Remez / 105 \\ 7.2. Initial Approximations / 116 \\ 7.3. Direct Methods / 122 \\ 7.4. Discretization. Other Methods / 124 \\ Part II. Non-linear Approximation \\ 8. General Theory of Non-linear Tchebycheff Approximation / 131 \\ 8.1. Survey of the Problem. A Generalization of the Kolmogoroff Theorem / 131 \\ 8.2. The Haar Uniqueness Theorem. Alternants / 141 \\ 8.3. The Investigations of Rice / 148 \\ 8.4. The Newton Iteration Method / 149 \\ 8.5. H-Sets / 153 \\ 9. Rational Approximation / 154 \\ 9.1. Existence. Invariants. A Theorem of Walsh / 154 \\ 9.2. Theorems on Alternants. Anomalies. Continuity. Examples / 160 \\ 9.3. Asymptotic Results. Small Intervals / 167 \\ 9.4. Numerical Methods / 170 \\ 10. Exponential Approximation / 176 \\ 10.1. The Results of Rice / 176 \\ 10.2. An Anomaly Theorem. Constructive Methods / 179 \\ 11. Segment Approximation / 183 \\ 11.1. Statement of the Problem. Hypotheses / 183 \\ 11.2. The principle of Lawson / 184 \\ H.3. Equidegree Polynomial Approximation / 188 \\ Bibliography / 189 \\ Subject Index / 197

entry:
@Book{Meinardus:1967:AFT,
  author =       "G{\"u}nter Meinardus",
  title =        "Approximation of functions: Theory and numerical
                 methods",
  volume =       "13",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 198",
  year =         "1967",
  ISBN =         "0-387-03985-6, 3-540-03985-6",
  ISBN-13 =      "978-0-387-03985-5, 978-3-540-03985-3",
  ISSN =         "0081-3877",
  LCCN =         "QA221 .M3813",
  bibdate =      "Thu Oct 19 17:07:54 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Springer Tracts in Natural Philosophy",
  URL =          "http://catalogue.bnf.fr/ark:/12148/cb37378349d",
  acknowledgement = ack-nhfb,
  author-dates = "(1926--2007)",
  remark =       "Translation by Larry L. Schumaker of
                 \cite{Meinardus:1964:AFI}.",
  subject =      "Approximation theory; Numerical analysis; Th{\'e}orie
                 de l'approximation; Analyse num{\'e}rique; Fonctions
                 (math{\'e}matiques); Approximation, Th{\'e}orie de l';
                 Analyse num{\'e}rique; Approximation theory; Numerical
                 analysis; Approximation; Funktion; Mathematik",
  tableofcontents = "Part I. Linear Approximation \\
                 1. The General Linear Approximation Problem / 1 \\
                 1.1. Statement of the Problem. Existence Theorem / 1
                 \\
                 1.2. Strictly Convex Spaces. Hilbert Space / 2 \\
                 1.3. Maximal Linear Functionals / 4 \\
                 2. Dense Systems / 5 \\
                 2.1. A General Criterion of Banach / 5 \\
                 2.2. Approximation Theorems of Weierstrass and Muntz /
                 6 \\
                 2.3. Approximation Theorems in the Complex Plane / 10
                 \\
                 3. General Theory of Linear Tchebycheff Approximation /
                 13 \\
                 3.1. Fundamentals. The Theorem of Kolmogoroff / 13 \\
                 3.2. The Haar Uniqueness Theorem. Linear Functionals
                 and Alternants / 16 \\
                 3.3. Further Uniqueness Results / 24 \\
                 3.4. Invariants / 26 \\
                 3.5. Vector-valued Functions / 28 \\
                 4. Special Tchebycheff Approximations / 28 \\
                 4.1. Tchebycheff Systems / 28 \\
                 4.2. Tchebycheff Polynomials / 31 \\
                 4.3. The Function ?? / 33 \\
                 4.4. A Problem of Bernstein and Achieser / 36 \\
                 4.5 Zolotareff's Problem / 41 \\
                 5. Estimating the Magnitude of Error in Trigonometric
                 and Polynomial Approximation / 45 \\
                 5.1. Projection Operators. Linear Polynomial Operators
                 / 45 \\
                 5.2. The Connection between Trigonometric and
                 Polynomial Approximation / 45 \\
                 5.3. The Fej{\'e}r Operator / 47 \\
                 5.4. The Korovkin Operators / 50 \\
                 5.5. The Theorems of D. Jackson / 52 \\
                 5.6. The Theorems of Bernstein and Zygmund / 57 \\
                 5.7. Supplements / 65 \\
                 6. Approximation by Polynomials and Related Functions /
                 72 \\
                 6.1. Foundations / 72 \\
                 6.2. Upper Bounds for En (??) / 77 \\
                 6.3. Lower Bounds for En (??) / 82 \\
                 6.4. Dependence of the Approximation on the Interval /
                 85 \\
                 6.5. Regular Haar Systems / 87 \\
                 6.6. Asymptotic Results / 90 \\
                 6.7. Results for tho Alternants / 101 \\
                 7. Numerical Methods for Linear Tchebycheff
                 Approximation / 105 \\
                 7.1. The Iterative Methods of Remez / 105 \\
                 7.2. Initial Approximations / 116 \\
                 7.3. Direct Methods / 122 \\
                 7.4. Discretization. Other Methods / 124 \\
                 Part II. Non-linear Approximation \\
                 8. General Theory of Non-linear Tchebycheff
                 Approximation / 131 \\
                 8.1. Survey of the Problem. A Generalization of the
                 Kolmogoroff Theorem / 131 \\
                 8.2. The Haar Uniqueness Theorem. Alternants / 141 \\
                 8.3. The Investigations of Rice / 148 \\
                 8.4. The Newton Iteration Method / 149 \\
                 8.5. H-Sets / 153 \\
                 9. Rational Approximation / 154 \\
                 9.1. Existence. Invariants. A Theorem of Walsh / 154
                 \\
                 9.2. Theorems on Alternants. Anomalies. Continuity.
                 Examples / 160 \\
                 9.3. Asymptotic Results. Small Intervals / 167 \\
                 9.4. Numerical Methods / 170 \\
                 10. Exponential Approximation / 176 \\
                 10.1. The Results of Rice / 176 \\
                 10.2. An Anomaly Theorem. Constructive Methods / 179
                 \\
                 11. Segment Approximation / 183 \\
                 11.1. Statement of the Problem. Hypotheses / 183 \\
                 11.2. The principle of Lawson / 184 \\
                 H.3. Equidegree Polynomial Approximation / 188 \\
                 Bibliography / 189 \\
                 Subject Index / 197",
}


bibtype: article
filename: elefunt.bib
label: Moody:1967:ADF
author: William T. Moody
title: Approximations for the Psi (Digamma) Function (in Technical Notes and Short Notices)
journal: j-MATH-COMPUT
volume: 21
number: 97
pages: 112--112
month: jan
monthnumber: 1
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: William T. Moody
rawtitle: Approximations for the Psi (Digamma) Function (in Technical Notes and Short Notices)
entry:
@Article{Moody:1967:ADF,
  author =       "William T. Moody",
  title =        "Approximations for the Psi (Digamma) Function (in
                 Technical Notes and Short Notices)",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "97",
  pages =        "112--112",
  month =        jan,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Moursund:1967:OSV
author: David G. Moursund
title: Optimal starting values for Newton--Raphson calculation of $ sqrt x $
journal: j-CACM
volume: 10
number: 7
pages: 430--432
month: jul
monthnumber: 7
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363427.363454
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.25
MRnumber: 39\#2297
bibdate: Thu Sep 1 10:15:43 1994
bibtimestamp: 1994.09.01 10:15:43 ???
note: See letter cite Fike:1967:LER.
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions
remark: Title of article has incorrect $ sqrt (x^1 / 2) $: the article discusses computation of tt sqrt(x).
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: David G. Moursund
rawnote: See letter \cite{Fike:1967:LER}.
rawtitle: Optimal starting values for {Newton--Raphson} calculation of $ \sqrt {x} $
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The problem of obtaining starting values for the Newton-Raphson calculation of $ sqrt x $ on a digital computer is considered. It is shown that the conventionally used best uniform approximations to $ sqrt x $ do not provide optimal starting values. The problem of obtaining optimal starting values is stated, and several basic results are proved. A table of optimal polynomial starting values is given.

rawabstract:
The problem of obtaining starting values for the Newton-Raphson calculation of $ \sqrt {x} $ on a digital computer is considered. It is shown that the conventionally used best uniform approximations to $ \sqrt {x} $ do not provide optimal starting values. The problem of obtaining optimal starting values is stated, and several basic results are proved. A table of optimal polynomial starting values is given.

entry:
@Article{Moursund:1967:OSV,
  author =       "David G. Moursund",
  title =        "Optimal starting values for {Newton--Raphson}
                 calculation of $ \sqrt {x} $",
  journal =      j-CACM,
  volume =       "10",
  number =       "7",
  pages =        "430--432",
  month =        jul,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363427.363454",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "39\#2297",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Fike:1967:LER}.",
  abstract =     "The problem of obtaining starting values for the
                 Newton-Raphson calculation of $ \sqrt {x} $ on a
                 digital computer is considered. It is shown that the
                 conventionally used best uniform approximations to $
                 \sqrt {x} $ do not provide optimal starting values. The
                 problem of obtaining optimal starting values is stated,
                 and several basic results are proved. A table of
                 optimal polynomial starting values is given.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  remark =       "Title of article has incorrect $ \sqrt (x^{1 / 2}) $:
                 the article discusses computation of {\tt sqrt(x)}.",
}


bibtype: article
filename: elefunt.bib
label: Olver:1967:BSS
author: F. W. J. Olver
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 71B
number: 4
pages: 161--166
month: oct
monthnumber: 10
year: 1967
ISSN: 0091-0635 OR 00910635
bibdate: Sat Oct 30 09:37:44 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 09:37:44 ???
fjournal: Journal of Research of the National Bureau of Standards
remark: Fullerton: Truncation error estimates of an earlier published algorithm.
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: F. W. J. Olver
title:
Bounds for the Solutions of Second-Order Linear Difference Equations [Anger--Weber and Struve Functions]

rawtitle:
Bounds for the Solutions of Second-Order Linear Difference Equations [{Anger--Weber} and {Struve} Functions]

entry:
@Article{Olver:1967:BSS,
  author =       "F. W. J. Olver",
  title =        "Bounds for the Solutions of Second-Order Linear
                 Difference Equations [{Anger--Weber} and {Struve}
                 Functions]",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "71B",
  number =       "4",
  pages =        "161--166",
  month =        oct,
  year =         "1967",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 09:37:44 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Truncation error estimates of an earlier
                 published algorithm.",
}


bibtype: article
filename: elefunt.bib
label: Olver:1967:NSS
author: F. W. J. Olver
title: Numerical solution of second-order linear difference equations
journal: j-J-RES-NATL-BUR-STAND-B
volume: 71B
number: 2--3
pages: 111--129
month: apr
monthnumber: 4
year: 1967
CODEN: JNBBAU
DOI: https://doi.org/10.6028/jres.071B.018
ISSN: 0022-4340 OR 00224340
MRclass: 65.70
MRnumber: 221789
MRreviewer: G. N. Lance
bibdate: Sun Nov 5 09:03:34 2023
bibtimestamp: 2023.11.05 09:03:34 ???
URL: https://nvlpubs.nist.gov/nistpubs/jres/71B/jresv71Bn2-3p111_A1b.pdf
acknowledgement: ack-nhfb
authordates: Frank William John Olver (15 December 1924--23 April 2013)
journalURL: http://www.nist.gov/nvl/jrespastpapers.cfm
rawauthor: F. W. J. Olver
rawtitle: Numerical solution of second-order linear difference equations
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
A new algorithm is given for computing the solution of any second-order linear difference equation which is applicable when simple recurrence procedures cannot be used because of instability. Compared with the well-known Miller algorithm the new method has the advantages of (i) automatically determining the correct number of recurrence steps. (ii) applying to inhomogeneous difference equations, (iii) enabling more powerful error analyses to be constructed.par The method is illustrated by numerical computations, including error analyses of Anger--Weber, Struve, and Bessel functions, and the solution of a differential equation in Chebyshev series

fjournal:
Journal of Research of the National Bureau of Standards. Section B. Mathematics and Mathematical Physics

keywords:
Chebyshev series; difference equations; error analysis; Miller algorithm. recurrence methods; special functions

rawabstract:
A new algorithm is given for computing the solution of any second-order linear difference equation which is applicable when simple recurrence procedures cannot be used because of instability. Compared with the well-known Miller algorithm the new method has the advantages of (i) automatically determining the correct number of recurrence steps. (ii) applying to inhomogeneous difference equations, (iii) enabling more powerful error analyses to be constructed.\par The method is illustrated by numerical computations, including error analyses of Anger--Weber, Struve, and Bessel functions, and the solution of a differential equation in Chebyshev series

entry:
@Article{Olver:1967:NSS,
  author =       "F. W. J. Olver",
  title =        "Numerical solution of second-order linear difference
                 equations",
  journal =      j-J-RES-NATL-BUR-STAND-B,
  volume =       "71B",
  number =       "2--3",
  pages =        "111--129",
  month =        apr,
  year =         "1967",
  CODEN =        "JNBBAU",
  DOI =          "https://doi.org/10.6028/jres.071B.018",
  ISSN =         "0022-4340",
  MRclass =      "65.70",
  MRnumber =     "221789",
  MRreviewer =   "G. N. Lance",
  bibdate =      "Sun Nov 5 09:03:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://nvlpubs.nist.gov/nistpubs/jres/71B/jresv71Bn2-3p111_A1b.pdf",
  abstract =     "A new algorithm is given for computing the solution of
                 any second-order linear difference equation which is
                 applicable when simple recurrence procedures cannot be
                 used because of instability. Compared with the
                 well-known Miller algorithm the new method has the
                 advantages of (i) automatically determining the correct
                 number of recurrence steps. (ii) applying to
                 inhomogeneous difference equations, (iii) enabling more
                 powerful error analyses to be constructed.\par

                 The method is illustrated by numerical computations,
                 including error analyses of Anger--Weber, Struve, and
                 Bessel functions, and the solution of a differential
                 equation in Chebyshev series",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards. Section B. Mathematics and Mathematical
                 Physics",
  journal-URL =  "http://www.nist.gov/nvl/jrespastpapers.cfm",
  keywords =     "Chebyshev series; difference equations; error
                 analysis; Miller algorithm. recurrence methods; special
                 functions",
}


bibtype: article
filename: elefunt.bib
label: Pike:1967:RAI
author: M. C. Pike and I. D. Hill
title: Remark on Algorithm 179: Incomplete Beta ratio
journal: j-CACM
volume: 10
number: 6
pages: 375--376
month: jun
monthnumber: 6
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:13 MST 2005
bibtimestamp: 2005.11.25 18:20:13 MST
fjournal: Communications of the ACM
keywords: $B(z,w)$; beta function; special functions
remark: Fullerton: Corrections to an Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: M. C. Pike and I. D. Hill
rawtitle: Remark on {Algorithm 179}: {Incomplete} {Beta} ratio
entry:
@Article{Pike:1967:RAI,
  author =       "M. C. Pike and I. D. Hill",
  title =        "Remark on {Algorithm 179}: {Incomplete} {Beta} ratio",
  journal =      j-CACM,
  volume =       "10",
  number =       "6",
  pages =        "375--376",
  month =        jun,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$B(z,w)$; beta function; special functions",
  remark =       "Fullerton: Corrections to an Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Pitteway:1967:RAA
author: M. L. V. Pitteway
title: Remark on Algorithm 301: Airy function
journal: j-CACM
volume: 10
number: 7
pages: 453--453
month: jul
monthnumber: 7
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:14 MST 2005
bibtimestamp: 2005.11.25 18:20:14 MST
fjournal: Communications of the ACM
keywords: Airy functions; special functions
remark: Fullerton: Corrections to an Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: M. L. V. Pitteway
rawtitle: Remark on {Algorithm 301}: {Airy} function
entry:
@Article{Pitteway:1967:RAA,
  author =       "M. L. V. Pitteway",
  title =        "Remark on {Algorithm 301}: {Airy} function",
  journal =      j-CACM,
  volume =       "10",
  number =       "7",
  pages =        "453--453",
  month =        jul,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:14 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Airy functions; special functions",
  remark =       "Fullerton: Corrections to an Algol procedure.",
}


bibtype: book
filename: elefunt.bib
label: Sen:1967:TSF
author: Bibhutibhusan Sen
title: A treatise on special functions, for scientists and engineers
publisher: Allied Publishers
address: Bombay, India
pages: 164
year: 1967
LCCN: QA351 .S45
bibdate: Fri Oct 29 21:30:38 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.29 21:30:38 MDT
subject: Functions, Special; Spherical harmonics
acknowledgement: ack-nhfb
rawauthor: Bibhutibhusan Sen
rawtitle: A treatise on special functions, for scientists and engineers
entry:
@Book{Sen:1967:TSF,
  author =       "Bibhutibhusan Sen",
  title =        "A treatise on special functions, for scientists and
                 engineers",
  publisher =    "Allied Publishers",
  address =      "Bombay, India",
  pages =        "164",
  year =         "1967",
  LCCN =         "QA351 .S45",
  bibdate =      "Fri Oct 29 21:30:38 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Spherical harmonics",
}


bibtype: book
filename: elefunt.bib
label: Tolke:1967:PFE
author: Friedrich Tolke
publisher: pub-SV
address: pub-SV:adr
pages: viii + 191
year: 1967
DOI: https://doi.org/10.1007/978-3-662-36381-2
bibdate: Mon Feb 13 19:01:10 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.13 19:01:10 ???
URL: http://www.springerlink.com/content/978-3-662-36381-2
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich T{\"o}lke
title:
Praktische Funktionenlehre. 4. Elliptische Integralgruppen und Jacobische elliptische Funktionen im Komplexen. (German) [Practical functional theory. 4. Elliptical integral groups and Jacobian elliptic functions in the complex plane]

ISBN:
3-662-36381-X, 3-662-35552-3 (print), 3-662-36381-X (e-book) OR 366236381X, 3662355523 (print), 366236381X (ebook)

ISBN13:
978-3-662-36381-2, 978-3-662-35552-7 (print), 978-3-662-36381-2 (e-book) OR 9783662363812, 9783662355527 (print), 9783662363812 (ebook)

rawtitle:
{Praktische Funktionenlehre. 4. Elliptische Integralgruppen und Jacobische elliptische Funktionen im Komplexen}. ({German}) [{Practical} functional theory. 4. {Elliptical} integral groups and {Jacobian} elliptic functions in the complex plane]

entry:
@Book{Tolke:1967:PFE,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 4. Elliptische
                 Integralgruppen und Jacobische elliptische Funktionen
                 im Komplexen}. ({German}) [{Practical} functional
                 theory. 4. {Elliptical} integral groups and {Jacobian}
                 elliptic functions in the complex plane]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 191",
  year =         "1967",
  DOI =          "https://doi.org/10.1007/978-3-662-36381-2",
  ISBN =         "3-662-36381-X, 3-662-35552-3 (print), 3-662-36381-X
                 (e-book)",
  ISBN-13 =      "978-3-662-36381-2, 978-3-662-35552-7 (print),
                 978-3-662-36381-2 (e-book)",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/978-3-662-36381-2",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: book
filename: elefunt.bib
label: Tolke:1967:PFJ
author: Friedrich Tolke
publisher: pub-SV
address: pub-SV:adr
pages: viii + 180
year: 1967
DOI: https://doi.org/10.1007/978-3-662-36379-9
bibdate: Mon Feb 13 19:01:10 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.13 19:01:10 ???
URL: http://www.springerlink.com/content/978-3-662-36379-9
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich T{\"o}lke
title:
Praktische Funktionenlehre. 3. Jacobische elliptische Funktionen, Legendresche elliptische Normalintegrale und spezielle Weierstrasssche Zeta- und Sigma-Funktionen. (German) [Practical functional theory. 3. Jacobian elliptic functions, Legendre elliptical normal Integrals and special Weierstrass zeta- and sigma functions]

ISBN:
3-642-50264-4, 3-662-36379-8, 3-662-35550-7 (print), 3-662-36379-8 (e-book) OR 3642502644, 3662363798, 3662355507 (print), 3662363798 (ebook)

ISBN13:
978-3-642-50264-4, 978-3-662-36379-9, 978-3-662-35550-3 (print), 978-3-662-36379-9 (e-book) OR 9783642502644, 9783662363799, 9783662355503 (print), 9783662363799 (ebook)

TOC:
5 Jacobische elliptische Funktionen und zugehorige logarithmische Ableitungen 108. Definitionen 109. Funktionalgleichungen 110. Periodenverhalten und Substitutionen 111. Funktionswerte an den Stellen $ 0, pm frac 12, pm frac ix2, pm frac 12, pm frac ix2 $ bzw. $ 0, pm K, pm iK', pm K pm iK' $ 112. Trigonometrische und hyperbolische Reihenentwicklungen 113. Potenzreihen-Entwicklungen 114. Imaginare Argumenttransformation, reziproke Modultransformation und imaginare Modultransformation 115. Ableitungen 116. Gausssche und Landensche Transformation. Substitutionen fur $ zeta pm frac 14$ und $zeta pm frac ix4 $ 117. Additionstheoreme. Transformationsgleichungen fur doppeltes und halbes Argument. Weitere Substitutionen fur $ zeta pm frac 14$ und $zeta pm frac ix4$ sowie fur $zeta pm frac 14 pm frac ix4 $ 118. Die Logarithmen der logarithmischen Ableitungen der Jacobischen elliptischen Funktionen 119. Ubergange vom (?,?)-System auf das $(z, k)$-System 120. Funktionsverlauf der Jacobischen elliptischen Funktionen und der zugehorigen Ableitungen und logarithmischen Ableitungen im Reellen. Ausartungen 121. Differentialgleichungen erster und zweiter Ordnung 122. Die Integrale der Jacobischen elliptischen Funktionen 123. Die Integrale der logarithmischen Ableitungen der Jacobischen elliptischen Funktionen 6 Umkehrfunktionen der Jacobischen elliptischen Funktionen und elliptische Normalintegrale erster Gattung. Elliptische Amplitudenfunktion sowie Legendresche $F$- und $E$-Funktion. Elliptische Normalintegrale zweiter Gattung. Jacobische Zeta- und Heumansche Lambda-Funktion 124. Die 18 Umkehrfunktionen der Jacobischen elliptischen Funktionen und ihrer logarithmischen Ableitungen. (Elliptische Normalintegrale erster Gattung.) Additionstheoreme der Umkehrfunktionen 125. Elliptische Normalintegrale erster Gattung in hyperbolischer Form 126. Potenzreihen-Entwicklungen der Umkehrfunktionen 127. Die elliptische Amplitudenfunktion $? = am (z, k)$ und ihre Umkehrfunktion $z = F(?, k)$. Die vier trigonometrischen Legendreschen Normalintegrale erster Gattung 128. Darstellung der 18 Umkehrfunktionen und der elliptischen Normalintegrale erster Gattung durch die Funktion F. Die vier hyperbolischen Legendreschen Normalintegrale erster Gattung und die Funktion $F$ fur imaginares Argument 129. Die Legendresche $E$-Funktion fur reelles und imaginares Argument 130. Die 18 Integrale der Quadrate der Jacobischen elliptischen Funktionen und ihrer logarithmischen Ableitungen, die 12 durch Umformung der letzteren entstehenden hyperbolischen Integrale, die 24 Normalintegrale zweiter Gattung und die acht trigonometrischen und hyperbolischen Legendreschen Normalintegrale zweiter Gattung 131. Die 46 Normalintegrale erster und zweiter Gattung mit linearen trigonometrischen und hyperbolischen Funktionen 132. Jacobische Zeta-Funktion und Heumansche Lambda-Funktion 7 Normalintegrale dritter Gattung. Legendresche $Pi $-Funktion. Zuruckfuhrung des allgemeinen elliptischen Integrals auf Normalintegrale erster, zweiter und dritter Gattung 133. Die 96 Normalintegrale dritter Gattung in Jacobischer Form 134. Die acht zu den logarithmischen Ableitungen der Jacobischen elliptischen Funktionen gehorigen Normalintegrale dritter Gattung 135. 48 Quotientenintegrale und 48 spezielle Normalintegrale dritter Gattung in der Jacobischen Form 136. Algebraische Form der elliptischen Normalintegrale dritter Gattung 137. Darstellung der vollstandigen Normalintegrale dritter Gattung durch Jacobische Zeta- und Heumansche Lambda-Funktionen 138. Die $Pi $-Funktion und die Integrale dritter Gattung in trigonometrischer Form 139. Die 48 speziellen Normalintegrale dritter Gattung in algebraischer Form 140. Weitere sechs spezielle Normalintegrale dritter Gattung 141. Zuruckfuhrung des allgemeinen elliptischen Integrals in der Legendreschen Form auf Normalintegrale erster, zweiter und dritter Gattung 8 Spezielle Weierstrass sche Zeta-Funktionen 142. Definitions- und Funktionalgleichungen 143. Substitutionen 144. Relatives Periodenverhalten. Spezielle Funktionswerte. Funktionsverlauf 145. Lineare Beziehungen zu den logarithmischen Ableitungen der Jacobischen elliptischen Funktionen und deren Ableitungen 146. Integrale der $Pi $-Funktionen als Weierstrasssche Zeta-Funktionen und Ableitungen der Zeta-Funktionen 147. Differentialtransformationen fur doppelte und halbe Parameter 148. Gausssche und Landensche Transformation 149. Additionstheoreme und Transformationsgleichungen fur doppeltes und halbes Argument 150. Trigonometrische, hyperbolische und Potenzreihen-Entwicklungen 151. Homogenitatstransformation der Funktionen

rawtitle:
{Praktische Funktionenlehre. 3. Jacobische elliptische Funktionen, Legendresche elliptische Normalintegrale und spezielle Weierstrasssche Zeta- und Sigma-Funktionen}. ({German}) [{Practical} functional theory. 3. {Jacobian} elliptic functions, Legendre elliptical normal Integrals and special {Weierstrass} zeta- and sigma functions]

rawTOC:
5 Jacobische elliptische Funktionen und zugeh{\"o}rige logarithmische Ableitungen \\ 108. Definitionen \\ 109. Funktionalgleichungen \\ 110. Periodenverhalten und Substitutionen \\ 111. Funktionswerte an den Stellen $ 0, \pm \frac{1}{2}, \pm \frac{ix}{2}, \pm \frac{1}{2}, \pm \frac{ix}{2} $ bzw. $ 0, \pm K, \pm iK', \pm K \pm iK' $ \\ 112. Trigonometrische und hyperbolische Reihenentwicklungen \\ 113. Potenzreihen-Entwicklungen \\ 114. Imagin{\"a}re Argumenttransformation, reziproke Modultransformation und imagin{\"a}re Modultransformation \\ 115. Ableitungen \\ 116. Gausssche und Landensche Transformation. Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und $\zeta \pm \frac{ix}{4} $ \\ 117. Additionstheoreme. Transformationsgleichungen f{\"u}r doppeltes und halbes Argument. Weitere Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und $\zeta \pm \frac{ix}{4}$ sowie f{\"u}r $\zeta \pm \frac{1}{4} \pm \frac{ix}{4} $ \\ 118. Die Logarithmen der logarithmischen Ableitungen der Jacobischen elliptischen Funktionen \\ 119. {\"U}berg{\"a}nge vom (?,?)-System auf das $(z, k)$-System \\ 120. Funktionsverlauf der Jacobischen elliptischen Funktionen und der zugeh{\"o}rigen Ableitungen und logarithmischen Ableitungen im Reellen. Ausartungen \\ 121. Differentialgleichungen erster und zweiter Ordnung \\ 122. Die Integrale der Jacobischen elliptischen Funktionen \\ 123. Die Integrale der logarithmischen Ableitungen der Jacobischen elliptischen Funktionen \\ 6 Umkehrfunktionen der Jacobischen elliptischen Funktionen und elliptische Normalintegrale erster Gattung. Elliptische Amplitudenfunktion sowie Legendresche $F$- und $E$-Funktion. Elliptische Normalintegrale zweiter Gattung. Jacobische Zeta- und Heumansche Lambda-Funktion \\ 124. Die 18 Umkehrfunktionen der Jacobischen elliptischen Funktionen und ihrer logarithmischen Ableitungen. (Elliptische Normalintegrale erster Gattung.) Additionstheoreme der Umkehrfunktionen \\ 125. Elliptische Normalintegrale erster Gattung in hyperbolischer Form \\ 126. Potenzreihen-Entwicklungen der Umkehrfunktionen \\ 127. Die elliptische Amplitudenfunktion $? = \am(z, k)$ und ihre Umkehrfunktion $z = F(?, k)$. Die vier trigonometrischen Legendreschen Normalintegrale erster Gattung \\ 128. Darstellung der 18 Umkehrfunktionen und der elliptischen Normalintegrale erster Gattung durch die Funktion F. Die vier hyperbolischen Legendreschen Normalintegrale erster Gattung und die Funktion $F$ f{\"u}r imagin{\"a}res Argument \\ 129. Die Legendresche $E$-Funktion f{\"u}r reelles und imagin{\"a}res Argument \\ 130. Die 18 Integrale der Quadrate der Jacobischen elliptischen Funktionen und ihrer logarithmischen Ableitungen, die 12 durch Umformung der letzteren entstehenden hyperbolischen Integrale, die 24 Normalintegrale zweiter Gattung und die acht trigonometrischen und hyperbolischen Legendreschen Normalintegrale zweiter Gattung \\ 131. Die 46 Normalintegrale erster und zweiter Gattung mit linearen trigonometrischen und hyperbolischen Funktionen \\ 132. Jacobische Zeta-Funktion und Heumansche Lambda-Funktion \\ 7 Normalintegrale dritter Gattung. Legendresche $\Pi$-Funktion. Zur{\"u}ckf{\"u}hrung des allgemeinen elliptischen Integrals auf Normalintegrale erster, zweiter und dritter Gattung \\ 133. Die 96 Normalintegrale dritter Gattung in Jacobischer Form \\ 134. Die acht zu den logarithmischen Ableitungen der Jacobischen elliptischen Funktionen geh{\"o}rigen Normalintegrale dritter Gattung \\ 135. 48 Quotientenintegrale und 48 spezielle Normalintegrale dritter Gattung in der Jacobischen Form \\ 136. Algebraische Form der elliptischen Normalintegrale dritter Gattung \\ 137. Darstellung der vollst{\"a}ndigen Normalintegrale dritter Gattung durch Jacobische Zeta- und Heumansche Lambda-Funktionen \\ 138. Die $\Pi$-Funktion und die Integrale dritter Gattung in trigonometrischer Form \\ 139. Die 48 speziellen Normalintegrale dritter Gattung in algebraischer Form \\ 140. Weitere sechs spezielle Normalintegrale dritter Gattung \\ 141. Zur{\"u}ckf{\"u}hrung des allgemeinen elliptischen Integrals in der Legendreschen Form auf Normalintegrale erster, zweiter und dritter Gattung \\ 8 Spezielle Weierstra{\ss}sche Zeta-Funktionen \\ 142. Definitions- und Funktionalgleichungen \\ 143. Substitutionen \\ 144. Relatives Periodenverhalten. Spezielle Funktionswerte. Funktionsverlauf \\ 145. Lineare Beziehungen zu den logarithmischen Ableitungen der Jacobischen elliptischen Funktionen und deren Ableitungen \\ 146. Integrale der $\Pi$-Funktionen als Weierstrasssche Zeta-Funktionen und Ableitungen der Zeta-Funktionen \\ 147. Differentialtransformationen f{\"u}r doppelte und halbe Parameter \\ 148. Gausssche und Landensche Transformation \\ 149. Additionstheoreme und Transformationsgleichungen f{\"u}r doppeltes und halbes Argument \\ 150. Trigonometrische, hyperbolische und Potenzreihen-Entwicklungen \\ 151. Homogenit{\"a}tstransformation der Funktionen

entry:
@Book{Tolke:1967:PFJ,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 3. Jacobische elliptische
                 Funktionen, Legendresche elliptische Normalintegrale
                 und spezielle Weierstrasssche Zeta- und
                 Sigma-Funktionen}. ({German}) [{Practical} functional
                 theory. 3. {Jacobian} elliptic functions, Legendre
                 elliptical normal Integrals and special {Weierstrass}
                 zeta- and sigma functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 180",
  year =         "1967",
  DOI =          "https://doi.org/10.1007/978-3-662-36379-9",
  ISBN =         "3-642-50264-4, 3-662-36379-8, 3-662-35550-7 (print),
                 3-662-36379-8 (e-book)",
  ISBN-13 =      "978-3-642-50264-4, 978-3-662-36379-9,
                 978-3-662-35550-3 (print), 978-3-662-36379-9 (e-book)",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/978-3-662-36379-9",
  acknowledgement = ack-nhfb,
  language =     "German",
  tableofcontents = "5 Jacobische elliptische Funktionen und
                 zugeh{\"o}rige logarithmische Ableitungen \\
                 108. Definitionen \\
                 109. Funktionalgleichungen \\
                 110. Periodenverhalten und Substitutionen \\
                 111. Funktionswerte an den Stellen $ 0, \pm
                 \frac{1}{2}, \pm \frac{ix}{2}, \pm \frac{1}{2}, \pm
                 \frac{ix}{2} $ bzw. $ 0, \pm K, \pm iK', \pm K \pm iK'
                 $ \\
                 112. Trigonometrische und hyperbolische
                 Reihenentwicklungen \\
                 113. Potenzreihen-Entwicklungen \\
                 114. Imagin{\"a}re Argumenttransformation, reziproke
                 Modultransformation und imagin{\"a}re
                 Modultransformation \\
                 115. Ableitungen \\
                 116. Gausssche und Landensche Transformation.
                 Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und
                 $\zeta \pm \frac{ix}{4} $ \\
                 117. Additionstheoreme. Transformationsgleichungen
                 f{\"u}r doppeltes und halbes Argument. Weitere
                 Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und
                 $\zeta \pm \frac{ix}{4}$ sowie f{\"u}r $\zeta \pm
                 \frac{1}{4} \pm \frac{ix}{4} $ \\
                 118. Die Logarithmen der logarithmischen Ableitungen
                 der Jacobischen elliptischen Funktionen \\
                 119. {\"U}berg{\"a}nge vom (?,?)-System auf das $(z,
                 k)$-System \\
                 120. Funktionsverlauf der Jacobischen elliptischen
                 Funktionen und der zugeh{\"o}rigen Ableitungen und
                 logarithmischen Ableitungen im Reellen. Ausartungen \\
                 121. Differentialgleichungen erster und zweiter Ordnung
                 \\
                 122. Die Integrale der Jacobischen elliptischen
                 Funktionen \\
                 123. Die Integrale der logarithmischen Ableitungen der
                 Jacobischen elliptischen Funktionen \\
                 6 Umkehrfunktionen der Jacobischen elliptischen
                 Funktionen und elliptische Normalintegrale erster
                 Gattung. Elliptische Amplitudenfunktion sowie
                 Legendresche $F$- und $E$-Funktion. Elliptische
                 Normalintegrale zweiter Gattung. Jacobische Zeta- und
                 Heumansche Lambda-Funktion \\
                 124. Die 18 Umkehrfunktionen der Jacobischen
                 elliptischen Funktionen und ihrer logarithmischen
                 Ableitungen. (Elliptische Normalintegrale erster
                 Gattung.) Additionstheoreme der Umkehrfunktionen \\
                 125. Elliptische Normalintegrale erster Gattung in
                 hyperbolischer Form \\
                 126. Potenzreihen-Entwicklungen der Umkehrfunktionen
                 \\
                 127. Die elliptische Amplitudenfunktion $? = \am(z, k)$
                 und ihre Umkehrfunktion $z = F(?, k)$. Die vier
                 trigonometrischen Legendreschen Normalintegrale erster
                 Gattung \\
                 128. Darstellung der 18 Umkehrfunktionen und der
                 elliptischen Normalintegrale erster Gattung durch die
                 Funktion F. Die vier hyperbolischen Legendreschen
                 Normalintegrale erster Gattung und die Funktion $F$
                 f{\"u}r imagin{\"a}res Argument \\
                 129. Die Legendresche $E$-Funktion f{\"u}r reelles und
                 imagin{\"a}res Argument \\
                 130. Die 18 Integrale der Quadrate der Jacobischen
                 elliptischen Funktionen und ihrer logarithmischen
                 Ableitungen, die 12 durch Umformung der letzteren
                 entstehenden hyperbolischen Integrale, die 24
                 Normalintegrale zweiter Gattung und die acht
                 trigonometrischen und hyperbolischen Legendreschen
                 Normalintegrale zweiter Gattung \\
                 131. Die 46 Normalintegrale erster und zweiter Gattung
                 mit linearen trigonometrischen und hyperbolischen
                 Funktionen \\
                 132. Jacobische Zeta-Funktion und Heumansche
                 Lambda-Funktion \\
                 7 Normalintegrale dritter Gattung. Legendresche
                 $\Pi$-Funktion. Zur{\"u}ckf{\"u}hrung des allgemeinen
                 elliptischen Integrals auf Normalintegrale erster,
                 zweiter und dritter Gattung \\
                 133. Die 96 Normalintegrale dritter Gattung in
                 Jacobischer Form \\
                 134. Die acht zu den logarithmischen Ableitungen der
                 Jacobischen elliptischen Funktionen geh{\"o}rigen
                 Normalintegrale dritter Gattung \\
                 135. 48 Quotientenintegrale und 48 spezielle
                 Normalintegrale dritter Gattung in der Jacobischen Form
                 \\
                 136. Algebraische Form der elliptischen Normalintegrale
                 dritter Gattung \\
                 137. Darstellung der vollst{\"a}ndigen Normalintegrale
                 dritter Gattung durch Jacobische Zeta- und Heumansche
                 Lambda-Funktionen \\
                 138. Die $\Pi$-Funktion und die Integrale dritter
                 Gattung in trigonometrischer Form \\
                 139. Die 48 speziellen Normalintegrale dritter Gattung
                 in algebraischer Form \\
                 140. Weitere sechs spezielle Normalintegrale dritter
                 Gattung \\
                 141. Zur{\"u}ckf{\"u}hrung des allgemeinen elliptischen
                 Integrals in der Legendreschen Form auf Normalintegrale
                 erster, zweiter und dritter Gattung \\
                 8 Spezielle Weierstra{\ss}sche Zeta-Funktionen \\
                 142. Definitions- und Funktionalgleichungen \\
                 143. Substitutionen \\
                 144. Relatives Periodenverhalten. Spezielle
                 Funktionswerte. Funktionsverlauf \\
                 145. Lineare Beziehungen zu den logarithmischen
                 Ableitungen der Jacobischen elliptischen Funktionen und
                 deren Ableitungen \\
                 146. Integrale der $\Pi$-Funktionen als Weierstrasssche
                 Zeta-Funktionen und Ableitungen der Zeta-Funktionen \\
                 147. Differentialtransformationen f{\"u}r doppelte und
                 halbe Parameter \\
                 148. Gausssche und Landensche Transformation \\
                 149. Additionstheoreme und Transformationsgleichungen
                 f{\"u}r doppeltes und halbes Argument \\
                 150. Trigonometrische, hyperbolische und
                 Potenzreihen-Entwicklungen \\
                 151. Homogenit{\"a}tstransformation der Funktionen",
}


bibtype: article
filename: elefunt.bib
label: Verma:1967:NSG
author: Arun Verma
journal: j-MATH-COMPUT
volume: 21
number: 98
pages: 232--236
month: apr
monthnumber: 4
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Arun Verma
title:
A Note on the Summation of the Generalised Hypergeometric Functions (in Technical Notes and Short Papers)

rawtitle:
A Note on the Summation of the Generalised Hypergeometric Functions (in {Technical Notes and Short Papers})

entry:
@Article{Verma:1967:NSG,
  author =       "Arun Verma",
  title =        "A Note on the Summation of the Generalised
                 Hypergeometric Functions (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "98",
  pages =        "232--236",
  month =        apr,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Wigner:1967:BRW
author: Eugene P. Wigner
journal: j-PHYS-TODAY
volume: 20
number: 12
pages: 81--81
month: dec
monthnumber: 12
year: 1967
CODEN: PHTOAD
DOI: https://doi.org/10.1063/1.3034082
ISSN: 0031-9228 (print), 1945-0699 (electronic) OR 00319228 (print), 19450699 (electronic)
ISSNL: 0031-9228 OR 00319228
bibdate: Sat Jul 28 07:53:52 MDT 2012
bibtimestamp: 2012.07.28 07:53:52 MDT
URL: http://link.aip.org/link/phtoad/v20/i12/p81/s1
fjournal: Physics Today
acknowledgement: ack-nhfb
journalURL: http://www.physicstoday.org/
rawauthor: Eugene P. Wigner
title:
Book Review: Wilhelm Magnus, Fritz Oberhettinger, and R. P. Soni, booktitle Formulas and Theorems for the Special Functions of Mathematical Physics

bibsource:
http://www.physicstoday.org/search; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Book Review: {Wilhelm Magnus, Fritz Oberhettinger, and R. P. Soni, \booktitle{Formulas and Theorems for the Special Functions of Mathematical Physics}}

entry:
@Article{Wigner:1967:BRW,
  author =       "Eugene P. Wigner",
  title =        "Book Review: {Wilhelm Magnus, Fritz Oberhettinger, and
                 R. P. Soni, \booktitle{Formulas and Theorems for the
                 Special Functions of Mathematical Physics}}",
  journal =      j-PHYS-TODAY,
  volume =       "20",
  number =       "12",
  pages =        "81--81",
  month =        dec,
  year =         "1967",
  CODEN =        "PHTOAD",
  DOI =          "https://doi.org/10.1063/1.3034082",
  ISSN =         "0031-9228 (print), 1945-0699 (electronic)",
  ISSN-L =       "0031-9228",
  bibdate =      "Sat Jul 28 07:53:52 MDT 2012",
  bibsource =    "http://www.physicstoday.org/search;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.aip.org/link/phtoad/v20/i12/p81/s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Today",
  journal-URL =  "http://www.physicstoday.org/",
}


bibtype: article
filename: elefunt.bib
label: Wood:1967:CEI
author: Van E. Wood
title: Chebyshev Expansions for Integrals of the Error Function (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 21
number: 99
pages: 494--496
month: jul
monthnumber: 7
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: 7-digit approximations for $ i^n erfc (x), n = 1, 2 $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Van E. Wood
rawtitle: {Chebyshev} Expansions for Integrals of the Error Function (in {Technical Notes and Short Papers})
entry:
@Article{Wood:1967:CEI,
  author =       "Van E. Wood",
  title =        "{Chebyshev} Expansions for Integrals of the Error
                 Function (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "494--496",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 7-digit approximations for $ i^n \erfc (x),
                 n = 1, 2 $.",
}


bibtype: article
filename: elefunt.bib
label: Yarbrough:1967:PCC
author: Lynn Yarbrough
title: Precision calculations of $e$ and $ pi $ constants
journal: j-CACM
volume: 10
number: 9
pages: 537--537
month: sep
monthnumber: 9
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363566.363578
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:15 MST 2005
bibtimestamp: 2005.11.25 18:20:15 MST
fjournal: Communications of the ACM
keywords: floating-point arithmetic; number base conversion
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Lynn Yarbrough
rawtitle: Precision calculations of $e$ and $ \pi $ constants
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
Gives decimal, octal, and hexadecimal values of $e$ and $ pi $ to 100 digits, and notes ``The difficulty arises because assemblers and compilers are hardly ever designed to convert decimal constants to a precision of more than a dozen or so digits. Thus, if calculations to greater precision are to be done, constants usually must be input in octal or other binary-derived representation.''. Cited in cite Sterbenz:1974:FPC.

entry:
@Article{Yarbrough:1967:PCC,
  author =       "Lynn Yarbrough",
  title =        "Precision calculations of $e$ and $ \pi $ constants",
  journal =      j-CACM,
  volume =       "10",
  number =       "9",
  pages =        "537--537",
  month =        sep,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363566.363578",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; number base conversion",
  remark =       "Gives decimal, octal, and hexadecimal values of $e$
                 and $ \pi $ to 100 digits, and notes ``The difficulty
                 arises because assemblers and compilers are hardly ever
                 designed to convert decimal constants to a precision of
                 more than a dozen or so digits. Thus, if calculations
                 to greater precision are to be done, constants usually
                 must be input in octal or other binary-derived
                 representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:1968:ISA
author: Anonymous
title: Index by Subject to Algorithms, 1960--1968
journal: j-CACM
volume: 11
number: 12
pages: 827--830
month: dec
monthnumber: 12
year: 1968
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sat Oct 30 09:29:34 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 09:29:34 ???
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Anonymous
rawtitle: Index by Subject to Algorithms, 1960--1968
entry:
@Article{Anonymous:1968:ISA,
  author =       "Anonymous",
  title =        "Index by Subject to Algorithms, 1960--1968",
  journal =      j-CACM,
  volume =       "11",
  number =       "12",
  pages =        "827--830",
  month =        dec,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 09:29:34 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: book
filename: elefunt.bib
label: Arsenin:1968:BES
author: V. Ja. (Vasilii Jakovlevich) Arsenin
title: Basic equations and special functions of mathematical physics
publisher: Iliffe
address: London, UK
pages: 7 + 361
year: 1968
ISBN: 0-592-05035-1 OR 0592050351
ISBN13: 978-0-592-05035-5 OR 9780592050355
LCCN: QC20 .A693
bibdate: Sat Oct 30 18:25:22 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 18:25:22 MDT
note: Translation by S. Chomet, Kings College, London of Matematicheskaeiia fizika.
subject: Mathematical physics
acknowledgement: ack-nhfb
rawauthor: V. Ja. (Vasilii Jakovlevich) Arsenin
rawnote: Translation by S. Chomet, Kings College, London of Matematicheska{\"e}i{\`\i}a fizika.
rawtitle: Basic equations and special functions of mathematical physics
entry:
@Book{Arsenin:1968:BES,
  author =       "V. Ja. (Vasilii Jakovlevich) Arsenin",
  title =        "Basic equations and special functions of mathematical
                 physics",
  publisher =    "Iliffe",
  address =      "London, UK",
  pages =        "7 + 361",
  year =         "1968",
  ISBN =         "0-592-05035-1",
  ISBN-13 =      "978-0-592-05035-5",
  LCCN =         "QC20 .A693",
  bibdate =      "Sat Oct 30 18:25:22 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translation by S. Chomet, Kings College, London of
                 Matematicheska{\"e}i{\`\i}a fizika.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematical physics",
}


bibtype: article
filename: elefunt.bib
label: Ascari:1968:LRG
author: A. Ascari and P. G. Novario
journal: j-CALCOLO
volume: 5
number: 1
pages: 162--173
year: 1968
CODEN: CALOBK
DOI: https://doi.org/10.1007/BF02576063
ISSN: 0008-0624 (print), 1126-5434 (electronic) OR 00080624 (print), 11265434 (electronic)
ISSNL: 0008-0624 OR 00080624
bibdate: Mon Aug 24 21:37:24 MDT 2020
bibtimestamp: 2020.08.24 21:37:24 MDT
URL: http://link.springer.com/article/10.1007/BF02576063
fjournal: Calcolo: a quarterly on numerical analysis and theory of computation
language: Italian
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10092
subjectdates: Heinz Rutishauser (30 January 1918--10 November 1970)
rawauthor: A. Ascari and P. G. Novario
title:
L'algoritmo $ Q D $ di Rutishauser e la generazione di funzioni speciali nel calcolo automatico. (Italian) [The $ Q D $ algorithm of Rutishauser and the generation of special functions in automatic calculation]

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
L'algoritmo {$ Q D $} di {Rutishauser} e la generazione di funzioni speciali nel calcolo automatico. ({Italian}) [{The} {$ Q D $} algorithm of {Rutishauser} and the generation of special functions in automatic calculation]

entry:
@Article{Ascari:1968:LRG,
  author =       "A. Ascari and P. G. Novario",
  title =        "L'algoritmo {$ Q D $} di {Rutishauser} e la
                 generazione di funzioni speciali nel calcolo
                 automatico. ({Italian}) [{The} {$ Q D $} algorithm of
                 {Rutishauser} and the generation of special functions
                 in automatic calculation]",
  journal =      j-CALCOLO,
  volume =       "5",
  number =       "1",
  pages =        "162--173",
  month =        "????",
  year =         "1968",
  CODEN =        "CALOBK",
  DOI =          "https://doi.org/10.1007/BF02576063",
  ISSN =         "0008-0624 (print), 1126-5434 (electronic)",
  ISSN-L =       "0008-0624",
  bibdate =      "Mon Aug 24 21:37:24 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02576063",
  acknowledgement = ack-nhfb,
  fjournal =     "Calcolo: a quarterly on numerical analysis and theory
                 of computation",
  journal-URL =  "http://link.springer.com/journal/10092",
  language =     "Italian",
  subject-dates = "Heinz Rutishauser (30 January 1918--10 November
                 1970)",
}


bibtype: book
filename: elefunt.bib
label: Bell:1968:SFS
author: W. W. (William Wallace) Bell
title: Special functions for scientists and engineers
publisher: Van Nostrand
address: London, UK
pages: xiv + 247
year: 1968
LCCN: QA351 .B4
bibdate: Fri Oct 29 21:30:38 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.29 21:30:38 MDT
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: W. W. (William Wallace) Bell
rawtitle: Special functions for scientists and engineers
remark:
Fullerton: Gamma, Beta, Legendre, Bessel, and Hypergeometric functions as well as orthogonal polynomials. Reprinted in cite Bell:2004:SFS.

entry:
@Book{Bell:1968:SFS,
  author =       "W. W. (William Wallace) Bell",
  title =        "Special functions for scientists and engineers",
  publisher =    "Van Nostrand",
  address =      "London, UK",
  pages =        "xiv + 247",
  year =         "1968",
  LCCN =         "QA351 .B4",
  bibdate =      "Fri Oct 29 21:30:38 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: Gamma, Beta, Legendre, Bessel, and
                 Hypergeometric functions as well as orthogonal
                 polynomials. Reprinted in \cite{Bell:2004:SFS}.",
  subject =      "Functions, Special",
}


bibtype: article
filename: elefunt.bib
label: Bergson:1968:ACR
author: A. Bergson
title: Certification of and remark on Algorithm 304 [S15]: Normal curve integral
journal: j-CACM
volume: 11
number: 4
pages: 271--271
month: apr
monthnumber: 4
year: 1968
CODEN: CACMA2
DOI: https://doi.org/10.1145/362991.363048
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:19 MST 2005
bibtimestamp: 2005.11.25 18:20:19 MST
note: See cite Hill:1967:ANCa,Hill:1967:RAS.
fjournal: Communications of the ACM
keywords: probability functions
remark: Fullerton: 50-line Algol Program that is superceded by numerous tt erf routines.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: A. Bergson
rawnote: See \cite{Hill:1967:ANCa,Hill:1967:RAS}.
rawtitle: Certification of and remark on {Algorithm 304} [{S15}]: {Normal} curve integral
entry:
@Article{Bergson:1968:ACR,
  author =       "A. Bergson",
  title =        "Certification of and remark on {Algorithm 304}
                 [{S15}]: {Normal} curve integral",
  journal =      j-CACM,
  volume =       "11",
  number =       "4",
  pages =        "271--271",
  month =        apr,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362991.363048",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:19 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Hill:1967:ANCa,Hill:1967:RAS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
  remark =       "Fullerton: 50-line Algol Program that is superceded by
                 numerous {\tt erf} routines.",
}


bibtype: article
filename: elefunt.bib
label: Bingulac:1968:RAA
author: S. P. Bingulac
title: R68-38 Accurate Analog Computer Generation of Bessel Functions for Large Ranges
journal: j-IEEE-TRANS-COMPUT
volume: C-17
number: 8
pages: 819--819
month: aug
monthnumber: 8
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1968.229133
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 17:40:50 MDT 2011
bibtimestamp: 2011.07.13 17:40:50 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687462
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. P. Bingulac
rawtitle: {R68-38} Accurate Analog Computer Generation of {Bessel} Functions for Large Ranges
entry:
@Article{Bingulac:1968:RAA,
  author =       "S. P. Bingulac",
  title =        "{R68-38} Accurate Analog Computer Generation of
                 {Bessel} Functions for Large Ranges",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "8",
  pages =        "819--819",
  month =        aug,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229133",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687462",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Chiarella:1968:EIR
author: C. Chiarella and A. Reichel
title: On the Evaluation of Integrals Related to the Error Function
journal: j-MATH-COMPUT
volume: 22
number: 101
pages: 137--143
month: jan
monthnumber: 1
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: C. Chiarella and A. Reichel
rawtitle: On the Evaluation of Integrals Related to the Error Function
entry:
@Article{Chiarella:1968:EIR,
  author =       "C. Chiarella and A. Reichel",
  title =        "On the Evaluation of Integrals Related to the Error
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "137--143",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Cody:1968:RCAa
author: W. J. Cody and H. C. Thacher, Jr.
title: Rational Chebyshev approximations for the exponential integral $ E_1 (x) $
journal: j-MATH-COMPUT
volume: 22
number: 103
pages: 641--649
month: jul
monthnumber: 7
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.25
MRnumber: 38\#6745
bibdate: Wed Jan 17 08:57:34 1996
bibtimestamp: 1996.01.17 08:57:34 ???
fjournal: Mathematics of Computation
remark: Fullerton: Relative errors down to $ 10^-21 $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody and H. C. {Thacher, Jr.}
rawtitle: Rational {Chebyshev} approximations for the exponential integral {$ E_1 (x) $}
entry:
@Article{Cody:1968:RCAa,
  author =       "W. J. Cody and H. C. {Thacher, Jr.}",
  title =        "Rational {Chebyshev} approximations for the
                 exponential integral {$ E_1 (x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "641--649",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "38\#6745",
  bibdate =      "Wed Jan 17 08:57:34 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 10^{-21} $.",
}


bibtype: article
filename: elefunt.bib
label: Dean:1968:GRB
author: K. J. Dean
title: Generator for the reciprocals of binary numbers
journal: j-PROC-IEE
volume: 115
number: 6
pages: 787
month: jun
monthnumber: 6
year: 1968
CODEN: PIEEAH
DOI: https://doi.org/10.1049/piee.1968.0142
ISSN: 0020-3270 (print), 2053-7891 (electronic) OR 00203270 (print), 20537891 (electronic)
ISSNL: 0020-3270 OR 00203270
bibdate: Thu Apr 10 13:07:02 2025
bibtimestamp: 2025.04.10 13:07:02 ???
fjournal: Proceedings of the Institution of Electrical Engineers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5247218
rawauthor: K. J. Dean
rawtitle: Generator for the reciprocals of binary numbers
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Dean:1968:GRB,
  author =       "K. J. Dean",
  title =        "Generator for the reciprocals of binary numbers",
  journal =      j-PROC-IEE,
  volume =       "115",
  number =       "6",
  pages =        "787",
  month =        jun,
  year =         "1968",
  CODEN =        "PIEEAH",
  DOI =          "https://doi.org/10.1049/piee.1968.0142",
  ISSN =         "0020-3270 (print), 2053-7891 (electronic)",
  ISSN-L =       "0020-3270",
  bibdate =      "Thu Apr 10 13:07:02 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Institution of Electrical
                 Engineers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5247218",
}


bibtype: article
filename: elefunt.bib
label: Dorrer:1968:ADS
author: Egon Dorrer
title: Algorithm 322: $F$-Distribution [S14]
journal: j-CACM
volume: 11
number: 2
pages: 116--117
month: feb
monthnumber: 2
year: 1968
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:18 MST 2005
bibtimestamp: 2005.11.25 18:20:18 MST
fjournal: Communications of the ACM
remark: Fullerton: 50-line Algol Program.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Egon Dorrer
rawtitle: {Algorithm 322}: {$F$}-Distribution [{S14}]
entry:
@Article{Dorrer:1968:ADS,
  author =       "Egon Dorrer",
  title =        "{Algorithm 322}: {$F$}-Distribution [{S14}]",
  journal =      j-CACM,
  volume =       "11",
  number =       "2",
  pages =        "116--117",
  month =        feb,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:18 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: 50-line Algol Program.",
}


bibtype: book
filename: elefunt.bib
label: Fike:1968:CEM
author: C. T. Fike
title: Computer Evaluation of Mathematical Functions
publisher: pub-PH
address: pub-PH:adr
pages: xii + 227
year: 1968
LCCN: QA297 .F5
bibdate: Thu Sep 1 10:12:51 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:12:51 ???
acknowledgement: ack-nj
rawauthor: C. T. Fike
rawtitle: Computer Evaluation of Mathematical Functions
entry:
@Book{Fike:1968:CEM,
  author =       "C. T. Fike",
  title =        "Computer Evaluation of Mathematical Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 227",
  year =         "1968",
  LCCN =         "QA297 .F5",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Fleckner:1968:MCF
author: Oscar L. Fleckner
title: A Method for the Computation of the Fresnel Integrals and Related Functions
journal: j-MATH-COMPUT
volume: 22
number: 103
pages: 635--640
month: jul
monthnumber: 7
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Oscar L. Fleckner
rawtitle: A Method for the Computation of the {Fresnel} Integrals and Related Functions
entry:
@Article{Fleckner:1968:MCF,
  author =       "Oscar L. Fleckner",
  title =        "A Method for the Computation of the {Fresnel}
                 Integrals and Related Functions",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "635--640",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Fox:1968:CPN
author: L. Fox and I. B. Parker
title: Chebyshev Polynomials in Numerical Analysis
publisher: pub-OXFORD
address: pub-OXFORD:adr
pages: ix + 205
year: 1968
ISBN: 0-19-859614-6 OR 0198596146
ISBN13: 978-0-19-859614-1 OR 9780198596141
LCCN: QA297 .F65
MRclass: 65.10
MRnumber: 228149
MRreviewer: G. N. Lance
bibdate: Mon Nov 13 14:02:18 2023
bibtimestamp: 2023.11.13 14:02:18 ???
note: Reprinted in 1972 with corrections, but same ISBN.
series: Oxford mathematical handbooks
subject: Chebyshev polynomials; Numerical analysis
TOC: TO DO: find this!
acknowledgement: ack-nhfb
authordates: Leslie Fox (30 September 1918--1 August 1992)
rawauthor: L. Fox and I. B. Parker
rawnote: Reprinted in 1972 with corrections, but same ISBN.
rawtitle: {Chebyshev} Polynomials in Numerical Analysis
rawTOC: TO DO: find this!
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; z3950.loc.gov:7090/Voyager

entry:
@Book{Fox:1968:CPN,
  author =       "L. Fox and I. B. Parker",
  title =        "{Chebyshev} Polynomials in Numerical Analysis",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "ix + 205",
  year =         "1968",
  ISBN =         "0-19-859614-6",
  ISBN-13 =      "978-0-19-859614-1",
  LCCN =         "QA297 .F65",
  MRclass =      "65.10",
  MRnumber =     "228149",
  MRreviewer =   "G. N. Lance",
  bibdate =      "Mon Nov 13 14:02:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Reprinted in 1972 with corrections, but same ISBN.",
  series =       "Oxford mathematical handbooks",
  acknowledgement = ack-nhfb,
  author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
  mynote =       "JRUL: 517",
  series-editor = "John Crank and C. C. Ritchie",
  subject =      "Chebyshev polynomials; Numerical analysis",
  tableofcontents = "TO DO: find this!",
  xxauthor =     "L. (Leslie) Fox and I. B. (Ian Bax) Parker",
}


bibtype: article
filename: elefunt.bib
label: Galant:1968:HAG
author: D. C. Galant and P. F. Byrd
journal: j-MATH-COMPUT
volume: 22
number: 104
pages: 885--887
month: oct
monthnumber: 10
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: D. C. Galant and P. F. Byrd
title:
High Accuracy Gamma Function Values for Some Rational Arguments (in Technical Notes and Short Papers)

rawtitle:
High Accuracy Gamma Function Values for Some Rational Arguments (in {Technical Notes and Short Papers})

entry:
@Article{Galant:1968:HAG,
  author =       "D. C. Galant and P. F. Byrd",
  title =        "High Accuracy Gamma Function Values for Some Rational
                 Arguments (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "104",
  pages =        "885--887",
  month =        oct,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Hart:1968:CAa
title: Computer Approximations
publisher: pub-R-E-KRIEGER
address: pub-R-E-KRIEGER:adr
pages: x + 343
year: 1968
ISBN: 0-88275-642-7 OR 0882756427
ISBN13: 978-0-88275-642-4 OR 9780882756424
LCCN: QA 297 C64 1978
bibdate: Tue Dec 14 22:55:11 1993
bibtimestamp: 1993.12.14 22:55:11 ???
note: Reprinted 1978 with corrections.
acknowledgement: ack-nhfb
rawnote: Reprinted 1978 with corrections.
rawtitle: Computer Approximations
author:
John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. Thatcher, Jr. and Christoph Witzgall

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

TOC:
1: The Design of a Function Subroutine / 1 1.1 Introduction / 1 1.2 General Considerations in Writing a Function Subroutine / 2 1.3 Relation of the Function Subroutine to the Computer System / 3 1.4 The Three Main Types of Function Subroutine / 4 1.5 Special Programming Techniques / 7 1.6 Subroutine Errors / 7 1.7 Final Steps / 9 2: General Methods of Computing Functions / 10 2.1 Introduction / 10 2.2 Application of Infinite Expansions / 11 2.3 Recurrence and Difference Relations / 23 2.4 Iterative Techniques / 27 2.5 Integral Representations / 28 2.6 Differential Equations / 29 2.7 Tabular Data / 32 2.8 Convergence Acceleration / 33 3: Least Maximum Approximations / 42 3.1 Introduction / 42 3.2 Properties of Least Maximum Approximations / 43 3.3 Nearly Least Maximum Approximations / 46 3.4 Rational Approximation / 51 3.5 Segmented Approximation / 54 3.6 Computation of the Tables / 55 4: The Choice and Application of Approximations / 58 4.1 Introduction / 5 8 4.2 Domain Considerations / 58 4.3 Machine Considerations / 62 4.4 Conditioning of Approximations / 65 4.5 Polynomial Forms / 67 4.6 Rational Forms / 73 4.7 Transformation Algorithms / 78 5: Description and Use of the Tables / 82 5.1 Introduction / 22 5.2 Function Notes / 82 5.3 Accuracy of the Coefficients / 83 5.4 How to Use the Tables / 86 5.5 Preparation of the Tables / 88 6: Function Notes / 89 6.1 Square Root, Cube Root / 89 6.2 Exponential and Hyperbolic Functions / 96 6.3 The Logarithm Function / 105 6.4 Trigonometric Functions / 112 6.5 The Inverse Trigonometric Functions / 120 6.6 The Gamma Function and Its Logarithm / 130 6.7 The Error Function / 136 6.8 Bessel Functions / 141 6.9 Complete Elliptic Integrals / 150 7: Tables of Coefficients / 155 Appendix A Conversion Algorithms / 307 Appendix B Bibliography of Approximations / 313 Appendix C Decimal and Octal Constants / 333 References / 336 Index / 341

rawauthor:
John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. {Thatcher, Jr.} and Christoph Witzgall

shortTOC:
1: The Design of a Function Subroutine / 1 2: General Methods of Computing Functions / 10 3: Least Maximum Approximations / 42 4: The Choice and Application of Approximations / 58 5: Description and Use of the Tables / 82 6: Function Notes / 89 7: Tables of Coefficients / 155 Appendix A: Conversion Algorithms / 307 Appendix B: Bibliography of Approximations / 313 Appendix C: Decimal and Octal Constants / 333 References / 336 Index / 341

rawshortTOC:
1: The Design of a Function Subroutine / 1 \\ 2: General Methods of Computing Functions / 10 \\ 3: Least Maximum Approximations / 42 \\ 4: The Choice and Application of Approximations / 58 \\ 5: Description and Use of the Tables / 82 \\ 6: Function Notes / 89 \\ 7: Tables of Coefficients / 155 \\ Appendix A: Conversion Algorithms / 307 \\ Appendix B: Bibliography of Approximations / 313 \\ Appendix C: Decimal and Octal Constants / 333 \\ References / 336 \\ Index / 341

rawTOC:
1: The Design of a Function Subroutine / 1 \\ 1.1 Introduction / 1 \\ 1.2 General Considerations in Writing a Function Subroutine / 2 \\ 1.3 Relation of the Function Subroutine to the Computer System / 3 \\ 1.4 The Three Main Types of Function Subroutine / 4 \\ 1.5 Special Programming Techniques / 7 \\ 1.6 Subroutine Errors / 7 \\ 1.7 Final Steps / 9 \\ 2: General Methods of Computing Functions / 10 \\ 2.1 Introduction / 10 \\ 2.2 Application of Infinite Expansions / 11 \\ 2.3 Recurrence and Difference Relations / 23 \\ 2.4 Iterative Techniques / 27 \\ 2.5 Integral Representations / 28 \\ 2.6 Differential Equations / 29 \\ 2.7 Tabular Data / 32 \\ 2.8 Convergence Acceleration / 33 \\ 3: Least Maximum Approximations / 42 \\ 3.1 Introduction / 42 \\ 3.2 Properties of Least Maximum Approximations / 43 \\ 3.3 Nearly Least Maximum Approximations / 46 \\ 3.4 Rational Approximation / 51 \\ 3.5 Segmented Approximation / 54 \\ 3.6 Computation of the Tables / 55 \\ 4: The Choice and Application of Approximations / 58 \\ 4.1 Introduction / 5 8 \\ 4.2 Domain Considerations / 58 \\ 4.3 Machine Considerations / 62 \\ 4.4 Conditioning of Approximations / 65 \\ 4.5 Polynomial Forms / 67 \\ 4.6 Rational Forms / 73 \\ 4.7 Transformation Algorithms / 78 \\ 5: Description and Use of the Tables / 82 \\ 5.1 Introduction / 22 \\ 5.2 Function Notes / 82 \\ 5.3 Accuracy of the Coefficients / 83 \\ 5.4 How to Use the Tables / 86 \\ 5.5 Preparation of the Tables / 88 \\ 6: Function Notes / 89 \\ 6.1 Square Root, Cube Root / 89 \\ 6.2 Exponential and Hyperbolic Functions / 96 \\ 6.3 The Logarithm Function / 105 \\ 6.4 Trigonometric Functions / 112 \\ 6.5 The Inverse Trigonometric Functions / 120 \\ 6.6 The Gamma Function and Its Logarithm / 130 \\ 6.7 The Error Function / 136 \\ 6.8 Bessel Functions / 141 \\ 6.9 Complete Elliptic Integrals / 150 \\ 7: Tables of Coefficients / 155 \\ Appendix A Conversion Algorithms / 307 \\ Appendix B Bibliography of Approximations / 313 \\ Appendix C Decimal and Octal Constants / 333 \\ References / 336 \\ Index / 341

entry:
@Book{Hart:1968:CAa,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-88275-642-7",
  ISBN-13 =      "978-0-88275-642-4",
  LCCN =         "QA 297 C64 1978",
  bibdate =      "Tue Dec 14 22:55:11 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Reprinted 1978 with corrections.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
                 2: General Methods of Computing Functions / 10 \\
                 3: Least Maximum Approximations / 42 \\
                 4: The Choice and Application of Approximations / 58
                 \\
                 5: Description and Use of the Tables / 82 \\
                 6: Function Notes / 89 \\
                 7: Tables of Coefficients / 155 \\
                 Appendix A: Conversion Algorithms / 307 \\
                 Appendix B: Bibliography of Approximations / 313 \\
                 Appendix C: Decimal and Octal Constants / 333 \\
                 References / 336 \\
                 Index / 341",
  tableofcontents = "1: The Design of a Function Subroutine / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 General Considerations in Writing a Function
                 Subroutine / 2 \\
                 1.3 Relation of the Function Subroutine to the Computer
                 System / 3 \\
                 1.4 The Three Main Types of Function Subroutine / 4 \\
                 1.5 Special Programming Techniques / 7 \\
                 1.6 Subroutine Errors / 7 \\
                 1.7 Final Steps / 9 \\
                 2: General Methods of Computing Functions / 10 \\
                 2.1 Introduction / 10 \\
                 2.2 Application of Infinite Expansions / 11 \\
                 2.3 Recurrence and Difference Relations / 23 \\
                 2.4 Iterative Techniques / 27 \\
                 2.5 Integral Representations / 28 \\
                 2.6 Differential Equations / 29 \\
                 2.7 Tabular Data / 32 \\
                 2.8 Convergence Acceleration / 33 \\
                 3: Least Maximum Approximations / 42 \\
                 3.1 Introduction / 42 \\
                 3.2 Properties of Least Maximum Approximations / 43 \\
                 3.3 Nearly Least Maximum Approximations / 46 \\
                 3.4 Rational Approximation / 51 \\
                 3.5 Segmented Approximation / 54 \\
                 3.6 Computation of the Tables / 55 \\
                 4: The Choice and Application of Approximations / 58
                 \\
                 4.1 Introduction / 5 8 \\
                 4.2 Domain Considerations / 58 \\
                 4.3 Machine Considerations / 62 \\
                 4.4 Conditioning of Approximations / 65 \\
                 4.5 Polynomial Forms / 67 \\
                 4.6 Rational Forms / 73 \\
                 4.7 Transformation Algorithms / 78 \\
                 5: Description and Use of the Tables / 82 \\
                 5.1 Introduction / 22 \\
                 5.2 Function Notes / 82 \\
                 5.3 Accuracy of the Coefficients / 83 \\
                 5.4 How to Use the Tables / 86 \\
                 5.5 Preparation of the Tables / 88 \\
                 6: Function Notes / 89 \\
                 6.1 Square Root, Cube Root / 89 \\
                 6.2 Exponential and Hyperbolic Functions / 96 \\
                 6.3 The Logarithm Function / 105 \\
                 6.4 Trigonometric Functions / 112 \\
                 6.5 The Inverse Trigonometric Functions / 120 \\
                 6.6 The Gamma Function and Its Logarithm / 130 \\
                 6.7 The Error Function / 136 \\
                 6.8 Bessel Functions / 141 \\
                 6.9 Complete Elliptic Integrals / 150 \\
                 7: Tables of Coefficients / 155 \\
                 Appendix A Conversion Algorithms / 307 \\
                 Appendix B Bibliography of Approximations / 313 \\
                 Appendix C Decimal and Octal Constants / 333 \\
                 References / 336 \\
                 Index / 341",
}


bibtype: book
filename: elefunt.bib
label: Hart:1968:CAb
title: Computer Approximations
publisher: pub-WILEY
address: pub-WILEY:adr
pages: x + 343
year: 1968
ISBN: 0-471-35630-1 OR 0471356301
ISBN13: 978-0-471-35630-1 OR 9780471356301
LCCN: QA297 .C64
bibdate: Sat Jan 14 14:53:06 2006
bibtimestamp: 2006.01.14 14:53:06 ???
series: The SIAM series in applied mathematics
acknowledgement: ack-nhfb
rawtitle: Computer Approximations
author:
John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. Thatcher, Jr. and Christoph Witzgall

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawauthor:
John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. {Thatcher, Jr.} and Christoph Witzgall

entry:
@Book{Hart:1968:CAb,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-471-35630-1",
  ISBN-13 =      "978-0-471-35630-1",
  LCCN =         "QA297 .C64",
  bibdate =      "Sat Jan 14 14:53:06 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "The SIAM series in applied mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1968:ADS
author: K. S. Kolbig
title: Algorithm 327: Dilogarithm [S22]
journal: j-CACM
volume: 11
number: 4
pages: 270--271
month: apr
monthnumber: 4
year: 1968
CODEN: CACMA2
DOI: https://doi.org/10.1145/362991.363043
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:19 MST 2005
bibtimestamp: 2005.11.25 18:20:19 MST
fjournal: Communications of the ACM
keywords: $d(x) = int _0^x (ln |1-y|/y)dy$; dilogarithm; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: K. S. K{\"o}lbig
rawtitle: {Algorithm 327}: {Dilogarithm} [{S22}]
entry:
@Article{Kolbig:1968:ADS,
  author =       "K. S. K{\"o}lbig",
  title =        "{Algorithm 327}: {Dilogarithm} [{S22}]",
  journal =      j-CACM,
  volume =       "11",
  number =       "4",
  pages =        "270--271",
  month =        apr,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362991.363043",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:19 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$d(x) = \int_0^x (\ln|1-y|/y)\,dy$; dilogarithm;
                 special functions",
}


bibtype: article
filename: elefunt.bib
label: Luke:1968:AEI
author: Yudell L. Luke
title: Approximations for Elliptic Integrals
journal: j-MATH-COMPUT
volume: 22
number: 103
pages: 627--634
month: jul
monthnumber: 7
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Yudell L. Luke
rawtitle: Approximations for Elliptic Integrals
entry:
@Article{Luke:1968:AEI,
  author =       "Yudell L. Luke",
  title =        "Approximations for Elliptic Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "627--634",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: MacLaren:1968:RAP
author: M. D. MacLaren
title: Remark on Algorithm 272: Procedure for the normal distribution functions
journal: j-CACM
volume: 11
number: 7
pages: 498--498
month: jul
monthnumber: 7
year: 1968
CODEN: CACMA2
DOI: https://doi.org/10.1145/363397.363553
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:20 MST 2005
bibtimestamp: 2005.11.25 18:20:20 MST
note: See cite MacLaren:1965:APN.
fjournal: Communications of the ACM
keywords: probability functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: M. D. MacLaren
rawnote: See \cite{MacLaren:1965:APN}.
rawtitle: Remark on {Algorithm 272}: {Procedure} for the normal distribution functions
entry:
@Article{MacLaren:1968:RAP,
  author =       "M. D. MacLaren",
  title =        "Remark on {Algorithm 272}: {Procedure} for the normal
                 distribution functions",
  journal =      j-CACM,
  volume =       "11",
  number =       "7",
  pages =        "498--498",
  month =        jul,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363397.363553",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:20 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{MacLaren:1965:APN}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
}


bibtype: article
filename: elefunt.bib
label: Mavromatis:1968:IFP
author: H. A. Mavromatis and K. Schilcher
title: Inverse Functions of the Products of Two Bessel Functions and Applications to Potential Scattering
journal: j-J-MATH-PHYS
volume: 9
number: 10
pages: 1627--1632
month: oct
monthnumber: 10
year: 1968
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.1664492
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Oct 28 11:55:17 MDT 2011
bibtimestamp: 2011.10.28 11:55:17 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v9/i10/p1627_s1
fjournal: Journal of Mathematical Physics
keywords: functions; mathematics; scattering
acknowledgement: ack-nhfb
corpsource: Dept. Physics, American Univ. Beirut, Lebanon
journalURL: http://jmp.aip.org/
onlinedate: 28 October 2003
rawauthor: H. A. Mavromatis and K. Schilcher
ISSN:
0022-2488 (print), 1089-7658 (electronic), 1527-2427 OR 00222488 (print), 10897658 (electronic), 15272427

bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib

rawtitle:
Inverse Functions of the Products of Two {Bessel} Functions and Applications to Potential Scattering

entry:
@Article{Mavromatis:1968:IFP,
  author =       "H. A. Mavromatis and K. Schilcher",
  title =        "Inverse Functions of the Products of Two {Bessel}
                 Functions and Applications to Potential Scattering",
  journal =      j-J-MATH-PHYS,
  volume =       "9",
  number =       "10",
  pages =        "1627--1632",
  month =        oct,
  year =         "1968",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1664492",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 11:55:17 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v9/i10/p1627_s1",
  acknowledgement = ack-nhfb,
  classification = "A0380 (General theory of scattering)",
  corpsource =   "Dept. Physics, American Univ. Beirut, Lebanon",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "functions; mathematics; scattering",
  onlinedate =   "28 October 2003",
  pagecount =    "6",
}


bibtype: article
filename: elefunt.bib
label: Mechel:1968:IRT
author: Fr. Mechel
journal: j-MATH-COMPUT
volume: 22
number: 101
pages: 202--205
month: jan
monthnumber: 1
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Fr. Mechel
title:
Improvement in Recurrence Techniques for the Computation of Bessel Functions of Integral Order (in Technical Notes and Short Papers)

rawtitle:
Improvement in Recurrence Techniques for the Computation of {Bessel} Functions of Integral Order (in {Technical Notes and Short Papers})

entry:
@Article{Mechel:1968:IRT,
  author =       "Fr. Mechel",
  title =        "Improvement in Recurrence Techniques for the
                 Computation of {Bessel} Functions of Integral Order (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "202--205",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Miller:1968:LTS
author: Willard Miller
title: Lie theory and special functions
volume: 43
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xv + 338
year: 1968
ISBN: 0-12-497450-3 OR 0124974503
ISBN13: 978-0-12-497450-0 OR 9780124974500
LCCN: QA387 .M55 1968eb
bibdate: Sat Oct 30 19:07:04 MDT 2010
bibsource: catalog.library.cornell.edu:7090/voyager; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:07:04 MDT
series: Mathematics in science and engineering
remark: Reprinted 1979 with same ISBN.
subject: Lie groups; Functions, Special
acknowledgement: ack-nhfb
rawauthor: Willard Miller
rawtitle: {Lie} theory and special functions
entry:
@Book{Miller:1968:LTS,
  author =       "Willard Miller",
  title =        "{Lie} theory and special functions",
  volume =       "43",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 338",
  year =         "1968",
  ISBN =         "0-12-497450-3",
  ISBN-13 =      "978-0-12-497450-0",
  LCCN =         "QA387 .M55 1968eb",
  bibdate =      "Sat Oct 30 19:07:04 MDT 2010",
  bibsource =    "catalog.library.cornell.edu:7090/voyager;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics in science and engineering",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted 1979 with same ISBN.",
  subject =      "Lie groups; Functions, Special",
}


bibtype: article
filename: elefunt.bib
label: Nagashima:1968:EFN
author: Takashi Nagashima
title: On elementary functions of natural numbers
journal: Hitotsubashi J. Arts Sci.
volume: 9
pages: 50--58
year: 1968
ISSN: 0073-2788 OR 00732788
MRclass: 02.72
MRnumber: MR0232678 (38 \#1001)
MRreviewer: R. L. Goodstein
bibdate: Mon Oct 24 11:33:08 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:33:08 ???
fjournal: Hitotsubashi Journal of Arts &amp; Sciences
acknowledgement: ack-nhfb
rawauthor: Takashi Nagashima
rawtitle: On elementary functions of natural numbers
entry:
@Article{Nagashima:1968:EFN,
  author =       "Takashi Nagashima",
  title =        "On elementary functions of natural numbers",
  journal =      "Hitotsubashi J. Arts Sci.",
  volume =       "9",
  pages =        "50--58",
  year =         "1968",
  ISSN =         "0073-2788",
  MRclass =      "02.72",
  MRnumber =     "MR0232678 (38 \#1001)",
  MRreviewer =   "R. L. Goodstein",
  bibdate =      "Mon Oct 24 11:33:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Hitotsubashi Journal of Arts \&amp; Sciences",
}


bibtype: article
filename: elefunt.bib
label: Ng:1968:DSS
author: Edward W. Ng
title: On the direct summation of series involving higher transcendental functions
journal: j-J-COMPUT-PHYS
volume: 3
number: 2
pages: 334--338
month: oct
monthnumber: 10
year: 1968
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(68)90029-6
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 08:28:02 MST 2012
bibtimestamp: 2012.01.01 08:28:02 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999168900296
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Edward W. Ng
rawtitle: On the direct summation of series involving higher transcendental functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib

entry:
@Article{Ng:1968:DSS,
  author =       "Edward W. Ng",
  title =        "On the direct summation of series involving higher
                 transcendental functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "3",
  number =       "2",
  pages =        "334--338",
  month =        oct,
  year =         "1968",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(68)90029-6",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 08:28:02 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999168900296",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: OBrien:1968:CAC
author: William M. O'Brien and Joan Wood
title: Certification of Algorithm 299 [S15]: Chi-squared integral
journal: j-CACM
volume: 11
number: 4
pages: 271--271
month: apr
monthnumber: 4
year: 1968
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:19 MST 2005
bibtimestamp: 2005.11.25 18:20:19 MST
fjournal: Communications of the ACM
keywords: chi-squared; probability functions
remark: Fullerton: Corrections to an Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: William M. O'Brien and Joan Wood
rawtitle: Certification of {Algorithm 299} [{S15}]: {Chi-squared} integral
entry:
@Article{OBrien:1968:CAC,
  author =       "William M. O'Brien and Joan Wood",
  title =        "Certification of {Algorithm 299} [{S15}]:
                 {Chi-squared} integral",
  journal =      j-CACM,
  volume =       "11",
  number =       "4",
  pages =        "271--271",
  month =        apr,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:19 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "chi-squared; probability functions",
  remark =       "Fullerton: Corrections to an Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Osborn:1968:IBF
author: David Osborn and Richard Madey
title: The Incomplete Beta Function and its Ratio to the Complete Beta Function
journal: j-MATH-COMPUT
volume: 22
number: 101
pages: 159--162
month: jan
monthnumber: 1
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: David Osborn and Richard Madey
rawtitle: The Incomplete Beta Function and its Ratio to the Complete Beta Function
entry:
@Article{Osborn:1968:IBF,
  author =       "David Osborn and Richard Madey",
  title =        "The Incomplete Beta Function and its Ratio to the
                 Complete Beta Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "159--162",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Richardson:1968:SUP
author: Daniel Richardson
title: Some Undecidable Problems Involving Elementary Functions of a Real Variable
journal: j-J-SYMBOLIC-LOGIC
volume: 33
number: 4
pages: 514--520
month: dec
monthnumber: 12
year: 1968
CODEN: JSYLA6
ISSN: 0022-4812 (print), 1943-5886 (electronic) OR 00224812 (print), 19435886 (electronic)
ISSNL: 0022-4812 OR 00224812
MRclass: 02.75
MRnumber: 39 #1330
bibdate: Mon May 19 13:04:20 1997
bibtimestamp: 1997.05.19 13:04:20 ???
fjournal: Journal of Symbolic Logic
acknowledgement: ack-nhfb
journalURL: http://projecteuclid.org/euclid.jsl; http://www.jstor.org/journal/jsymboliclogic
rawauthor: Daniel Richardson
rawtitle: Some Undecidable Problems Involving Elementary Functions of a Real Variable
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Richardson:1968:SUP,
  author =       "Daniel Richardson",
  title =        "Some Undecidable Problems Involving Elementary
                 Functions of a Real Variable",
  journal =      j-J-SYMBOLIC-LOGIC,
  volume =       "33",
  number =       "4",
  pages =        "514--520",
  month =        dec,
  year =         "1968",
  CODEN =        "JSYLA6",
  ISSN =         "0022-4812 (print), 1943-5886 (electronic)",
  ISSN-L =       "0022-4812",
  MRclass =      "02.75",
  MRnumber =     "39 #1330",
  bibdate =      "Mon May 19 13:04:20 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Logic",
  journal-URL =  "http://projecteuclid.org/euclid.jsl;
                 http://www.jstor.org/journal/jsymboliclogic",
}


bibtype: article
filename: elefunt.bib
label: Schmidt:1968:AEK
author: Jochen W. Schmidt
journal: j-NUM-MATH
volume: 11
number: 1
pages: 53--56
month: jan
monthnumber: 1
year: 1968
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 16:12:48 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.17 16:12:48 MDT
fjournal: Numerische Mathematik
keywords: convergence acceleration
language: German
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Jochen W. Schmidt
title:
Asymptotische Einschliess ung bei konvergenzbeschleunigenden Verfahren. II. (German) [Asymptotic enclosure with convergence acceleration method. II]

rawtitle:
{Asymptotische Einschlie{\ss}ung bei konvergenzbeschleunigenden Verfahren. II}. ({German}) [{Asymptotic enclosure with convergence acceleration method. II}]

entry:
@Article{Schmidt:1968:AEK,
  author =       "Jochen W. Schmidt",
  title =        "{Asymptotische Einschlie{\ss}ung bei
                 konvergenzbeschleunigenden Verfahren. II}. ({German})
                 [{Asymptotic enclosure with convergence acceleration
                 method. II}]",
  journal =      j-NUM-MATH,
  volume =       "11",
  number =       "1",
  pages =        "53--56",
  month =        jan,
  year =         "1968",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Strecok:1968:CIE
author: Anthony J. Strecok
title: On the Calculation of the Inverse of the Error Function
journal: j-MATH-COMPUT
volume: 22
number: 101
pages: 144--158
month: jan
monthnumber: 1
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.jstor.org/stable/2004772
fjournal: Mathematics of Computation
remark: Fullerton: 18-digit approximations.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Anthony J. Strecok
rawtitle: On the Calculation of the Inverse of the Error Function
entry:
@Article{Strecok:1968:CIE,
  author =       "Anthony J. Strecok",
  title =        "On the Calculation of the Inverse of the Error
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "144--158",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2004772",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 18-digit approximations.",
}


bibtype: book
filename: elefunt.bib
label: Talman:1968:SFG
author: James D. Talman
title: Special Functions: a Group Theoretic Approach Based on Lectures by Eugene P. Wigner
publisher: pub-BENJAMIN
address: pub-BENJAMIN:adr
pages: xii + 260
year: 1968
bibdate: Sat Oct 30 16:57:02 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 16:57:02 ???
note: With an introduction by Eugene P. Wigner.
series: The mathematical physics monograph series
keywords: group theory; mathematical function; special functions
acknowledgement: ack-nhfb
rawauthor: James D. Talman
rawnote: With an introduction by Eugene P. Wigner.
rawtitle: Special Functions: a Group Theoretic Approach Based on Lectures by {Eugene P. Wigner}
entry:
@Book{Talman:1968:SFG,
  author =       "James D. Talman",
  title =        "Special Functions: a Group Theoretic Approach Based on
                 Lectures by {Eugene P. Wigner}",
  publisher =    pub-BENJAMIN,
  address =      pub-BENJAMIN:adr,
  pages =        "xii + 260",
  year =         "1968",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 16:57:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "With an introduction by Eugene P. Wigner.",
  series =       "The mathematical physics monograph series",
  acknowledgement = ack-nhfb,
  keywords =     "group theory; mathematical function; special
                 functions",
}


bibtype: book
filename: elefunt.bib
label: Tolke:1968:PFA
author: Friedrich Tolke
publisher: pub-SV
address: pub-SV:adr
pages: viii + 158
year: 1968
ISBN: 3-662-11121-7, 3-662-11120-9 OR 3662111217, 3662111209
ISBN13: 978-3-662-11121-5, 978-3-662-11120-8 OR 9783662111215, 9783662111208
bibdate: Mon Feb 13 19:01:10 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.13 19:01:10 ???
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich T{\"o}lke
title:
Praktische Funktionenlehre. 5. Allgemeine Weierstrasssche Funktionen und Ableitungen nach dem Parameter: Integrale der Theta-Funktionen und Bilinear-Entwicklungen. (German) [Practical functional theory. 5. General information on Weierstrass functions and derivatives according to the parameters: integrals of theta functions and bilinear developments]

TOC:
12 Allgemeine Weierstrass sche Funktionen. Doppelreihen-Entwicklungen 13 Die Ableitungen nach dem Parameter und dem Modul 14 Integrale von Theta-Funktionen (D-Funktionen) 15 Mehrdimensionale Theta- und D-Funktionen 16 Theta- und D-Funktionen mit imaginaren Parametern 17 Greensche Funktionen und Bilinear-Entwicklungen

rawtitle:
{Praktische Funktionenlehre. 5. Allgemeine Weierstrasssche Funktionen und Ableitungen nach dem Parameter: Integrale der Theta-Funktionen und Bilinear-Entwicklungen}. ({German}) [{Practical} functional theory. 5. {General} information on {Weierstrass} functions and derivatives according to the parameters: integrals of theta functions and bilinear developments]

rawTOC:
12 Allgemeine Weierstra{\ss}sche Funktionen. Doppelreihen-Entwicklungen \\ 13 Die Ableitungen nach dem Parameter und dem Modul \\ 14 Integrale von Theta-Funktionen (D-Funktionen) \\ 15 Mehrdimensionale Theta- und D-Funktionen \\ 16 Theta- und D-Funktionen mit imagin{\"a}ren Parametern \\ 17 Greensche Funktionen und Bilinear-Entwicklungen

entry:
@Book{Tolke:1968:PFA,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 5. Allgemeine
                 Weierstrasssche Funktionen und Ableitungen nach dem
                 Parameter: Integrale der Theta-Funktionen und
                 Bilinear-Entwicklungen}. ({German}) [{Practical}
                 functional theory. 5. {General} information on
                 {Weierstrass} functions and derivatives according to
                 the parameters: integrals of theta functions and
                 bilinear developments]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 158",
  year =         "1968",
  ISBN =         "3-662-11121-7, 3-662-11120-9",
  ISBN-13 =      "978-3-662-11121-5, 978-3-662-11120-8",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
  tableofcontents = "12 Allgemeine Weierstra{\ss}sche Funktionen.
                 Doppelreihen-Entwicklungen \\
                 13 Die Ableitungen nach dem Parameter und dem Modul \\
                 14 Integrale von Theta-Funktionen (D-Funktionen) \\
                 15 Mehrdimensionale Theta- und D-Funktionen \\
                 16 Theta- und D-Funktionen mit imagin{\"a}ren
                 Parametern \\
                 17 Greensche Funktionen und Bilinear-Entwicklungen",
  xxISBN =       "3-662-11031-8",
  xxISBN-13 =    "978-3-662-11031-7",
}


bibtype: article
filename: elefunt.bib
label: Tooper:1968:SCP
author: Robert F. Tooper and John Mark
journal: j-MATH-COMPUT
volume: 22
number: 102
pages: 448--449
month: apr
monthnumber: 4
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: exponential integral ($operatorname Ei(x)$); hyperbolic sine integral ($operatorname Shi(x)$)
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Robert F. Tooper and John Mark
title:
Simplified Calculation of $ operatorname Ei(x) $ for Positive Arguments, and a Short Table of $ operatorname Shi(x) $ (in Technical Notes and Short Papers)

rawtitle:
Simplified Calculation of {$ \operatorname {Ei}(x) $} for Positive Arguments, and a Short Table of $ \operatorname {Shi}(x) $ (in {Technical Notes and Short Papers})

entry:
@Article{Tooper:1968:SCP,
  author =       "Robert F. Tooper and John Mark",
  title =        "Simplified Calculation of {$ \operatorname {Ei}(x) $}
                 for Positive Arguments, and a Short Table of $
                 \operatorname {Shi}(x) $ (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "102",
  pages =        "448--449",
  month =        apr,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "exponential integral ($\operatorname{Ei}(x)$);
                 hyperbolic sine integral ($\operatorname{Shi}(x)$)",
}


bibtype: article
filename: elefunt.bib
label: Wilcox:1968:ZTN
author: Peter H. Wilcox
journal: j-MATH-COMPUT
volume: 22
number: 101
pages: 205--208
month: jan
monthnumber: 1
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.jstor.org/stable/2004783
fjournal: Mathematics of Computation
remark: Fullerton: $ P_nu ^1 $ are Legendre functions.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Peter H. Wilcox
title:
The Zeros of $ P^1_nu (cos theta ) $ and $ frac partial partial theta P^1_mu (cos theta ) $ (in Technical Notes and Short Papers)

rawtitle:
The Zeros of $ {P}^1_\nu (\cos \theta) $ and $ \frac {\partial }{\partial \theta } {P}^1_\mu (\cos \theta) $ (in {Technical Notes and Short Papers})

entry:
@Article{Wilcox:1968:ZTN,
  author =       "Peter H. Wilcox",
  title =        "The Zeros of $ {P}^1_\nu (\cos \theta) $ and $ \frac
                 {\partial }{\partial \theta } {P}^1_\mu (\cos \theta) $
                 (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "205--208",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2004783",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: $ P_\nu^1 $ are Legendre functions.",
}


bibtype: article
filename: elefunt.bib
label: Wimp:1968:RFH
author: Jet Wimp
title: Recursion Formulae of Hypergeometric Functions
journal: j-MATH-COMPUT
volume: 22
number: 102
pages: 363--373
month: apr
monthnumber: 4
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Jet Wimp
rawtitle: Recursion Formulae of Hypergeometric Functions
entry:
@Article{Wimp:1968:RFH,
  author =       "Jet Wimp",
  title =        "Recursion Formulae of Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "102",
  pages =        "363--373",
  month =        apr,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Witte:1968:AAJ
author: B. F. W. Witte
title: ACM Algorithm 332: Jacobi Polynomials
journal: j-CACM
volume: 11
number: 6
pages: 436--437
month: jun
monthnumber: 6
year: 1968
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 08 09:33:08 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 09:33:08 ???
note: See remark cite Skovgaard:1975:RAJ.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: B. F. W. Witte
rawnote: See remark \cite{Skovgaard:1975:RAJ}.
rawtitle: {ACM Algorithm 332}: {Jacobi} Polynomials
entry:
@Article{Witte:1968:AAJ,
  author =       "B. F. W. Witte",
  title =        "{ACM Algorithm 332}: {Jacobi} Polynomials",
  journal =      j-CACM,
  volume =       "11",
  number =       "6",
  pages =        "436--437",
  month =        jun,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:33:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Skovgaard:1975:RAJ}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: elefunt.bib
label: Wrench:1968:CTS
author: John W. Wrench, Jr.
title: Concerning Two Series for the Gamma Function
journal: j-MATH-COMPUT
volume: 22
number: 103
pages: 617--626
month: jul
monthnumber: 7
year: 1968
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRnumber: MR 0237078 (38:5371)
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: John W. {Wrench, Jr.}
rawtitle: Concerning Two Series for the Gamma Function
entry:
@Article{Wrench:1968:CTS,
  author =       "John W. {Wrench, Jr.}",
  title =        "Concerning Two Series for the Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "617--626",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRnumber =     "MR 0237078 (38:5371)",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Aharoni:1969:C
author: Amikam Aharoni
title: Computation of $ K_p(x) $
journal: j-J-COMPUT-PHYS
volume: 4
number: 2
pages: 270--271
month: aug
monthnumber: 8
year: 1969
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(69)90072-2
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 08:28:03 MST 2012
bibtimestamp: 2012.01.01 08:28:03 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999169900722
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Amikam Aharoni
rawtitle: Computation of {$ K_p(x) $}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib

entry:
@Article{Aharoni:1969:C,
  author =       "Amikam Aharoni",
  title =        "Computation of {$ K_p(x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "4",
  number =       "2",
  pages =        "270--271",
  month =        aug,
  year =         "1969",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(69)90072-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 08:28:03 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999169900722",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Boersma:1969:ECW
author: J. Boersma
title: Expansions for Coulomb Wave Functions
journal: j-MATH-COMPUT
volume: 23
number: 105
pages: 51--59
month: jan
monthnumber: 1
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: J. Boersma
rawtitle: Expansions for {Coulomb} Wave Functions
entry:
@Article{Boersma:1969:ECW,
  author =       "J. Boersma",
  title =        "Expansions for {Coulomb} Wave Functions",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "105",
  pages =        "51--59",
  month =        jan,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Buchholz:1969:CHF
author: Herbert Buchholz
title: The confluent hypergeometric function with special emphasis on its applications
volume: 15
publisher: pub-SV
address: pub-SV:adr
pages: xviii + 238
year: 1969
LCCN: QA351 .B813
bibdate: Sat Oct 30 21:06:31 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:06:31 MDT
series: Springer tracts in natural philosophy
subject: Hypergeometric functions
acknowledgement: ack-nhfb
rawauthor: Herbert Buchholz
rawtitle: The confluent hypergeometric function with special emphasis on its applications
note:
Translation by H. Lichtblau and K. Wetzel to English from German ``Die konfluente hypergeometrische Funktion.''

rawnote:
Translation by H. Lichtblau and K. Wetzel to English from German ``Die konfluente hypergeometrische Funktion.''

entry:
@Book{Buchholz:1969:CHF,
  author =       "Herbert Buchholz",
  title =        "The confluent hypergeometric function with special
                 emphasis on its applications",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xviii + 238",
  year =         "1969",
  LCCN =         "QA351 .B813",
  bibdate =      "Sat Oct 30 21:06:31 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translation by H. Lichtblau and K. Wetzel to English
                 from German ``Die konfluente hypergeometrische
                 Funktion.''",
  series =       "Springer tracts in natural philosophy",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions",
}


bibtype: article
filename: elefunt.bib
label: Bulirsch:1969:EBT
author: R. Bulirsch
title: An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind
journal: j-NUM-MATH
volume: 13
number: 3
pages: 266--284
month: jul
monthnumber: 7
year: 1969
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 19:01:15 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.17 19:01:15 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: R. Bulirsch
rawtitle: An extension of the {Bartky}-transformation to incomplete elliptic integrals of the third kind
entry:
@Article{Bulirsch:1969:EBT,
  author =       "R. Bulirsch",
  title =        "An extension of the {Bartky}-transformation to
                 incomplete elliptic integrals of the third kind",
  journal =      j-NUM-MATH,
  volume =       "13",
  number =       "3",
  pages =        "266--284",
  month =        jul,
  year =         "1969",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Bulirsch:1969:NCE
author: R. Bulirsch
title: Numerical calculation of elliptic integrals and elliptic functions. III
journal: j-NUM-MATH
volume: 13
number: 4
pages: 305--315
month: aug
monthnumber: 8
year: 1969
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 19:01:15 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.17 19:01:15 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: R. Bulirsch
rawtitle: Numerical calculation of elliptic integrals and elliptic functions. {III}
entry:
@Article{Bulirsch:1969:NCE,
  author =       "R. Bulirsch",
  title =        "Numerical calculation of elliptic integrals and
                 elliptic functions. {III}",
  journal =      j-NUM-MATH,
  volume =       "13",
  number =       "4",
  pages =        "305--315",
  month =        aug,
  year =         "1969",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1969:CBE
author: B. C. Carlson
title: A connection between elementary functions and higher transcendental functions
journal: j-SIAM-J-APPL-MATH
volume: 17
pages: 116--148
year: 1969
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
MRclass: 33.20 (30.00)
MRnumber: 40 \#408
MRreviewer: S. K. Bose
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: SIAM Journal on Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siap
rawauthor: B. C. Carlson
rawtitle: A connection between elementary functions and higher transcendental functions
entry:
@Article{Carlson:1969:CBE,
  author =       "B. C. Carlson",
  title =        "A connection between elementary functions and higher
                 transcendental functions",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "17",
  pages =        "116--148",
  year =         "1969",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "33.20 (30.00)",
  MRnumber =     "40 \#408",
  MRreviewer =   "S. K. Bose",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
}


bibtype: inproceedings
filename: elefunt.bib
label: Clark:1969:SCE
author: N. W. Clark and W. J. Cody
title: Self-contained exponentiation
crossref: AFIPS:1969:ACPb
pages: 701--706
year: 1969
bibdate: Wed Sep 07 10:49:33 1994
bibtimestamp: 1994.09.07 10:49:33 ???
acknowledgement: ack-nj
rawauthor: N. W. Clark and W. J. Cody
rawtitle: Self-contained exponentiation
bibsource:
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Clark:1969:SCE,
  author =       "N. W. Clark and W. J. Cody",
  title =        "Self-contained exponentiation",
  crossref =     "AFIPS:1969:ACPb",
  pages =        "701--706",
  year =         "1969",
  bibdate =      "Wed Sep 07 10:49:33 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Clemm:1969:ACV
author: Donald S. Clemm
journal: j-CACM
volume: 12
number: 7
pages: 399--407
month: jul
monthnumber: 7
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:27 MST 2005
bibtimestamp: 2005.11.25 18:20:27 MST
note: See remark cite Frisch:1972:RAR.
fjournal: Communications of the ACM
keywords: differential equations; function evaluation; subroutines
acknowledgement: ack-nhfb
classcodes: C4170 (Differential equations); C7300 (Natural sciences computing)
corpsource: Wright-Patterson Air Force Base, USA
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Donald S. Clemm
rawnote: See remark \cite{Frisch:1972:RAR}.
title:
Algorithm 352: Characteristic Values and Associated Solutions of Mathieu's Differential Equation [S22]

remark:
Fullerton: Long set of FORTRAN routines to evaluate Mathieu functions as well as several Bessel functions.

rawtitle:
{Algorithm 352}: {Characteristic} Values and Associated Solutions of {Mathieu}'s Differential Equation [{S22}]

entry:
@Article{Clemm:1969:ACV,
  author =       "Donald S. Clemm",
  title =        "{Algorithm 352}: {Characteristic} Values and
                 Associated Solutions of {Mathieu}'s Differential
                 Equation [{S22}]",
  journal =      j-CACM,
  volume =       "12",
  number =       "7",
  pages =        "399--407",
  month =        jul,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:27 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Frisch:1972:RAR}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4170 (Differential equations); C7300 (Natural
                 sciences computing)",
  corpsource =   "Wright-Patterson Air Force Base, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "differential equations; function evaluation;
                 subroutines",
  remark =       "Fullerton: Long set of FORTRAN routines to evaluate
                 Mathieu functions as well as several Bessel
                 functions.",
}


bibtype: article
filename: elefunt.bib
label: Cobb:1969:CAS
author: S. M. Cobb
journal: j-CACM
volume: 12
number: 11
pages: 635--636
month: nov
monthnumber: 11
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:28 MST 2005
bibtimestamp: 2005.11.25 18:20:28 MST
fjournal: Communications of the ACM
keywords: associated Legendre functions of the first kind; special functions
remark: Fullerton: Numerous additional corrections and changes to an Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: S. M. Cobb
title:
Certification of Algorithm 47 [S16]: Associated Legendre functions of the first kind for real or imaginary arguments

rawtitle:
Certification of {Algorithm 47} [{S16}]: {Associated} {Legendre} functions of the first kind for real or imaginary arguments

entry:
@Article{Cobb:1969:CAS,
  author =       "S. M. Cobb",
  title =        "Certification of {Algorithm 47} [{S16}]: {Associated}
                 {Legendre} functions of the first kind for real or
                 imaginary arguments",
  journal =      j-CACM,
  volume =       "12",
  number =       "11",
  pages =        "635--636",
  month =        nov,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:28 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "associated Legendre functions of the first kind;
                 special functions",
  remark =       "Fullerton: Numerous additional corrections and changes
                 to an Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Cody:1969:CAE
author: W. J. Cody and Henry C. Thacher, Jr.
title: Chebyshev Approximations for the Exponential Integral $ hbox Ei(x) $
journal: j-MATH-COMPUT
volume: 23
number: 106
pages: 289--303
month: apr
monthnumber: 4
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.25
MRnumber: 39\#3680
bibdate: Wed Jan 17 08:57:33 1996
bibtimestamp: 1996.01.17 08:57:33 ???
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody and Henry C. {Thacher, Jr.}
rawtitle: {Chebyshev} Approximations for the Exponential Integral {$ \hbox {Ei}(x) $}
entry:
@Article{Cody:1969:CAE,
  author =       "W. J. Cody and Henry C. {Thacher, Jr.}",
  title =        "{Chebyshev} Approximations for the Exponential
                 Integral {$ \hbox {Ei}(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "106",
  pages =        "289--303",
  month =        apr,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "39\#3680",
  bibdate =      "Wed Jan 17 08:57:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Cody:1969:CRA
author: W. J. Cody and G. Meinardus and R. S. Varga
journal: j-J-APPROX-THEORY
volume: 2
pages: 50--65
year: 1969
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
MRclass: 65.67 (41.00)
MRnumber: 40\#999
bibdate: Wed Jan 17 08:57:33 1996
bibtimestamp: 1996.01.17 08:57:33 ???
fjournal: Journal of Approximation Theory
acknowledgement: ack-wjc
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: W. J. Cody and G. Meinardus and R. S. Varga
title:
Chebyshev rational approximations to $ e^-x $ on $ [0, infty ) $ and applications to heat conduction problems

rawtitle:
{Chebyshev} rational approximations to $ e^{-x} $ on $ [0, \infty) $ and applications to heat conduction problems

entry:
@Article{Cody:1969:CRA,
  author =       "W. J. Cody and G. Meinardus and R. S. Varga",
  title =        "{Chebyshev} rational approximations to $ e^{-x} $ on $
                 [0, \infty) $ and applications to heat conduction
                 problems",
  journal =      j-J-APPROX-THEORY,
  volume =       "2",
  number =       "??",
  pages =        "50--65",
  month =        "??",
  year =         "1969",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "65.67 (41.00)",
  MRnumber =     "40\#999",
  bibdate =      "Wed Jan 17 08:57:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
}


bibtype: article
filename: elefunt.bib
label: Cody:1969:RCA
author: W. J. Cody
title: Rational Chebyshev Approximations for the Error Function
journal: j-MATH-COMPUT
volume: 23
number: 107
pages: 631--637
month: jul
monthnumber: 7
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody
rawtitle: Rational {Chebyshev} Approximations for the Error Function
entry:
@Article{Cody:1969:RCA,
  author =       "W. J. Cody",
  title =        "Rational {Chebyshev} Approximations for the Error
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "107",
  pages =        "631--637",
  month =        jul,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Farkas:1969:CAS
author: I. Farkas
title: Certification of Algorithm 165 [S21]: Complete elliptic integrals
journal: j-CACM
volume: 12
number: 1
pages: 38--38
month: jan
monthnumber: 1
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:24 MST 2005
bibtimestamp: 2005.11.25 18:20:24 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: I. Farkas
rawtitle: Certification of {Algorithm 165} [{S21}]: {Complete} elliptic integrals
entry:
@Article{Farkas:1969:CAS,
  author =       "I. Farkas",
  title =        "Certification of {Algorithm 165} [{S21}]: {Complete}
                 elliptic integrals",
  journal =      j-CACM,
  volume =       "12",
  number =       "1",
  pages =        "38--38",
  month =        jan,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:24 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1969:ACE
author: Walter Gautschi
title: Algorithm 363: Complex Error Function [S15]
journal: j-CACM
volume: 12
number: 11
pages: 635--635
month: nov
monthnumber: 11
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:28 MST 2005
bibtimestamp: 2005.11.25 18:20:28 MST
note: See certification cite Kolbig:1972:CAC.
fjournal: Communications of the ACM
keywords: $erf (z)$; special functions
remark: Fullerton: 50-line Algol procedure with accuracy to 10 decimal places.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi
rawnote: See certification \cite{Kolbig:1972:CAC}.
rawtitle: {Algorithm 363}: {Complex} Error Function [{S15}]
entry:
@Article{Gautschi:1969:ACE,
  author =       "Walter Gautschi",
  title =        "{Algorithm 363}: {Complex} Error Function [{S15}]",
  journal =      j-CACM,
  volume =       "12",
  number =       "11",
  pages =        "635--635",
  month =        nov,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:28 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Kolbig:1972:CAC}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\erf(z)$; special functions",
  remark =       "Fullerton: 50-line Algol procedure with accuracy to 10
                 decimal places.",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1969:RAS
author: Walter Gautschi
title: Remark on Algorithm 292 [S22]: Regular Coulomb wave functions
journal: j-CACM
volume: 12
number: 5
pages: 280--280
month: may
monthnumber: 5
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:26 MST 2005
bibtimestamp: 2005.11.25 18:20:26 MST
fjournal: Communications of the ACM
keywords: Coulomb wave functions; special functions
remark: Fullerton: The first of many remarks.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi
rawtitle: Remark on {Algorithm 292} [{S22}]: {Regular} {Coulomb} wave functions
entry:
@Article{Gautschi:1969:RAS,
  author =       "Walter Gautschi",
  title =        "Remark on {Algorithm 292} [{S22}]: {Regular} {Coulomb}
                 wave functions",
  journal =      j-CACM,
  volume =       "12",
  number =       "5",
  pages =        "280--280",
  month =        may,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: The first of many remarks.",
}


bibtype: article
filename: elefunt.bib
label: Herman:1969:NHE
author: G. T. Herman
title: A new hierarchy of elementary functions
journal: j-PROC-AM-MATH-SOC
volume: 20
pages: 557--562
year: 1969
CODEN: PAMYAR
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 02.77
MRnumber: 40 \#4110
MRreviewer: G. E. Sacks
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Proceedings of the American Mathematical Society
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/proc
rawauthor: G. T. Herman
rawtitle: A new hierarchy of elementary functions
entry:
@Article{Herman:1969:NHE,
  author =       "G. T. Herman",
  title =        "A new hierarchy of elementary functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "20",
  pages =        "557--562",
  year =         "1969",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "02.77",
  MRnumber =     "40 \#4110",
  MRreviewer =   "G. E. Sacks",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}


bibtype: article
filename: elefunt.bib
label: Holzwarth:1969:VBB
author: A. Holzwarth
journal: j-COMPUTING
volume: 4
number: 2
pages: 168--177
month: jun
monthnumber: 6
year: 1969
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:51 MST 2001
bibtimestamp: 2001.01.02 17:40:51 MST
fjournal: Computing
language: German
acknowledgement: ack-nj
affiliation: Tubingen, West Germany
journalURL: http://link.springer.com/journal/607
rawauthor: A. Holzwarth
title:
Ein Verfahren zur Bestimmung bester Tschebyscheff-Approximationen der Quadratwurzelfunktion. (German) A Method for Determination of Best Chebyshev Approximations to the Square Root Function

bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date)

rawtitle:
{Ein Verfahren zur Bestimmung bester Tscheb\-y\-scheff-Ap\-prox\-i\-ma\-tion\-en der Quadratwurzelfunktion}. ({German}) {A Method for Determination of Best Chebyshev Approximations to the Square Root Function}

entry:
@Article{Holzwarth:1969:VBB,
  author =       "A. Holzwarth",
  title =        "{Ein Verfahren zur Bestimmung bester
                 Tscheb\-y\-scheff-Ap\-prox\-i\-ma\-tion\-en der
                 Quadratwurzelfunktion}. ({German}) {A Method for
                 Determination of Best Chebyshev Approximations to the
                 Square Root Function}",
  journal =      j-COMPUTING,
  volume =       "4",
  number =       "2",
  pages =        "168--177",
  month =        jun,
  year =         "1969",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "T{\"u}bingen, West Germany",
  classification = "C4130",
  description =  "Chebyshev approximation; numerical analysis",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: King:1969:LEN
author: Richard F. King and David L. Phillips
title: The Logarithmic Error and Newton's Method for the Square Root
journal: j-CACM
volume: 12
number: 2
pages: 87--88
month: feb
monthnumber: 2
year: 1969
CODEN: CACMA2
DOI: https://doi.org/10.1145/362848.362861
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.50
MRnumber: 44\#2333
bibdate: Fri Nov 25 18:20:24 MST 2005
bibtimestamp: 2005.11.25 18:20:24 MST
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions; function evaluation; iterative methods
acknowledgement: ack-nj
classcodes: C4120 (Functional analysis)
corpsource: Argonne Nat. Lab., Argonne, IL, USA
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Richard F. King and David L. Phillips
rawtitle: The Logarithmic Error and {Newton}'s Method for the Square Root
abstract:
The problem of obtaining optimal starting values for the calculation of the square root using Newton's method is considered. It has been pointed out elsewhere that if relative error is used as the measure of goodness of fit, optimal results are not obtained when the initial approximation is a best fit. It is shown here that if, instead, the so-called logarithmic error is used, then a best initial fit is optimal for both types of error. Moreover, use of the logarithmic error appears to simplify the problem of determining the optimal initial approximation.

rawabstract:
The problem of obtaining optimal starting values for the calculation of the square root using Newton's method is considered. It has been pointed out elsewhere that if relative error is used as the measure of goodness of fit, optimal results are not obtained when the initial approximation is a best fit. It is shown here that if, instead, the so-called logarithmic error is used, then a best initial fit is optimal for both types of error. Moreover, use of the logarithmic error appears to simplify the problem of determining the optimal initial approximation.

entry:
@Article{King:1969:LEN,
  author =       "Richard F. King and David L. Phillips",
  title =        "The Logarithmic Error and {Newton}'s Method for the
                 Square Root",
  journal =      j-CACM,
  volume =       "12",
  number =       "2",
  pages =        "87--88",
  month =        feb,
  year =         "1969",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362848.362861",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "44\#2333",
  bibdate =      "Fri Nov 25 18:20:24 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The problem of obtaining optimal starting values for
                 the calculation of the square root using Newton's
                 method is considered. It has been pointed out elsewhere
                 that if relative error is used as the measure of
                 goodness of fit, optimal results are not obtained when
                 the initial approximation is a best fit. It is shown
                 here that if, instead, the so-called logarithmic error
                 is used, then a best initial fit is optimal for both
                 types of error. Moreover, use of the logarithmic error
                 appears to simplify the problem of determining the
                 optimal initial approximation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Argonne Nat. Lab., Argonne, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; function evaluation;
                 iterative methods",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1969:CASa
author: K. S. Kolbig
journal: j-CACM
volume: 12
number: 5
pages: 278--279
month: may
monthnumber: 5
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:26 MST 2005
bibtimestamp: 2005.11.25 18:20:26 MST
fjournal: Communications of the ACM
keywords: Coulomb wave functions; special functions
remark: Fullerton: Tests of an Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: K. S. K{\"o}lbig
title:
Certification of Algorithm 292 [S22]: Regular Coulomb wave functions and of remark on Algorithm 292 [S22]: Regular Coulomb wave functions

rawtitle:
Certification of {Algorithm 292} [{S22}]: {Regular} {Coulomb} wave functions and of remark on {Algorithm 292} [{S22}]: {Regular} {Coulomb} wave functions

entry:
@Article{Kolbig:1969:CASa,
  author =       "K. S. K{\"o}lbig",
  title =        "Certification of {Algorithm 292} [{S22}]: {Regular}
                 {Coulomb} wave functions and of remark on {Algorithm
                 292} [{S22}]: {Regular} {Coulomb} wave functions",
  journal =      j-CACM,
  volume =       "12",
  number =       "5",
  pages =        "278--279",
  month =        may,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: Tests of an Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1969:CASb
author: K. S. Kolbig
title: Certification of Algorithm 300 [S22]: Coulomb wave functions
journal: j-CACM
volume: 12
number: 5
pages: 279--280
month: may
monthnumber: 5
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:26 MST 2005
bibtimestamp: 2005.11.25 18:20:26 MST
fjournal: Communications of the ACM
keywords: Coulomb wave functions; special functions
remark: Fullerton: The first of many remarks.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: K. S. K{\"o}lbig
rawtitle: Certification of {Algorithm 300} [{S22}]: {Coulomb} wave functions
entry:
@Article{Kolbig:1969:CASb,
  author =       "K. S. K{\"o}lbig",
  title =        "Certification of {Algorithm 300} [{S22}]: {Coulomb}
                 wave functions",
  journal =      j-CACM,
  volume =       "12",
  number =       "5",
  pages =        "279--280",
  month =        may,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: The first of many remarks.",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1969:RAS
author: K. S. Kolbig
title: Remark on Algorithm 300 [S22]: Coulomb wave functions
journal: j-CACM
volume: 12
number: 12
pages: 692--692
month: dec
monthnumber: 12
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:29 MST 2005
bibtimestamp: 2005.11.25 18:20:29 MST
fjournal: Communications of the ACM
keywords: Coulomb wave functions; special functions
remark: Fullerton: One of many remarks.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: K. S. K{\"o}lbig
rawtitle: Remark on {Algorithm 300} [{S22}]: {Coulomb} wave functions
entry:
@Article{Kolbig:1969:RAS,
  author =       "K. S. K{\"o}lbig",
  title =        "Remark on {Algorithm 300} [{S22}]: {Coulomb} wave
                 functions",
  journal =      j-CACM,
  volume =       "12",
  number =       "12",
  pages =        "692--692",
  month =        dec,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:29 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: One of many remarks.",
}


bibtype: article
filename: elefunt.bib
label: Lardner:1969:RBB
author: Thomas J. Lardner
title: Relations Between $_0 F_3 $ and Bessel Functions
journal: j-SIAM-REVIEW
volume: 11
number: 1
pages: 69--72
year: 1969
CODEN: SIREAD
DOI: https://doi.org/10.1137/1011007
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:06:04 MDT 2014
bibtimestamp: 2014.03.27 09:06:04 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1969
rawauthor: Thomas J. Lardner
rawtitle: Relations Between {${}_0 F_3 $} and {Bessel} Functions
bibsource:
http://epubs.siam.org/toc/siread/11/1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Lardner:1969:RBB,
  author =       "Thomas J. Lardner",
  title =        "Relations Between {${}_0 F_3 $} and {Bessel}
                 Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "11",
  number =       "1",
  pages =        "69--72",
  month =        "????",
  year =         "1969",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1011007",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:04 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/11/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1969",
}


bibtype: article
filename: elefunt.bib
label: Lewis:1969:FII
author: Richard L. Lewis
title: On Finite Integrals Involving Trigonometric, Bessel, and Legendre Functions
journal: j-MATH-COMPUT
volume: 23
number: 106
pages: 259--273
month: apr
monthnumber: 4
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Richard L. Lewis
rawtitle: On Finite Integrals Involving Trigonometric, {Bessel}, and {Legendre} Functions
entry:
@Article{Lewis:1969:FII,
  author =       "Richard L. Lewis",
  title =        "On Finite Integrals Involving Trigonometric, {Bessel},
                 and {Legendre} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "106",
  pages =        "259--273",
  month =        apr,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Luke:1969:SFTa
author: Yudell L. Luke
title: The Special Functions and Their Approximations
volume: I
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xx + 349
year: 1969
ISBN: 0-12-459901-X OR 012459901X
ISBN13: 978-0-12-459901-7 OR 9780124599017
LCCN: QA351 .L94 1969
bibdate: Wed Dec 15 17:55:35 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1993.12.15 17:55:35 ???
series: Mathematics in Science and Engineering, Volume 53-I, Editor: Richard Bellman
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawtitle: The Special Functions and Their Approximations
entry:
@Book{Luke:1969:SFTa,
  author =       "Yudell L. Luke",
  title =        "The Special Functions and Their Approximations",
  volume =       "I",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xx + 349",
  year =         "1969",
  ISBN =         "0-12-459901-X",
  ISBN-13 =      "978-0-12-459901-7",
  LCCN =         "QA351 .L94 1969",
  bibdate =      "Wed Dec 15 17:55:35 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics in Science and Engineering, Volume 53-I,
                 Editor: Richard Bellman",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Luke:1969:SFTb
author: Yudell L. Luke
title: The Special Functions and Their Approximations
volume: II
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xx + 485
year: 1969
ISBN: 0-12-459902-8 OR 0124599028
ISBN13: 978-0-12-459902-4 OR 9780124599024
LCCN: QA351 .L797
bibdate: Wed Dec 15 17:55:38 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib
bibtimestamp: 1993.12.15 17:55:38 ???
series: Mathematics in Science and Engineering, Volume 53-II, Editor: Richard Bellman
URL: http://www.sciencedirect.com/science/book/9780124599024
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawtitle: The Special Functions and Their Approximations
TOC:
Dedication / v Preface / vii--ix Contents of Volume I / xv Introduction / xvii--xx IX: Expansions of Generalized Hypergeometric Functions in Series of Functions of the Same Kind / 1--65 X: The $tau $-Method / 66--91 XI: Polynomial and Rational Approximations to Generalized Hypergeometric Functions / 92--132 XII: Recursion Formulas for Polynomials and Functions which Occur in Infinite Series and Rational Approximations to Generalized Hypergeometric Functions / 133--166 XIII: Polynomial and Rational Approximations for $E(z) = _2F_1(1, sigma ; rho + 1; 1/z)$ / 167--185 XIV: Polynomial and Rational Approximations for the Incomplete Gamma Function / 186--213 XV: Trapezoidal Rule Integration Formulas / 214--226 XVI: Applications / 227--281 XVII: Tables of Coefficients / 282--452 Bibliography / 453--461 Notation Index / 463--467 Subject Index to Volumes I and II / 468--485

rawTOC:
Dedication / v \\ Preface / vii--ix \\ Contents of Volume I / xv \\ Introduction / xvii--xx \\ IX: Expansions of Generalized Hypergeometric Functions in Series of Functions of the Same Kind / 1--65 \\ X: The $\tau$-Method / 66--91 \\ XI: Polynomial and Rational Approximations to Generalized Hypergeometric Functions / 92--132 \\ XII: Recursion Formulas for Polynomials and Functions which Occur in Infinite Series and Rational Approximations to Generalized Hypergeometric Functions / 133--166 \\ XIII: Polynomial and Rational Approximations for $E(z) = _2F_1(1, \sigma; \rho + 1; 1/z)$ / 167--185 \\ XIV: Polynomial and Rational Approximations for the Incomplete Gamma Function / 186--213 \\ XV: Trapezoidal Rule Integration Formulas / 214--226 \\ XVI: Applications / 227--281 \\ XVII: Tables of Coefficients / 282--452 \\ Bibliography / 453--461 \\ Notation Index / 463--467 \\ Subject Index to Volumes I and II / 468--485

entry:
@Book{Luke:1969:SFTb,
  author =       "Yudell L. Luke",
  title =        "The Special Functions and Their Approximations",
  volume =       "II",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xx + 485",
  year =         "1969",
  ISBN =         "0-12-459902-8",
  ISBN-13 =      "978-0-12-459902-4",
  LCCN =         "QA351 .L797",
  bibdate =      "Wed Dec 15 17:55:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "Mathematics in Science and Engineering, Volume 53-II,
                 Editor: Richard Bellman",
  URL =          "http://www.sciencedirect.com/science/book/9780124599024",
  acknowledgement = ack-nhfb,
  tableofcontents = "Dedication / v \\
                 Preface / vii--ix \\
                 Contents of Volume I / xv \\
                 Introduction / xvii--xx \\
                 IX: Expansions of Generalized Hypergeometric Functions
                 in Series of Functions of the Same Kind / 1--65 \\
                 X: The $\tau$-Method / 66--91 \\
                 XI: Polynomial and Rational Approximations to
                 Generalized Hypergeometric Functions / 92--132 \\
                 XII: Recursion Formulas for Polynomials and Functions
                 which Occur in Infinite Series and Rational
                 Approximations to Generalized Hypergeometric Functions
                 / 133--166 \\
                 XIII: Polynomial and Rational Approximations for $E(z)
                 = _2F_1(1, \sigma; \rho + 1; 1/z)$ / 167--185 \\
                 XIV: Polynomial and Rational Approximations for the
                 Incomplete Gamma Function / 186--213 \\
                 XV: Trapezoidal Rule Integration Formulas / 214--226
                 \\
                 XVI: Applications / 227--281 \\
                 XVII: Tables of Coefficients / 282--452 \\
                 Bibliography / 453--461 \\
                 Notation Index / 463--467 \\
                 Subject Index to Volumes I and II / 468--485",
}


bibtype: techreport
filename: elefunt.bib
label: Moses:1969:ICS
author: Joel Moses
title: The integration of a class of special functions with the Risch algorithm
type: AI Memo (180)
number: MAC-M-421
institution: Artificial Intelligence Laboratory, Massachusetts Institute of Technology
address: Cambridge, MA, USA
pages: 13 + 1
year: 1969
LCCN: Q334 M533 no. 180
bibdate: Sat Oct 30 18:37:28 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 18:37:28 ???
acknowledgement: ack-nhfb
rawauthor: Joel Moses
rawtitle: The integration of a class of special functions with the {Risch} algorithm
entry:
@TechReport{Moses:1969:ICS,
  author =       "Joel Moses",
  title =        "The integration of a class of special functions with
                 the {Risch} algorithm",
  type =         "{AI} Memo (180)",
  number =       "MAC-M-421",
  institution =  "Artificial Intelligence Laboratory, Massachusetts
                 Institute of Technology",
  address =      "Cambridge, MA, USA",
  pages =        "13 + 1",
  year =         "1969",
  LCCN =         "Q334 M533 no. 180",
  bibdate =      "Sat Oct 30 18:37:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Ng:1969:CPE
author: Edward W. Ng and C. J. Devine and R. F. Tooper
title: Chebyshev Polynomial Expansion of Bose--Einstein Functions of Orders $1$ to $ 10$
journal: j-MATH-COMPUT
volume: 23
number: 107
pages: 639--643
month: jul
monthnumber: 7
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Edward W. Ng and C. J. Devine and R. F. Tooper
rawtitle: {Chebyshev} Polynomial Expansion of {Bose--Einstein} Functions of Orders $1$ to $ 10$
remark:
Fullerton: $ B_p(eta ) = frac 1Gamma (p - 1) int _0^infty frac x^pe^x - eta - 1 d t $. Relative errors down to $ 3 times 10^-19 $.

entry:
@Article{Ng:1969:CPE,
  author =       "Edward W. Ng and C. J. Devine and R. F. Tooper",
  title =        "{Chebyshev} Polynomial Expansion of {Bose--Einstein}
                 Functions of Orders $1$ to $ 10$",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "107",
  pages =        "639--643",
  month =        jul,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: $ B_p(\eta) = \frac {1}{\Gamma (p - 1)}
                 \int_0^\infty \frac {x^p}{e^{x - \eta } - 1} \, d t $.
                 Relative errors down to $ 3 \times 10^{-19} $.",
}


bibtype: article
filename: elefunt.bib
label: Reichel:1969:IPV
author: Alex Reichel
title: The Integral of the $n$ th Power of the Voigt Function
journal: j-MATH-COMPUT
volume: 23
number: 107
pages: 645--649
month: jul
monthnumber: 7
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Alex Reichel
rawtitle: The Integral of the $n$ th Power of the {Voigt} Function
remark:
Fullerton: The function $ chi _n(t) = int _- infty ^infty U_0 (x, t) ^n d x $, where $ U_0 (x, t) = frac 1sqrt 4 pi t frac exp [ - (x - y)^2 / 4 t]1 + y^2 d y $ is considered.

entry:
@Article{Reichel:1969:IPV,
  author =       "Alex Reichel",
  title =        "The Integral of the $n$ th Power of the {Voigt}
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "107",
  pages =        "645--649",
  month =        jul,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: The function $ \chi_n(t) = \int_{- \infty
                 }^\infty \{ U_0 (x, t) \}^n \, d x $, where $ U_0 (x,
                 t) = \frac {1}{\sqrt {4 \pi t}} \frac {\exp [ - (x -
                 y)^2 / 4 t]}{1 + y^2} \, d y $ is considered.",
}


bibtype: article
filename: elefunt.bib
label: Robertson:1969:CNC
author: G. H. Robertson
title: Computation of the Noncentral Chi-Square Distribution
journal: j-BELL-SYST-TECH-J
volume: 48
number: 1
pages: 201--207
month: jan
monthnumber: 1
year: 1969
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:55 MST 2010
bibtimestamp: 2010.11.09 11:15:55 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol48/bstj48-1-201.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: G. H. Robertson
rawtitle: Computation of the Noncentral Chi-Square Distribution
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1969/BSTJ.1969.4801.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Robertson:1969:CNC,
  author =       "G. H. Robertson",
  title =        "Computation of the Noncentral Chi-Square
                 Distribution",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "48",
  number =       "1",
  pages =        "201--207",
  month =        jan,
  year =         "1969",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1969/BSTJ.1969.4801.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol48/bstj48-1-201.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: elefunt.bib
label: Sollfrey:1969:IFP
author: William Sollfrey
title: Inverse Functions of the Products of Two Bessel Functions
journal: j-J-MATH-PHYS
volume: 10
number: 8
pages: 1429--1430
month: aug
monthnumber: 8
year: 1969
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.1664985
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Oct 28 11:55:26 MDT 2011
bibtimestamp: 2011.10.28 11:55:26 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v10/i8/p1429_s1
fjournal: Journal of Mathematical Physics
keywords: functions
acknowledgement: ack-nhfb
corpsource: RAND Corp., Santa Monica, CA, USA
journalURL: http://jmp.aip.org/
onlinedate: 4 November 2003
rawauthor: William Sollfrey
rawtitle: Inverse Functions of the Products of Two {Bessel} Functions
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib

entry:
@Article{Sollfrey:1969:IFP,
  author =       "William Sollfrey",
  title =        "Inverse Functions of the Products of Two {Bessel}
                 Functions",
  journal =      j-J-MATH-PHYS,
  volume =       "10",
  number =       "8",
  pages =        "1429--1430",
  month =        aug,
  year =         "1969",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1664985",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 11:55:26 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v10/i8/p1429_s1",
  acknowledgement = ack-nhfb,
  classification = "A0200 (Mathematical methods in physics)",
  corpsource =   "RAND Corp., Santa Monica, CA, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "functions",
  onlinedate =   "4 November 2003",
  pagecount =    "2",
}


bibtype: article
filename: elefunt.bib
label: TadeudeMedeiros:1969:APF
author: Adilson Tadeu de Medeiros and Georges Schwachheim
title: Algorithm 349: Polygamma Functions with Arbitrary Precision [S14]
journal: j-CACM
volume: 12
number: 4
pages: 213--214
month: apr
monthnumber: 4
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:25 MST 2005
bibtimestamp: 2005.11.25 18:20:25 MST
note: See certification cite Lewis:1975:CPF.
fjournal: Communications of the ACM
remark: Fullerton: 150-line Algol procedure.
acknowledgement: ack-nhfb
classcodes: C7300 (Natural sciences computing)
corpsource: Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Adilson {Tadeu de Medeiros} and Georges Schwachheim
rawnote: See certification \cite{Lewis:1975:CPF}.
rawtitle: {Algorithm 349}: {Polygamma} Functions with Arbitrary Precision [{S14}]
abstract:
This procedure assigns to polygam the value of the polygamma function of order n for any real argument $z$. For $ n = 0$, we have the psi or digamma function, for $ n = 1$ the trigamma function, for $ n = 2$ the tetragamma function, and so on.

keywords:
digamma function; mathematics; polygamma function; psi function; special functions; subroutines; tetragamma function; trigamma function

rawabstract:
This procedure assigns to polygam the value of the polygamma function of order n for any real argument $z$. For $ n = 0$, we have the psi or digamma function, for $ n = 1$ the trigamma function, for $ n = 2$ the tetragamma function, and so on.

entry:
@Article{TadeudeMedeiros:1969:APF,
  author =       "Adilson {Tadeu de Medeiros} and Georges Schwachheim",
  title =        "{Algorithm 349}: {Polygamma} Functions with Arbitrary
                 Precision [{S14}]",
  journal =      j-CACM,
  volume =       "12",
  number =       "4",
  pages =        "213--214",
  month =        apr,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:25 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Lewis:1975:CPF}.",
  abstract =     "This procedure assigns to polygam the value of the
                 polygamma function of order n for any real argument
                 $z$. For $ n = 0$, we have the psi or digamma function,
                 for $ n = 1$ the trigamma function, for $ n = 2$ the
                 tetragamma function, and so on.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7300 (Natural sciences computing)",
  corpsource =   "Centro Brasileiro de Pesquisas Fisicas, Rio de
                 Janeiro, Brazil",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "digamma function; mathematics; polygamma function; psi
                 function; special functions; subroutines; tetragamma
                 function; trigamma function",
  remark =       "Fullerton: 150-line Algol procedure.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tesler:1969:AEF
author: G. S. Tesler
title: The approximation of elementary functions by means of polynomials of degree zero and one. (Russian)
publisher: Akad. Nauk Ukrain. SSR
address: Kiev, USSR
pages: 75--88
year: 1969
MRclass: 65D15
MRnumber: 45 \#4600
MRreviewer: I. Selihova
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: G. S. Tesler
booktitle:
Mathematical provisioning of electronic digital computers and effective organization of the computing process (Proc. Sem., Kiev, 1969) (Russian), No. 2

rawbooktitle:
Mathematical provisioning of electronic digital computers and effective organization of the computing process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2

rawtitle:
The approximation of elementary functions by means of polynomials of degree zero and one. ({Russian})

entry:
@InProceedings{Tesler:1969:AEF,
  author =       "G. S. Tesler",
  booktitle =    "Mathematical provisioning of electronic digital
                 computers and effective organization of the computing
                 process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2",
  title =        "The approximation of elementary functions by means of
                 polynomials of degree zero and one. ({Russian})",
  publisher =    "Akad. Nauk Ukrain. SSR",
  address =      "Kiev, USSR",
  pages =        "75--88",
  year =         "1969",
  MRclass =      "65D15",
  MRnumber =     "45 \#4600",
  MRreviewer =   "I. Selihova",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: book
filename: elefunt.bib
label: Tolke:1969:PFT
author: Friedrich Tolke
publisher: pub-SV
address: pub-SV:adr
pages: lxxxii + 449 (vol. 1)
year: 1969
bibdate: Mon Feb 13 19:01:10 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.13 19:01:10 ???
note: Two volumes
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich T{\"o}lke
rawnote: Two volumes
title:
Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet der Theta-Funktionen und der elliptischen Funtionen. (German) [Practical functional theory. 6. Tables from the field of theta functions and elliptic functions]

rawtitle:
{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet der Theta-Funktionen und der elliptischen Funtionen}. ({German}) [{Practical} functional theory. 6. {Tables} from the field of theta functions and elliptic functions]

entry:
@Book{Tolke:1969:PFT,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet
                 der Theta-Funktionen und der elliptischen Funtionen}.
                 ({German}) [{Practical} functional theory. 6. {Tables}
                 from the field of theta functions and elliptic
                 functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "lxxxii + 449 (vol. 1)",
  year =         "1969",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Turner:1969:DSC
author: L. R. Turner
title: Difficulty in $ sin $ / $ cos $ Routine
journal: j-SIGNUM
volume: 4
number: 3
pages: 13--13
year: 1969
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Thu Feb 15 15:23:23 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.02.15 15:23:23 ???
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: L. R. Turner
rawtitle: Difficulty in {$ \sin $ \slash$ \cos $} Routine
entry:
@Article{Turner:1969:DSC,
  author =       "L. R. Turner",
  title =        "Difficulty in {$ \sin $ \slash$ \cos $} Routine",
  journal =      j-SIGNUM,
  volume =       "4",
  number =       "3",
  pages =        "13--13",
  year =         "1969",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Feb 15 15:23:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: elefunt.bib
label: VandeVel:1969:SEM
author: H. Van de Vel
journal: j-MATH-COMPUT
volume: 23
number: 105
pages: 61--69
month: jan
monthnumber: 1
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: H. {Van de Vel}
title:
On the Series Expansion Method for Computing Incomplete Elliptic Integrals of the First and Second Kinds

rawtitle:
On the Series Expansion Method for Computing Incomplete Elliptic Integrals of the First and Second Kinds

entry:
@Article{VandeVel:1969:SEM,
  author =       "H. {Van de Vel}",
  title =        "On the Series Expansion Method for Computing
                 Incomplete Elliptic Integrals of the First and Second
                 Kinds",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "105",
  pages =        "61--69",
  month =        jan,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Zaker:1969:CCE
author: T. A. Zaker
title: Calculation of the complementary error function of complex argument
journal: j-J-COMPUT-PHYS
volume: 4
number: 3
pages: 427--430
month: oct
monthnumber: 10
year: 1969
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(69)90011-4
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Thu Dec 04 16:20:39 2008
bibtimestamp: 2008.12.04 16:20:39 ???
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: T. A. Zaker
rawtitle: Calculation of the complementary error function of complex argument
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib

entry:
@Article{Zaker:1969:CCE,
  author =       "T. A. Zaker",
  title =        "Calculation of the complementary error function of
                 complex argument",
  journal =      j-J-COMPUT-PHYS,
  volume =       "4",
  number =       "3",
  pages =        "427--430",
  month =        oct,
  year =         "1969",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(69)90011-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Thu Dec 04 16:20:39 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Bray:1970:CAR
author: T. Bray
title: Certification of Algorithm 22, Ricatti--Bessel Functions of First and Second Kind
journal: j-CACM
volume: 13
number: 7
pages: 448--448
month: jul
monthnumber: 7
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Oct 29 21:49:15 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.29 21:49:15 ???
fjournal: Communications of the ACM
remark: Fullerton: An error in an Algol procedure is reported.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: T. Bray
rawtitle: Certification of {Algorithm 22, Ricatti--Bessel Functions of First and Second Kind}
entry:
@Article{Bray:1970:CAR,
  author =       "T. Bray",
  title =        "Certification of {Algorithm 22, Ricatti--Bessel
                 Functions of First and Second Kind}",
  journal =      j-CACM,
  volume =       "13",
  number =       "7",
  pages =        "448--448",
  month =        jul,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Oct 29 21:49:15 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: An error in an Algol procedure is
                 reported.",
}


bibtype: article
filename: elefunt.bib
label: Carlitz:1970:SRF
author: L. Carlitz
title: Some Reduction Formulas for Generalized Hypergeometric Functions
journal: j-SIAM-J-MATH-ANA
volume: 1
number: 2
pages: 243--245
month: may
monthnumber: 5
year: 1970
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
bibdate: Sun Nov 28 19:21:58 MST 2010
bibtimestamp: 2010.11.28 19:21:58 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: L. Carlitz
rawtitle: Some Reduction Formulas for Generalized Hypergeometric Functions
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/2; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib

entry:
@Article{Carlitz:1970:SRF,
  author =       "L. Carlitz",
  title =        "Some Reduction Formulas for Generalized Hypergeometric
                 Functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "1",
  number =       "2",
  pages =        "243--245",
  month =        may,
  year =         "1970",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Sun Nov 28 19:21:58 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1970:HSS
author: B. C. Carlson
title: Hidden Symmetries of Special Functions
journal: j-SIAM-REVIEW
volume: 12
number: 3
pages: 332--345
month: jul
monthnumber: 7
year: 1970
CODEN: SIREAD
DOI: https://doi.org/10.1137/1012078
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:06:20 MDT 2014
bibtimestamp: 2014.03.27 09:06:20 MDT
URL: http://www.jstor.org/stable/2028552
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: July 1970
rawauthor: B. C. Carlson
rawtitle: Hidden Symmetries of Special Functions
bibsource:
http://epubs.siam.org/toc/siread/12/3; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Carlson:1970:HSS,
  author =       "B. C. Carlson",
  title =        "Hidden Symmetries of Special Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "12",
  number =       "3",
  pages =        "332--345",
  month =        jul,
  year =         "1970",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1012078",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:20 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/12/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://www.jstor.org/stable/2028552",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1970",
}


bibtype: article
filename: elefunt.bib
label: Chen:1970:CGI
author: Reuven Chen
title: On the Computation of the Generalized Integral in Glow Curve Theory
journal: j-J-COMPUT-PHYS
volume: 6
number: 2
pages: 314--316
month: oct
monthnumber: 10
year: 1970
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(70)90027-6
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Fri Oct 29 22:09:19 2010
bibtimestamp: 2010.10.29 22:09:19 ???
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Reuven Chen
rawtitle: On the Computation of the Generalized Integral in Glow Curve Theory
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib

entry:
@Article{Chen:1970:CGI,
  author =       "Reuven Chen",
  title =        "On the Computation of the Generalized Integral in Glow
                 Curve Theory",
  journal =      j-J-COMPUT-PHYS,
  volume =       "6",
  number =       "2",
  pages =        "314--316",
  month =        oct,
  year =         "1970",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(70)90027-6",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Fri Oct 29 22:09:19 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Cochran:1970:NTF
author: James Alan Cochran and Judith N. Hoffspiegel
title: Numerical Techniques for Finding $ nu $-Zeros of Hankel Functions
journal: j-MATH-COMPUT
volume: 24
number: 110
pages: 413--422
month: apr
monthnumber: 4
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: James Alan Cochran and Judith N. Hoffspiegel
rawtitle: Numerical Techniques for Finding $ \nu $-Zeros of {Hankel} Functions
entry:
@Article{Cochran:1970:NTF,
  author =       "James Alan Cochran and Judith N. Hoffspiegel",
  title =        "Numerical Techniques for Finding $ \nu $-Zeros of
                 {Hankel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "413--422",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Cody:1970:CAC
author: W. J. Cody and K. E. Hillstrom
title: Chebyshev Approximations for the Coulomb Phase Shift
journal: j-MATH-COMPUT
volume: 24
number: 111
pages: 671--677
month: jul
monthnumber: 7
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.25
MRnumber: 42\#8661
bibdate: Wed Jan 17 08:57:04 1996
bibtimestamp: 1996.01.17 08:57:04 ???
fjournal: Mathematics of Computation
remark: Fullerton: Relative errors down to $ 4 times 10^-19 $.
acknowledgement: ack-wjc
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody and K. E. Hillstrom
rawtitle: {Chebyshev} Approximations for the {Coulomb} Phase Shift
entry:
@Article{Cody:1970:CAC,
  author =       "W. J. Cody and K. E. Hillstrom",
  title =        "{Chebyshev} Approximations for the {Coulomb} Phase
                 Shift",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "111",
  pages =        "671--677",
  month =        jul,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "42\#8661",
  bibdate =      "Wed Jan 17 08:57:04 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 4 \times 10^{-19}
                 $.",
}


bibtype: article
filename: elefunt.bib
label: Cody:1970:CAD
author: W. J. Cody and Kathleen A. Paciorek and Henry C. Thacher, Jr.
title: Chebyshev approximations for Dawson's integral
journal: j-MATH-COMPUT
volume: 24
number: 109
pages: 171--178
month: jan
monthnumber: 1
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.20
MRnumber: 41\#2883
bibdate: Wed Jan 17 08:57:30 1996
bibtimestamp: 1996.01.17 08:57:30 ???
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody and Kathleen A. Paciorek and Henry C. {Thacher, Jr.}
rawtitle: {Chebyshev} approximations for {Dawson}'s integral
entry:
@Article{Cody:1970:CAD,
  author =       "W. J. Cody and Kathleen A. Paciorek and Henry C.
                 {Thacher, Jr.}",
  title =        "{Chebyshev} approximations for {Dawson}'s integral",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "109",
  pages =        "171--178",
  month =        jan,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.20",
  MRnumber =     "41\#2883",
  bibdate =      "Wed Jan 17 08:57:30 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Cody:1970:RAC
author: W. J. Cody and Kathleen A. Paciorek
title: Remark on Algorithm 292 [S22]: Regular Coulomb Wave Functions
journal: j-CACM
volume: 13
number: 9
pages: 573
month: sep
monthnumber: 9
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Nov 16 23:58:51 1994
bibtimestamp: 1994.11.16 23:58:51 ???
fjournal: Communications of the ACM
remark: Fullerton: More modifications to an Algol procedure.
acknowledgement: ack-wjc
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. J. Cody and Kathleen A. Paciorek
rawtitle: Remark on {Algorithm} 292 [{S22}]: Regular {Coulomb} Wave Functions
entry:
@Article{Cody:1970:RAC,
  author =       "W. J. Cody and Kathleen A. Paciorek",
  title =        "Remark on {Algorithm} 292 [{S22}]: Regular {Coulomb}
                 Wave Functions",
  journal =      j-CACM,
  volume =       "13",
  number =       "9",
  pages =        "573",
  month =        sep,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Nov 16 23:58:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: More modifications to an Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Darlington:1970:AAA
author: Sidney Darlington
title: Analytical Approximations to Approximations in the Chebyshev Sense
journal: j-BELL-SYST-TECH-J
volume: 49
number: 1
pages: 1--32
month: jan
monthnumber: 1
year: 1970
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:55 MST 2010
bibtimestamp: 2010.11.09 11:15:55 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-1-1.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: Sidney Darlington
rawtitle: Analytical Approximations to Approximations in the {Chebyshev} Sense
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4901.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Darlington:1970:AAA,
  author =       "Sidney Darlington",
  title =        "Analytical Approximations to Approximations in the
                 {Chebyshev} Sense",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "49",
  number =       "1",
  pages =        "1--32",
  month =        jan,
  year =         "1970",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4901.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-1-1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: techreport
filename: elefunt.bib
label: DeLugish:1970:CAA
author: Bruce Gene DeLugish
title: A Class of Algorithms for Automatic Evaluation of Certain Elementary Functions in a Binary Computer
number: 399
institution: Department of Computer Science, University of Illinois at Urbana-Champaign
address: Urbana, Illinois
pages: 191
year: 1970
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
acknowledgement: ack-nhfb
rawauthor: Bruce Gene DeLugish
rawtitle: A Class of Algorithms for Automatic Evaluation of Certain Elementary Functions in a Binary Computer
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{DeLugish:1970:CAA,
  author =       "Bruce Gene DeLugish",
  title =        "A Class of Algorithms for Automatic Evaluation of
                 Certain Elementary Functions in a Binary Computer",
  number =       "399",
  institution =  "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, Illinois",
  pages =        "191",
  year =         "1970",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Flynn:1970:DFI
author: M. J. Flynn
title: On Division by Functional Iteration
journal: j-IEEE-TRANS-COMPUT
volume: C-19
number: 8
pages: 702--706
month: aug
monthnumber: 8
year: 1970
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1970.223019
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Nov 15 07:59:25 2007
bibtimestamp: 2007.11.15 07:59:25 ???
note: Reprinted in cite Swartzlander:1990:CAa.
URL: http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Flynn.pdf
fjournal: IEEE Transactions on Computers
keywords: ARITH-1
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. J. Flynn
rawnote: Reprinted in \cite{Swartzlander:1990:CAa}.
rawtitle: On Division by Functional Iteration
abstract:
In order to avoid the time delays associated with linearly convergent division based on subtraction, other iterative schemes can be used. These are based on (1) series expansion of the reciprocal, (2) multiplicative sequence, or (3) additive sequence convergent to the quotient. These latter techniques are based on finding the root of an arbitrary function at either the quotient or reciprocal value. A Newton--Raphson iteration or root finding iteration can be used. The most useful techniques are quadratically convergent (i.e., $ mathrm error_i + 1 = O((mathrm error_i)^2) $). These techniques generally require two arithmetic operations (add or multiply) to double the precision of the quotient.

rawabstract:
In order to avoid the time delays associated with linearly convergent division based on subtraction, other iterative schemes can be used. These are based on (1) series expansion of the reciprocal, (2) multiplicative sequence, or (3) additive sequence convergent to the quotient. These latter techniques are based on finding the root of an arbitrary function at either the quotient or reciprocal value. A Newton--Raphson iteration or root finding iteration can be used. The most useful techniques are quadratically convergent (i.e., $ \mathrm {error}_{i + 1} = O((\mathrm {error}_i)^2) $). These techniques generally require two arithmetic operations (add or multiply) to double the precision of the quotient.

entry:
@Article{Flynn:1970:DFI,
  author =       "M. J. Flynn",
  title =        "On Division by Functional Iteration",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "702--706",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223019",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Swartzlander:1990:CAa}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Flynn.pdf",
  abstract =     "In order to avoid the time delays associated with
                 linearly convergent division based on subtraction,
                 other iterative schemes can be used. These are based on
                 (1) series expansion of the reciprocal, (2)
                 multiplicative sequence, or (3) additive sequence
                 convergent to the quotient. These latter techniques are
                 based on finding the root of an arbitrary function at
                 either the quotient or reciprocal value. A
                 Newton--Raphson iteration or root finding iteration can
                 be used.

                 The most useful techniques are quadratically convergent
                 (i.e., $ \mathrm {error}_{i + 1} = O((\mathrm
                 {error}_i)^2) $). These techniques generally require
                 two arithmetic operations (add or multiply) to double
                 the precision of the quotient.",
  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",
  keywords =     "ARITH-1",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1970:RAD
author: Walter Gautschi and Bruce J. Klein
title: Remark on Algorithm 282, Derivatives of $ e^x / x $, $ cos (x) / x $, and $ sin (x) / x $
journal: j-CACM
volume: 13
number: 1
pages: 53--54
month: jan
monthnumber: 1
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sat Oct 30 07:27:17 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 07:27:17 ???
note: See cite Gautschi:1966:AD.
fjournal: Communications of the ACM
remark: Fullerton: Corrections are given for several Algol procedures.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi and Bruce J. Klein
rawnote: See \cite{Gautschi:1966:AD}.
rawtitle: Remark on {Algorithm 282, Derivatives of $ e^x / x $, $ \cos (x) / x $, and $ \sin (x) / x $}
entry:
@Article{Gautschi:1970:RAD,
  author =       "Walter Gautschi and Bruce J. Klein",
  title =        "Remark on {Algorithm 282, Derivatives of $ e^x / x $,
                 $ \cos (x) / x $, and $ \sin (x) / x $}",
  journal =      j-CACM,
  volume =       "13",
  number =       "1",
  pages =        "53--54",
  month =        jan,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 07:27:17 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1966:AD}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Corrections are given for several Algol
                 procedures.",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1970:RCC
author: Walter Gautschi and Bruce J. Klein
title: Recursive computation of certain derivatives --- a study of error propagation
journal: j-CACM
volume: 13
number: 1
pages: 7--9
month: jan
monthnumber: 1
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65Q05
MRnumber: 46 1115
MRreviewer: D. F. Mayers
bibdate: Tue Mar 25 13:26:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.25 13:26:09 MST
fjournal: Communications of the ACM
remark: Fullerton: Recursive calculation of derivatives of $ e^x / x $ and $ cos (x) / x $ is considered.
acknowledgement: ack-nhfb
classcodes: C4110 (Error analysis in numerical methods)
corpsource: Purdue Univ., Lafayette, IN, USA
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi and Bruce J. Klein
rawtitle: Recursive computation of certain derivatives --- a study of error propagation
abstract:
A brief study is made of the propagation of errors in linear first-order difference equations. The recursive computation of successive derivatives of $ (e^x) / x $ and $ (cos x) / x $ is considered as an illustration.

keywords:
difference equations; error analysis; error propagation; recursive computation; successive derivatives

rawabstract:
A brief study is made of the propagation of errors in linear first-order difference equations. The recursive computation of successive derivatives of $ (e^x) / x $ and $ (\cos x) / x $ is considered as an illustration.

entry:
@Article{Gautschi:1970:RCC,
  author =       "Walter Gautschi and Bruce J. Klein",
  title =        "Recursive computation of certain derivatives --- a
                 study of error propagation",
  journal =      j-CACM,
  volume =       "13",
  number =       "1",
  pages =        "7--9",
  month =        jan,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65Q05",
  MRnumber =     "46 1115",
  MRreviewer =   "D. F. Mayers",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A brief study is made of the propagation of errors in
                 linear first-order difference equations. The recursive
                 computation of successive derivatives of $ (e^x) / x $
                 and $ (\cos x) / x $ is considered as an
                 illustration.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4110 (Error analysis in numerical methods)",
  corpsource =   "Purdue Univ., Lafayette, IN, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "difference equations; error analysis; error
                 propagation; recursive computation; successive
                 derivatives",
  remark =       "Fullerton: Recursive calculation of derivatives of $
                 e^x / x $ and $ \cos (x) / x $ is considered.",
}


bibtype: article
filename: elefunt.bib
label: Hill:1970:AASa
author: G. W. Hill
title: ACM Algorithm 395: Student's $t$-Distribution
journal: j-CACM
volume: 13
number: 10
pages: 617--619
month: oct
monthnumber: 10
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Mar 25 13:26:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.25 13:26:09 MST
note: See also cite elLozy:1979:RAS,Hill:1981:RSD.
fjournal: Communications of the ACM
keywords: statistics; subroutines
remark: Fullerton: Description of a 50-line Algol procedure.
acknowledgement: ack-nhfb
classcodes: C7310 (Mathematics computing)
corpsource: CSIRO, Glen Osmond, Australia
journalURL: https://dl.acm.org/loi/cacm
rawauthor: G. W. Hill
rawnote: See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.
rawtitle: {ACM Algorithm 395}: {Student}'s $t$-Distribution
entry:
@Article{Hill:1970:AASa,
  author =       "G. W. Hill",
  title =        "{ACM Algorithm 395}: {Student}'s $t$-Distribution",
  journal =      j-CACM,
  volume =       "13",
  number =       "10",
  pages =        "617--619",
  month =        oct,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "CSIRO, Glen Osmond, Australia",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "statistics; subroutines",
  remark =       "Fullerton: Description of a 50-line Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Hill:1970:AASb
author: G. W. Hill
title: ACM Algorithm 396: Student's $t$-Quantiles
journal: j-CACM
volume: 13
number: 10
pages: 619--620
month: oct
monthnumber: 10
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Mar 25 13:26:09 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.25 13:26:09 MST
note: See also cite Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS.
fjournal: Communications of the ACM
keywords: function evaluation; statistics; subroutines
remark: Fullerton: Description of a 50-line Algol procedure.
acknowledgement: ack-nhfb
classcodes: C4120 (Functional analysis); C7310 (Mathematics computing)
corpsource: CSIRO, Glen Osmond, Australia
journalURL: https://dl.acm.org/loi/cacm
rawauthor: G. W. Hill
rawnote: See also \cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.
rawtitle: {ACM Algorithm 396}: {Student}'s $t$-Quantiles
entry:
@Article{Hill:1970:AASb,
  author =       "G. W. Hill",
  title =        "{ACM Algorithm 396}: {Student}'s $t$-Quantiles",
  journal =      j-CACM,
  volume =       "13",
  number =       "10",
  pages =        "619--620",
  month =        oct,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also
                 \cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4120 (Functional analysis); C7310 (Mathematics
                 computing)",
  corpsource =   "CSIRO, Glen Osmond, Australia",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "function evaluation; statistics; subroutines",
  remark =       "Fullerton: Description of a 50-line Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Holmgren:1970:RAN
author: Bo Holmgren
title: Remark on Algorithm 304, Normal Curve Integral
journal: j-CACM
volume: 13
number: 10
pages: 624--624
month: oct
monthnumber: 10
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sat Oct 30 08:18:38 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 08:18:38 ???
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Bo Holmgren
rawtitle: Remark on {Algorithm 304, Normal Curve Integral}
entry:
@Article{Holmgren:1970:RAN,
  author =       "Bo Holmgren",
  title =        "Remark on {Algorithm 304, Normal Curve Integral}",
  journal =      j-CACM,
  volume =       "13",
  number =       "10",
  pages =        "624--624",
  month =        oct,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 08:18:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: elefunt.bib
label: Jones:1970:GHF
author: Alan L. Jones
title: The generalized hypergeometric function
journal: j-SIGPLAN
volume: 5
number: 3
pages: 26--27
month: mar
monthnumber: 3
year: 1970
CODEN: SINODQ
ISSN: 0362-1340 (print), 1523-2867 (print), 1558-1160 OR 03621340 (print), 15232867 (print), 15581160
ISSNL: 0362-1340 OR 03621340
bibdate: Thu May 25 06:40:57 MDT 2006
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2006.05.25 06:40:57 MDT
fjournal: ACM SIGPLAN Notices
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J706
rawauthor: Alan L. Jones
rawtitle: The generalized hypergeometric function
entry:
@Article{Jones:1970:GHF,
  author =       "Alan L. Jones",
  title =        "The generalized hypergeometric function",
  journal =      j-SIGPLAN,
  volume =       "5",
  number =       "3",
  pages =        "26--27",
  month =        mar,
  year =         "1970",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu May 25 06:40:57 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1970:CZI
author: K. S. Kolbig
title: Complex Zeros of an Incomplete Riemann Zeta Function and of the Incomplete Gamma Function
journal: j-MATH-COMPUT
volume: 24
number: 111
pages: 679--696
month: jul
monthnumber: 7
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: K. S. Kolbig
rawtitle: Complex Zeros of an Incomplete {Riemann} Zeta Function and of the Incomplete Gamma Function
entry:
@Article{Kolbig:1970:CZI,
  author =       "K. S. Kolbig",
  title =        "Complex Zeros of an Incomplete {Riemann} Zeta Function
                 and of the Incomplete Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "111",
  pages =        "679--696",
  month =        jul,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Lehman:1970:DZR
author: R. S. Lehman
title: On the distribution of zeros of the Riemann zeta-function
journal: j-PROC-LONDON-MATH-SOC-1
volume: 3
number: 20
pages: 303--320
year: 1970
ISSN: 0024-6115 (print), 1460-244X (electronic) OR 00246115 (print), 1460244X (electronic)
ISSNL: 0024-6115 OR 00246115
MRnumber: MR0258768 (41:3414)
bibdate: Mon Oct 24 12:42:07 2011
bibtimestamp: 2011.10.24 12:42:07 ???
note: This paper corrects several errors in cite Turing:1953:SCR. See also cite Trudgian:2011:ITM.
fjournal: Proceedings of the London Mathematical Society. First Series
acknowledgement: ack-nhfb
journalURL: http://plms.oxfordjournals.org/content/by/year
rawauthor: R. S. Lehman
rawnote: This paper corrects several errors in \cite{Turing:1953:SCR}. See also \cite{Trudgian:2011:ITM}.
rawtitle: On the distribution of zeros of the {Riemann} zeta-function
entry:
@Article{Lehman:1970:DZR,
  author =       "R. S. Lehman",
  title =        "On the distribution of zeros of the {Riemann}
                 zeta-function",
  journal =      j-PROC-LONDON-MATH-SOC-1,
  volume =       "3",
  number =       "20",
  pages =        "303--320",
  month =        "????",
  year =         "1970",
  ISSN =         "0024-6115 (print), 1460-244X (electronic)",
  ISSN-L =       "0024-6115",
  MRnumber =     "MR0258768 (41:3414)",
  bibdate =      "Mon Oct 24 12:42:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "This paper corrects several errors in
                 \cite{Turing:1953:SCR}. See also
                 \cite{Trudgian:2011:ITM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the London Mathematical Society. First
                 Series",
  journal-URL =  "http://plms.oxfordjournals.org/content/by/year",
}


bibtype: techreport
filename: elefunt.bib
label: Lugish:1970:CAA
author: B. G. de Lugish
title: A Class of Algorithms for Automatic Evaluation of Certain Elementary Function in a Binary Computer
type: Report
number: 399
institution: Department of Computer Science, University of Illinois
month: jun
monthnumber: 6
year: 1970
bibdate: Fri Sep 02 22:49:20 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.02 22:49:20 ???
acknowledgement: ack-nj
rawauthor: B. G. de Lugish
rawtitle: A Class of Algorithms for Automatic Evaluation of Certain Elementary Function in a Binary Computer
entry:
@TechReport{Lugish:1970:CAA,
  author =       "B. G. de Lugish",
  title =        "A Class of Algorithms for Automatic Evaluation of
                 Certain Elementary Function in a Binary Computer",
  type =         "Report",
  number =       "399",
  institution =  "Department of Computer Science, University of
                 Illinois",
  pages =        "????",
  month =        jun,
  year =         "1970",
  bibdate =      "Fri Sep 02 22:49:20 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Luke:1970:FAE
author: Yudell L. Luke
title: Further Approximations for Elliptic Integrals
journal: j-MATH-COMPUT
volume: 24
number: 109
pages: 191--198
month: jan
monthnumber: 1
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Yudell L. Luke
rawtitle: Further Approximations for Elliptic Integrals
entry:
@Article{Luke:1970:FAE,
  author =       "Yudell L. Luke",
  title =        "Further Approximations for Elliptic Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "109",
  pages =        "191--198",
  month =        jan,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Minton:1970:GHF
author: Barry M. Minton
title: Generalized Hypergeometric Function of Unit Argument
journal: j-J-MATH-PHYS
volume: 11
number: 4
pages: 1375--1376
month: apr
monthnumber: 4
year: 1970
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.1665270
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Oct 28 16:39:25 MDT 2011
bibtimestamp: 2011.10.28 16:39:25 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v11/i4/p1375_s1
fjournal: Journal of Mathematical Physics
keywords: functions
acknowledgement: ack-nhfb
corpsource: Univ. Calgary, Alta., Canada
journalURL: http://jmp.aip.org/
onlinedate: 28 October 2003
rawauthor: Barry M. Minton
rawtitle: Generalized Hypergeometric Function of Unit Argument
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib

entry:
@Article{Minton:1970:GHF,
  author =       "Barry M. Minton",
  title =        "Generalized Hypergeometric Function of Unit Argument",
  journal =      j-J-MATH-PHYS,
  volume =       "11",
  number =       "4",
  pages =        "1375--1376",
  month =        apr,
  year =         "1970",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1665270",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 16:39:25 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v11/i4/p1375_s1",
  acknowledgement = ack-nhfb,
  classification = "A0200 (Mathematical methods in physics)",
  corpsource =   "Univ. Calgary, Alta., Canada",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "functions",
  onlinedate =   "28 October 2003",
  pagecount =    "2",
}


bibtype: article
filename: elefunt.bib
label: Ng:1970:CAE
author: E. N. Ng
title: Certification of Algorithm 385, Exponential Integral $ operatorname Ei(x) $
journal: j-CACM
volume: 13
number: 7
pages: 448--449
month: jul
monthnumber: 7
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sat Oct 30 09:18:14 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 09:18:14 ???
fjournal: Communications of the ACM
remark: Fullerton: Comments on a FORTRAN routine.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: E. N. Ng
rawtitle: Certification of {Algorithm 385, Exponential Integral $ \operatorname {Ei}(x) $}
entry:
@Article{Ng:1970:CAE,
  author =       "E. N. Ng",
  title =        "Certification of {Algorithm 385, Exponential Integral
                 $ \operatorname {Ei}(x) $}",
  journal =      j-CACM,
  volume =       "13",
  number =       "7",
  pages =        "448--449",
  month =        jul,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 09:18:14 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Comments on a FORTRAN routine.",
}


bibtype: article
filename: elefunt.bib
label: Ng:1970:CDF
author: E. W. Ng and C. J. Devine
title: On the Computation of Debye Functions of Integer Orders
journal: j-MATH-COMPUT
volume: 24
number: 110
pages: 405--407
month: apr
monthnumber: 4
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: E. W. Ng and C. J. Devine
rawtitle: On the Computation of {Debye} Functions of Integer Orders
remark:
Fullerton: Debye functions are incomplete Riemann zeta functions. $ overbar D_p(x) = frac 1Gamma (p - 1) int _0^x frac t^pe^t - 1 d t $ and the complementary integral are calculated to 20 digits.

entry:
@Article{Ng:1970:CDF,
  author =       "E. W. Ng and C. J. Devine",
  title =        "On the Computation of {Debye} Functions of Integer
                 Orders",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "405--407",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Debye functions are incomplete Riemann zeta
                 functions. $ \overbar {D}_p(x) = \frac {1}{\Gamma (p -
                 1)} \int_0^x \frac {t^p}{e^t - 1} \, d t $ and the
                 complementary integral are calculated to 20 digits.",
}


bibtype: article
filename: elefunt.bib
label: Ninomiya:1970:BRS
author: Ichizo Ninomiya
title: Best Rational Starting Approximations and Improved Newton Iteration for the Square Root
journal: j-MATH-COMPUT
volume: 24
number: 110
pages: 391--404
month: apr
monthnumber: 4
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Nagoya Univ., Chikua ku, Japan
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Ichizo Ninomiya
rawtitle: Best Rational Starting Approximations and Improved {Newton} Iteration for the Square Root
bibsource:
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

keywords:
computing procedure; function approximation; iterative methods; Newton iteration; rational approximation; square root

entry:
@Article{Ninomiya:1970:BRS,
  author =       "Ichizo Ninomiya",
  title =        "Best Rational Starting Approximations and Improved
                 {Newton} Iteration for the Square Root",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "391--404",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Nagoya Univ., Chikua ku, Japan",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computing procedure; function approximation; iterative
                 methods; Newton iteration; rational approximation;
                 square root",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Paciorek:1970:AEI
author: K. A. Paciorek
title: Algorithm 385: Exponential Integral $ operatorname Ei(x) $
journal: j-CACM
volume: 13
number: 7
pages: 446--447
month: jul
monthnumber: 7
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Mar 25 13:26:09 MST 1997
bibtimestamp: 1997.03.25 13:26:09 MST
note: See remark cite Redish:1970:RAE,Frisch:1972:RAR.
fjournal: Communications of the ACM
keywords: integration; subroutines
remark: Fullerton: A 100-line FORTRAN routine for both $ operatorname E1(x) $ and $ operatorname Ei(x) $.
acknowledgement: ack-nhfb
classcodes: C4160 (Numerical integration and differentiation); C7300 (Natural sciences computing)
corpsource: Argonne Nat. Lab., IL, USA
journalURL: https://dl.acm.org/loi/cacm
rawauthor: K. A. Paciorek
rawnote: See remark \cite{Redish:1970:RAE,Frisch:1972:RAR}.
rawtitle: {Algorithm 385}: {Exponential} Integral {$ \operatorname {Ei}(x) $}
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Paciorek:1970:AEI,
  author =       "K. A. Paciorek",
  title =        "{Algorithm 385}: {Exponential} Integral {$
                 \operatorname {Ei}(x) $}",
  journal =      j-CACM,
  volume =       "13",
  number =       "7",
  pages =        "446--447",
  month =        jul,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Redish:1970:RAE,Frisch:1972:RAR}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4160 (Numerical integration and differentiation);
                 C7300 (Natural sciences computing)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "integration; subroutines",
  remark =       "Fullerton: A 100-line FORTRAN routine for both $
                 \operatorname {E1}(x) $ and $ \operatorname {Ei}(x)
                 $.",
}


bibtype: article
filename: elefunt.bib
label: Raff:1970:CGF
author: Morton S. Raff
title: On Calculating the Gamma Function of Non-Integral Arguments
journal: j-AMER-STAT
volume: 24
number: 2
pages: 22--24
month: apr
monthnumber: 4
year: 1970
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Fri Jan 27 10:52:18 MST 2012
bibtimestamp: 2012.01.27 10:52:18 MST
URL: http://www.jstor.org/stable/2681926
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: Morton S. Raff
rawtitle: On Calculating the Gamma Function of Non-Integral Arguments
bibsource:
http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326364; https://www.math.utah.edu/pub/tex/bib/amstat1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Raff:1970:CGF,
  author =       "Morton S. Raff",
  title =        "On Calculating the Gamma Function of Non-Integral
                 Arguments",
  journal =      j-AMER-STAT,
  volume =       "24",
  number =       "2",
  pages =        "22--24",
  month =        apr,
  year =         "1970",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 10:52:18 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326364;
                 https://www.math.utah.edu/pub/tex/bib/amstat1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2681926",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: article
filename: elefunt.bib
label: Redish:1970:RAE
author: K. A. Redish
title: Remark on Algorithm 385, Exponential Integral $ operatorname Ei(x) $
journal: j-CACM
volume: 13
number: 12
pages: 750--750
month: dec
monthnumber: 12
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sat Oct 30 09:56:59 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 09:56:59 ???
note: See cite Paciorek:1970:AEI
fjournal: Communications of the ACM
remark: Fullerton: Minor corrections to a FORTRAN routine.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: K. A. Redish
rawnote: See \cite{Paciorek:1970:AEI}
rawtitle: Remark on {Algorithm 385, Exponential Integral $ \operatorname {Ei}(x) $}
entry:
@Article{Redish:1970:RAE,
  author =       "K. A. Redish",
  title =        "Remark on {Algorithm 385, Exponential Integral $
                 \operatorname {Ei}(x) $}",
  journal =      j-CACM,
  volume =       "13",
  number =       "12",
  pages =        "750--750",
  month =        dec,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 09:56:59 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Paciorek:1970:AEI}",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Minor corrections to a FORTRAN routine.",
}


bibtype: techreport
filename: elefunt.bib
label: Rothmaier:1970:BQN
author: B. Rothmaier
type: Interner Bericht
number: Nr. 70/17
institution: Institut fur Informatik, Universitat Karlsruhe
year: 1970
bibdate: Fri Sep 16 16:30:41 1994
bibtimestamp: 1994.09.16 16:30:41 ???
acknowledgement: ack-nj
rawauthor: B. Rothmaier
title:
Die Berechnung der Quadratwurzel nebst Schranken auf Dualmaschinen toenglish The Computation of the Square Root together with [Interval] Bounds on Binary Machines endtoenglish 

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

rawtitle:
{Die Berechnung der Quadratwurzel nebst Schranken auf Dualmaschinen} \toenglish {The Computation of the Square Root together with [Interval] Bounds on Binary Machines} \endtoenglish

entry:
@TechReport{Rothmaier:1970:BQN,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der Quadratwurzel nebst Schranken auf
                 Dualmaschinen} \toenglish {The Computation of the
                 Square Root together with [Interval] Bounds on Binary
                 Machines} \endtoenglish",
  type =         "{Interner Bericht}",
  number =       "Nr. 70/17",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  pages =        "??",
  year =         "1970",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: elefunt.bib
label: Rothmaier:1970:DSB
author: B. Rothmaier
type: Interner Bericht
number: Nr. 70/8
institution: Institut fur Informatik, Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1970
bibdate: Fri Jun 11 12:37:53 1999
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.06.11 12:37:53 ???
acknowledgement: ack-nj
rawauthor: B. Rothmaier
title:
Dokumentation der Standardfunktionen des Betriebssystems Hydra X8 toenglish Documentation of the Elementary Functions of the Operating System Hydra X8 endtoenglish 

rawtitle:
{Dokumentation der Standardfunktionen des Betriebssystems Hydra X8} \toenglish {Documentation} of the Elementary Functions of the Operating System {Hydra X8} \endtoenglish

entry:
@TechReport{Rothmaier:1970:DSB,
  author =       "B. Rothmaier",
  title =        "{Dokumentation der Standardfunktionen des
                 Betriebssystems Hydra X8} \toenglish {Documentation} of
                 the Elementary Functions of the Operating System {Hydra
                 X8} \endtoenglish",
  type =         "Interner {Bericht}",
  number =       "Nr. 70/8",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1970",
  bibdate =      "Fri Jun 11 12:37:53 1999",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Smith:1970:ASH
author: Robert R. Smith and Dennis McCall
title: Algorithm 392: Systems of Hyperbolic P.D.E.
journal: j-CACM
volume: 13
number: 9
pages: 567--570
month: sep
monthnumber: 9
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Mar 25 13:26:09 MST 1997
bibtimestamp: 1997.03.25 13:26:09 MST
note: See remark cite Frisch:1972:RAR.
fjournal: Communications of the ACM
keywords: boundary-value problems; partial differential equations
acknowledgement: ack-nhfb
classcodes: C4170 (Differential equations); C7310 (Mathematics computing)
corpsource: US Naval Electronics Lab. Center, San Diego, CA, USA
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Robert R. Smith and Dennis McCall
rawnote: See remark \cite{Frisch:1972:RAR}.
rawtitle: {Algorithm 392}: {Systems} of Hyperbolic {P.D.E.}
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Smith:1970:ASH,
  author =       "Robert R. Smith and Dennis McCall",
  title =        "{Algorithm 392}: {Systems} of Hyperbolic {P.D.E.}",
  journal =      j-CACM,
  volume =       "13",
  number =       "9",
  pages =        "567--570",
  month =        sep,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Frisch:1972:RAR}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C4170 (Differential equations); C7310 (Mathematics
                 computing)",
  corpsource =   "US Naval Electronics Lab. Center, San Diego, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "boundary-value problems; partial differential
                 equations",
}


bibtype: book
filename: elefunt.bib
label: Spain:1970:FMP
author: Barry Spain and M. G. (Michael Gambier) Smith
title: Functions of Mathematical Physics
publisher: pub-VAN-NOSTRAND-REINHOLD
address: pub-VAN-NOSTRAND-REINHOLD:adr
pages: xi + 208
year: 1970
ISBN: 0-442-07871-4, 0-442-07876-5 (hardcover) OR 0442078714, 0442078765 (hardcover)
ISBN13: 978-0-442-07871-3, 978-0-442-07876-8 (hardcover) OR 9780442078713, 9780442078768 (hardcover)
LCCN: QA351 .S69
bibdate: Tue Dec 5 10:54:45 MST 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.12.05 10:54:45 MST
series: The New university mathematics series
URL: http://books.google.com/books?id=kYgZAQAAIAAJ
acknowledgement: ack-nhfb
rawauthor: Barry Spain and M. G. (Michael Gambier) Smith
rawtitle: Functions of Mathematical Physics
subject:
Functions, Special; Mathematical physics; Fonctions speciales; Physique mathematique; Functions, Special; Mathematical physics; Functions, Special; Fonctions

TOC:
1: Series solution of second-order linear homogeneous equations 2: Contour integral solutions of an ordinary linear differential equation 3: Oscillation Theorems and Sturm--Liouville Theory 4: Asymptotics 5: The Gamma function 6: The Hypergeometric Equation 7: The confluent hypergeometric function 8: The Legendre Functions 9: Bessel Functions 10: Laguerre Polynomials 11: Hermite Polynomials Appendix 1: The Laplace and Helmholtz Equations Appendix 2: The Schrodinger Equation References Index

rawTOC:
1: Series solution of second-order linear homogeneous equations \\ 2: Contour integral solutions of an ordinary linear differential equation \\ 3: Oscillation Theorems and Sturm--Liouville Theory \\ 4: Asymptotics \\ 5: The Gamma function \\ 6: The Hypergeometric Equation \\ 7: The confluent hypergeometric function \\ 8: The Legendre Functions \\ 9: Bessel Functions \\ 10: Laguerre Polynomials \\ 11: Hermite Polynomials \\ Appendix 1: The Laplace and Helmholtz Equations \\ Appendix 2: The Schr{\"o}dinger Equation \\ References \\ Index

entry:
@Book{Spain:1970:FMP,
  author =       "Barry Spain and M. G. (Michael Gambier) Smith",
  title =        "Functions of Mathematical Physics",
  publisher =    pub-VAN-NOSTRAND-REINHOLD,
  address =      pub-VAN-NOSTRAND-REINHOLD:adr,
  pages =        "xi + 208",
  year =         "1970",
  ISBN =         "0-442-07871-4, 0-442-07876-5 (hardcover)",
  ISBN-13 =      "978-0-442-07871-3, 978-0-442-07876-8 (hardcover)",
  LCCN =         "QA351 .S69",
  bibdate =      "Tue Dec 5 10:54:45 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "The New university mathematics series",
  URL =          "http://books.google.com/books?id=kYgZAQAAIAAJ",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Mathematical physics; Fonctions
                 sp{\'e}ciales; Physique math{\'e}matique; Functions,
                 Special; Mathematical physics; Functions, Special;
                 Fonctions",
  tableofcontents = "1: Series solution of second-order linear
                 homogeneous equations \\
                 2: Contour integral solutions of an ordinary linear
                 differential equation \\
                 3: Oscillation Theorems and Sturm--Liouville Theory \\
                 4: Asymptotics \\
                 5: The Gamma function \\
                 6: The Hypergeometric Equation \\
                 7: The confluent hypergeometric function \\
                 8: The Legendre Functions \\
                 9: Bessel Functions \\
                 10: Laguerre Polynomials \\
                 11: Hermite Polynomials \\
                 Appendix 1: The Laplace and Helmholtz Equations \\
                 Appendix 2: The Schr{\"o}dinger Equation \\
                 References \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: Squire:1970:RAI
author: William Squire
title: A Rational Approximation to an Integral Appearing in Glow Curve Theory
journal: j-J-COMPUT-PHYS
volume: 6
number: 1
pages: 152--253
month: aug
monthnumber: 8
year: 1970
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(70)90016-1
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sat Oct 30 10:57:00 2010
bibtimestamp: 2010.10.30 10:57:00 ???
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: William Squire
rawtitle: A Rational Approximation to an Integral Appearing in Glow Curve Theory
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib

entry:
@Article{Squire:1970:RAI,
  author =       "William Squire",
  title =        "A Rational Approximation to an Integral Appearing in
                 Glow Curve Theory",
  journal =      j-J-COMPUT-PHYS,
  volume =       "6",
  number =       "1",
  pages =        "152--253",
  month =        aug,
  year =         "1970",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(70)90016-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 10:57:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Srivastava:1970:CRI
author: H. M. Srivastava
title: Certain Results Involving Generalized Hypergeometric Functions
journal: j-SIAM-J-MATH-ANA
volume: 1
number: 1
pages: 75--81
month: feb
monthnumber: 2
year: 1970
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
bibdate: Sun Nov 28 19:21:56 MST 2010
bibtimestamp: 2010.11.28 19:21:56 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: H. M. Srivastava
rawtitle: Certain Results Involving Generalized Hypergeometric Functions
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib

entry:
@Article{Srivastava:1970:CRI,
  author =       "H. M. Srivastava",
  title =        "Certain Results Involving Generalized Hypergeometric
                 Functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "1",
  number =       "1",
  pages =        "75--81",
  month =        feb,
  year =         "1970",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Sun Nov 28 19:21:56 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Stegun:1970:ACM
author: I. A. Stegun and R. Zucker
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 74B
number: 3
pages: 211--224
month: jul
monthnumber: 7
year: 1970
ISSN: 0091-0635 OR 00910635
bibdate: Sat Oct 30 10:58:39 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:58:39 ???
fjournal: Journal of Research of the National Bureau of Standards (1934)
remark: Fullerton: Adjustable double precision FORTRAN routines for $ erf $ and $ erfc $.
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: I. A. Stegun and R. Zucker
title:
Automatic Computing Methods for Special Functions. Part 1. Error, Probability, and Related Functions

rawtitle:
Automatic Computing Methods for Special Functions. Part 1. {Error}, Probability, and Related Functions

entry:
@Article{Stegun:1970:ACM,
  author =       "I. A. Stegun and R. Zucker",
  title =        "Automatic Computing Methods for Special Functions.
                 Part 1. {Error}, Probability, and Related Functions",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "74B",
  number =       "3",
  pages =        "211--224",
  month =        jul,
  year =         "1970",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:58:39 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Adjustable double precision FORTRAN
                 routines for $ \erf $ and $ \erfc $.",
}


bibtype: book
filename: elefunt.bib
label: Tolke:1970:PFT
author: Friedrich Tolke
publisher: pub-SV
address: pub-SV:adr
pages: 452--1047 (vol. 2)
year: 1970
ISBN: 3-662-13079-3 (print), 3-662-13078-5 OR 3662130793 (print), 3662130785
ISBN13: 978-3-662-13079-7 (print), 978-3-662-13078-0 OR 9783662130797 (print), 9783662130780
bibdate: Mon Feb 13 19:01:10 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.13 19:01:10 ???
note: Two volumes
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich T{\"o}lke
rawnote: Two volumes
title:
Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet der Theta-Funktionen und der elliptischen Funtionen. (German) [Practical functional theory. 6. Tables from the field of theta functions and elliptic functions]

TOC:
Sechsstellige Tafel III der Theta-Funktionen und ihrer logarithmischen Ableitungen, der Jacobischen elliptischen Funktionen und ihrer logarithmischen Ableitungen sowie der Weierstrassschen $z$, $?$, und $?$-Funktionen einschliess lich einiger Parameterfunktionen fur $? = z/2K$ als Argument und bzw. $1/?$ als Parameter $2$ Halfte, Parameterbereich $1 ? 1 / ? 0$ Neunstellige Tafel IV der Legendreschen Normalintegrale erster und zweiter Gattung sowie der Jacobischen Zeta-Funktion und der abgewandelten Heumanschen Lambda-Funktion Sechsstellige Tafel V der $D$-Funktionen erster bis vierter Ordnung fur die Charakteristiken 1 bis 4 Sechsstellige Tafel VI der Legendreschen Normalintegrale erster und zweiter Gattung sowie der Funktion ldots 

rawtitle:
{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet der Theta-Funktionen und der elliptischen Funtionen}. ({German}) [{Practical} functional theory. 6. {Tables} from the field of theta functions and elliptic functions]

rawTOC:
Sechsstellige Tafel III der Theta-Funktionen und ihrer logarithmischen Ableitungen, der Jacobischen elliptischen Funktionen und ihrer logarithmischen Ableitungen sowie der Weierstrassschen $z$, $?$, und $?$-Funktionen einschlie{\ss}lich einiger Parameterfunktionen f{\"u}r $? = z/2K$ als Argument und bzw. $1/?$ als Parameter $2$ H{\"a}lfte, Parameterbereich $1 ? 1 / ? 0$ \\ Neunstellige Tafel IV der Legendreschen Normalintegrale erster und zweiter Gattung sowie der Jacobischen Zeta-Funktion und der abgewandelten Heumanschen Lambda-Funktion \\ Sechsstellige Tafel V der $D$-Funktionen erster bis vierter Ordnung f{\"u}r die Charakteristiken 1 bis 4 \\ Sechsstellige Tafel VI der Legendreschen Normalintegrale erster und zweiter Gattung sowie der Funktion \\ \ldots{}

entry:
@Book{Tolke:1970:PFT,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet
                 der Theta-Funktionen und der elliptischen Funtionen}.
                 ({German}) [{Practical} functional theory. 6. {Tables}
                 from the field of theta functions and elliptic
                 functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "452--1047 (vol. 2)",
  year =         "1970",
  ISBN =         "3-662-13079-3 (print), 3-662-13078-5",
  ISBN-13 =      "978-3-662-13079-7 (print), 978-3-662-13078-0",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes",
  acknowledgement = ack-nhfb,
  language =     "German",
  tableofcontents = "Sechsstellige Tafel III der Theta-Funktionen und
                 ihrer logarithmischen Ableitungen, der Jacobischen
                 elliptischen Funktionen und ihrer logarithmischen
                 Ableitungen sowie der Weierstrassschen $z$, $?$, und
                 $?$-Funktionen einschlie{\ss}lich einiger
                 Parameterfunktionen f{\"u}r $? = z/2K$ als Argument und
                 bzw. $1/?$ als Parameter $2$ H{\"a}lfte,
                 Parameterbereich $1 ? 1 / ? 0$ \\
                 Neunstellige Tafel IV der Legendreschen Normalintegrale
                 erster und zweiter Gattung sowie der Jacobischen
                 Zeta-Funktion und der abgewandelten Heumanschen
                 Lambda-Funktion \\
                 Sechsstellige Tafel V der $D$-Funktionen erster bis
                 vierter Ordnung f{\"u}r die Charakteristiken 1 bis 4
                 \\
                 Sechsstellige Tafel VI der Legendreschen
                 Normalintegrale erster und zweiter Gattung sowie der
                 Funktion \\
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Wilson:1970:OSA
author: M. Wayne Wilson
title: Optimal Starting Approximations for Generating Square Root for Slow or No Divide
journal: j-CACM
volume: 13
number: 9
pages: 559--560
month: sep
monthnumber: 9
year: 1970
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.50
MRnumber: 44\#2338
MRreviewer: J. E. {Dennis, Jr.}
bibdate: Tue Apr 08 20:38:30 1997
bibtimestamp: 1997.04.08 20:38:30 ???
fjournal: Communications of the ACM
keywords: CACMA; digital arithmetic; ele; iterative methods; mathematics; numerical methods; optimisation
acknowledgement: ack-nj
classcodes: C5230 (Digital arithmetic methods)
corpsource: IBM, Houston, TX, USA
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
rawauthor: M. Wayne Wilson
rawtitle: Optimal Starting Approximations for Generating Square Root for Slow or No Divide
bibsource:
Compendex database; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
On computing machines with slow or no division, it is preferable to use an iterative scheme for the square root different from the classical Heron scheme. The problem of optimal initial approximants is considered, and some optimal polynomial initial approximations are tabulated.

rawabstract:
On computing machines with slow or no division, it is preferable to use an iterative scheme for the square root different from the classical Heron scheme. The problem of optimal initial approximants is considered, and some optimal polynomial initial approximations are tabulated.

entry:
@Article{Wilson:1970:OSA,
  author =       "M. Wayne Wilson",
  title =        "Optimal Starting Approximations for Generating Square
                 Root for Slow or No Divide",
  journal =      j-CACM,
  volume =       "13",
  number =       "9",
  pages =        "559--560",
  month =        sep,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "44\#2338",
  MRreviewer =   "J. E. {Dennis, Jr.}",
  bibdate =      "Tue Apr 08 20:38:30 1997",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "On computing machines with slow or no division, it is
                 preferable to use an iterative scheme for the square
                 root different from the classical Heron scheme. The
                 problem of optimal initial approximants is considered,
                 and some optimal polynomial initial approximations are
                 tabulated.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, Houston, TX, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "CACMA; digital arithmetic; ele; iterative methods;
                 mathematics; numerical methods; optimisation",
}


bibtype: article
filename: elefunt.bib
label: Winograd:1970:NMN
author: Shmuel Winograd
title: On the number of multiplications necessary to compute certain functions
journal: j-COMM-PURE-APPL-MATH
volume: 23
number: 2
pages: 165--179
month: mar
monthnumber: 3
year: 1970
CODEN: CPAMAT, CPMAMV
DOI: https://doi.org/10.1002/cpa.3160230204
ISSN: 0010-3640 (print), 1097-0312 (electronic) OR 00103640 (print), 10970312 (electronic)
ISSNL: 0010-3640 OR 00103640
bibdate: Sat Oct 21 12:05:50 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.21 12:05:50 ???
fjournal: Communications on Pure and Applied Mathematics (New York)
keywords: number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
ajournal: Comm. Pure Appl. Math.
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312
rawauthor: Shmuel Winograd
rawtitle: On the number of multiplications necessary to compute certain functions
remark:
From the second paragraph: ``Motzkin [3] introduced the notion of preconditioning of the coefficients. Motzkin showed that if, in the course of computing $ P_n(x) = sum _i = 0^n a_i x^i $, operations which depend only the $ a_i $ are not counted, then only about $ n / 2 $ multiplications are necessary to evaluate $ P_n(x) $. The obvious application of this result is when the same polynomial $ P_n(x) $ has to be evaluated at many different points.''.

entry:
@Article{Winograd:1970:NMN,
  author =       "Shmuel Winograd",
  title =        "On the number of multiplications necessary to compute
                 certain functions",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "23",
  number =       "2",
  pages =        "165--179",
  month =        mar,
  year =         "1970",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160230204",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  bibdate =      "Sat Oct 21 12:05:50 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Pure Appl. Math.",
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "From the second paragraph: ``Motzkin [3] introduced
                 the notion of preconditioning of the coefficients.
                 Motzkin showed that if, in the course of computing $
                 P_n(x) = \sum_{i = 0}^n a_i x^i $, operations which
                 depend only the $ a_i $ are not counted, then only
                 about $ n / 2 $ multiplications are necessary to
                 evaluate $ P_n(x) $. The obvious application of this
                 result is when the same polynomial $ P_n(x) $ has to be
                 evaluated at many different points.''.",
}


bibtype: techreport
filename: elefunt.bib
label: Yohe:1970:RBC
author: J. M. Yohe
title: Rigorous Bounds on Computed Approximations to Square Roots and Cube Roots
type: MRC Technical Summary
number: 1088
institution: University of Wisconsin, Madison
pages: 165--179
year: 1970
bibdate: Fri Jan 12 11:37:56 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.01.12 11:37:56 ???
acknowledgement: ack-jr
rawauthor: J. M. Yohe
rawtitle: Rigorous Bounds on Computed Approximations to Square Roots and Cube Roots
entry:
@TechReport{Yohe:1970:RBC,
  author =       "J. M. Yohe",
  title =        "Rigorous Bounds on Computed Approximations to Square
                 Roots and Cube Roots",
  type =         "MRC Technical Summary",
  number =       "1088",
  institution =  "University of Wisconsin, Madison",
  year =         "1970",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-jr,
}


bibtype: article
filename: elefunt.bib
label: Yong:1970:GBA
author: Lam Lay Yong
title: The Geometrical Basis of the Ancient Chinese Square-Root Method
journal: j-ISIS
volume: 61
number: 1
pages: 92--102
month: Spring
year: 1970
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:28:39 MDT 2013
bibtimestamp: 2013.07.30 21:28:39 MDT
URL: http://www.jstor.org/stable/229151
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: Lam Lay Yong
rawtitle: The Geometrical Basis of the {Ancient Chinese} Square-Root Method
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302287; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/isis1970.bib

entry:
@Article{Yong:1970:GBA,
  author =       "Lam Lay Yong",
  title =        "The Geometrical Basis of the {Ancient Chinese}
                 Square-Root Method",
  journal =      j-ISIS,
  volume =       "61",
  number =       "1",
  pages =        "92--102",
  month =        "Spring",
  year =         "1970",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:28:39 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302287;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
  URL =          "http://www.jstor.org/stable/229151",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: article
filename: elefunt.bib
label: Zill:1970:SEI
author: D. G. Zill and B. C. Carlson
title: Symmetric Elliptic Integrals of the Third Kind
journal: j-MATH-COMPUT
volume: 24
number: 109
pages: 199--214
month: jan
monthnumber: 1
year: 1970
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: D. G. Zill and B. C. Carlson
rawtitle: Symmetric Elliptic Integrals of the Third Kind
entry:
@Article{Zill:1970:SEI,
  author =       "D. G. Zill and B. C. Carlson",
  title =        "Symmetric Elliptic Integrals of the Third Kind",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "109",
  pages =        "199--214",
  month =        jan,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Bohan:1971:ADC
author: K. A. Bohan and K. V. Lascenov
journal: Leningrad. Gos. Ped. Inst. Ucen. Zap.
volume: 404
pages: 59--78
year: 1971
MRclass: 26A09
MRnumber: 55 \#10612
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov
title:
The analytic definition of certain elementary functions. (Russian) Questions of modern mathematics and methods of teaching it at institutions of higher learning

rawtitle:
The analytic definition of certain elementary functions. ({Russian}) Questions of modern mathematics and methods of teaching it at institutions of higher learning

entry:
@Article{Bohan:1971:ADC,
  author =       "K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov",
  title =        "The analytic definition of certain elementary
                 functions. ({Russian}) Questions of modern mathematics
                 and methods of teaching it at institutions of higher
                 learning",
  journal =      "Leningrad. Gos. Ped. Inst. U{\v{c}}en. Zap.",
  volume =       "404",
  pages =        "59--78",
  year =         "1971",
  MRclass =      "26A09",
  MRnumber =     "55 \#10612",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: book
filename: elefunt.bib
label: Byrd:1971:HEI
author: Paul F. Byrd and Morris D. Friedman
title: Handbook of Elliptic Integrals for Engineers and Scientists
volume: 67
publisher: pub-SV
address: pub-SV:adr
edition: Second
pages: xvi + 358
year: 1971
DOI: https://doi.org/10.1007/978-3-642-65138-0
ISBN: 0-387-05318-2 (New York) OR 0387053182 (New York)
ISBN13: 978-0-387-05318-9 (New York) OR 9780387053189 (New York)
LCCN: QA343 .B95 1971
bibdate: Mon Oct 15 16:40:14 MDT 2007
bibtimestamp: 2007.10.15 16:40:14 MDT
series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen
subject: Elliptic functions
acknowledgement: ack-nhfb
rawauthor: Paul F. Byrd and Morris D. Friedman
rawtitle: Handbook of Elliptic Integrals for Engineers and Scientists
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; z3950.loc.gov:7090/Voyager

TOC:
Introduction / 1--7 Definitions and Fundamental Relations / 8--41 Reduction of Algebraic Integrands to Jacobian Elliptic Functions / 42--161 Reduction of Trigonometric Integrands to Jacobian Elliptic Functions / 162--181 Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions / 182--190 Table of Integrals of Jacobian Elliptic Functions / 191--222 Elliptic Integrals of the Third Kind / 223--239 Miscellaneous Elliptic Integrals Involving Trigonometric and Hyperbolic Integrands / 240--248 Elliptic Integrals Resulting from Laplace Transformations / 249--251 Hyperelliptic Integrals / 252--271 Integrals of the Elliptic Integrals / 272--281 Derivatives / 282--287 Miscellaneous Integrals and Formulas / 288--297 Expansions in Series / 298--307 Appendix / 308 Bibliography / 351 Supplemental Bibliography / 353 Index / 355

rawTOC:
Introduction / 1--7 \\ Definitions and Fundamental Relations / 8--41 \\ Reduction of Algebraic Integrands to Jacobian Elliptic Functions / 42--161 \\ Reduction of Trigonometric Integrands to Jacobian Elliptic Functions / 162--181 \\ Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions / 182--190 \\ Table of Integrals of Jacobian Elliptic Functions / 191--222 \\ Elliptic Integrals of the Third Kind / 223--239 \\ Miscellaneous Elliptic Integrals Involving Trigonometric and Hyperbolic Integrands / 240--248 \\ Elliptic Integrals Resulting from Laplace Transformations / 249--251 \\ Hyperelliptic Integrals / 252--271 \\ Integrals of the Elliptic Integrals / 272--281 \\ Derivatives / 282--287 \\ Miscellaneous Integrals and Formulas / 288--297 \\ Expansions in Series / 298--307 \\ Appendix / 308 \\ Bibliography / 351 \\ Supplemental Bibliography / 353 \\ Index / 355

entry:
@Book{Byrd:1971:HEI,
  author =       "Paul F. Byrd and Morris D. Friedman",
  title =        "Handbook of Elliptic Integrals for Engineers and
                 Scientists",
  volume =       "67",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xvi + 358",
  year =         "1971",
  DOI =          "https://doi.org/10.1007/978-3-642-65138-0",
  ISBN =         "0-387-05318-2 (New York)",
  ISBN-13 =      "978-0-387-05318-9 (New York)",
  LCCN =         "QA343 .B95 1971",
  bibdate =      "Mon Oct 15 16:40:14 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Die Grundlehren der mathematischen Wissenschaften in
                 Einzeldarstellungen",
  acknowledgement = ack-nhfb,
  subject =      "Elliptic functions",
  tableofcontents = "Introduction / 1--7 \\
                 Definitions and Fundamental Relations / 8--41 \\
                 Reduction of Algebraic Integrands to Jacobian Elliptic
                 Functions / 42--161 \\
                 Reduction of Trigonometric Integrands to Jacobian
                 Elliptic Functions / 162--181 \\
                 Reduction of Hyperbolic Integrands to Jacobian Elliptic
                 Functions / 182--190 \\
                 Table of Integrals of Jacobian Elliptic Functions /
                 191--222 \\
                 Elliptic Integrals of the Third Kind / 223--239 \\
                 Miscellaneous Elliptic Integrals Involving
                 Trigonometric and Hyperbolic Integrands / 240--248 \\
                 Elliptic Integrals Resulting from Laplace
                 Transformations / 249--251 \\
                 Hyperelliptic Integrals / 252--271 \\
                 Integrals of the Elliptic Integrals / 272--281 \\
                 Derivatives / 282--287 \\
                 Miscellaneous Integrals and Formulas / 288--297 \\
                 Expansions in Series / 298--307 \\
                 Appendix / 308 \\
                 Bibliography / 351 \\
                 Supplemental Bibliography / 353 \\
                 Index / 355",
}


bibtype: misc
filename: elefunt.bib
label: Chen:1971:BAU
author: Tien Chi Chen
pages: xvi + 358
day: 28
month: dec
monthnumber: 12
year: 1971
bibdate: Tue Jan 08 21:54:11 2008
bibtimestamp: 2008.01.08 21:54:11 ???
URL: http://www.freepatentsonline.com/3631230.html
acknowledgement: ack-nhfb
howpublished: United States Patent 3,631,230
rawauthor: Tien Chi Chen
title:
Binary arithmetic unit implementing a multiplicative iteration for the exponential, logarithm, quotient and square root functions

abstract:
Apparatus and a method is described for efficiently achieving arithmetic evaluations for functions such as exponential, logarithm, quotient, and square root with a minimum use of multiplications or divisions. Basically, use is made of the fact that $ x(1 pm 2^-m) $ can be evaluated by a shift followed by an add. A pair of numbers $ (x_k, y_k) $ can represent a function $ x : f(x) = g(x_k, y_k) $, such that $ g(l, y_n) = y_n $ for logarithm, quotient and square root. Then, multiplication by shifting is applied to $ x_k $ with suitable adjustments on $ y_k $, until $ x_k $ is close to unity, at which time $ y_k $ represents the desired answer. The exponential is computed by essentially reversing the logarithm procedure. A termination algorithm further improves accuracy. The apparatus involves two registers for $ x_k $ and $ y_k $, a local memory, an adder and a shift register.

rawabstract:
Apparatus and a method is described for efficiently achieving arithmetic evaluations for functions such as exponential, logarithm, quotient, and square root with a minimum use of multiplications or divisions. Basically, use is made of the fact that $ x(1 \pm 2^{-m}) $ can be evaluated by a shift followed by an add. A pair of numbers $ (x_k, y_k) $ can represent a function $ x : f(x) = g(x_k, y_k) $, such that $ g(l, y_n) = y_n $ for logarithm, quotient and square root. Then, multiplication by shifting is applied to $ x_k $ with suitable adjustments on $ y_k $, until $ x_k $ is close to unity, at which time $ y_k $ represents the desired answer. The exponential is computed by essentially reversing the logarithm procedure. A termination algorithm further improves accuracy. The apparatus involves two registers for $ x_k $ and $ y_k $, a local memory, an adder and a shift register.

rawtitle:
Binary arithmetic unit implementing a multiplicative iteration for the exponential, logarithm, quotient and square root functions

entry:
@Misc{Chen:1971:BAU,
  author =       "Tien Chi Chen",
  title =        "Binary arithmetic unit implementing a multiplicative
                 iteration for the exponential, logarithm, quotient and
                 square root functions",
  howpublished = "United States Patent 3,631,230",
  day =          "28",
  month =        dec,
  year =         "1971",
  bibdate =      "Tue Jan 08 21:54:11 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/3631230.html",
  abstract =     "Apparatus and a method is described for efficiently
                 achieving arithmetic evaluations for functions such as
                 exponential, logarithm, quotient, and square root with
                 a minimum use of multiplications or divisions.
                 Basically, use is made of the fact that $ x(1 \pm
                 2^{-m}) $ can be evaluated by a shift followed by an
                 add. A pair of numbers $ (x_k, y_k) $ can represent a
                 function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
                 y_n) = y_n $ for logarithm, quotient and square root.
                 Then, multiplication by shifting is applied to $ x_k $
                 with suitable adjustments on $ y_k $, until $ x_k $ is
                 close to unity, at which time $ y_k $ represents the
                 desired answer. The exponential is computed by
                 essentially reversing the logarithm procedure. A
                 termination algorithm further improves accuracy. The
                 apparatus involves two registers for $ x_k $ and $ y_k
                 $, a local memory, an adder and a shift register.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Choong:1971:RA
author: K. Y. Choong and D. E. Daykin and C. R. Rathbone
title: Rational Approximations to $ pi $
journal: j-MATH-COMPUT
volume: 25
number: 114
pages: 387--392
month: apr
monthnumber: 4
year: 1971
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1971-0300981-0
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
note: See errata cite Shanks:1976:TER.
URL: http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0300981-0
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: K. Y. Choong and D. E. Daykin and C. R. Rathbone
rawnote: See errata \cite{Shanks:1976:TER}.
rawtitle: Rational Approximations to $ \pi $
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR database

entry:
@Article{Choong:1971:RA,
  author =       "K. Y. Choong and D. E. Daykin and C. R. Rathbone",
  title =        "Rational Approximations to $ \pi $",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "387--392",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1971-0300981-0",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
                 database",
  note =         "See errata \cite{Shanks:1976:TER}.",
  URL =          "http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0300981-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Cody:1971:CAR
author: W. J. Cody and K. E. Hillstrom and Henry C. Thatcher, Jr.
title: Chebyshev approximations for the Riemann zeta function
journal: j-MATH-COMPUT
volume: 25
number: 115
pages: 537--547
month: jul
monthnumber: 7
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D20
MRnumber: 47 2785
bibdate: Wed Jan 17 08:57:00 1996
bibtimestamp: 1996.01.17 08:57:00 ???
fjournal: Mathematics of Computation
remark: Fullerton: 20-digit approximations for either $ zeta (s) $ or $ zeta (s) - 1 $.
acknowledgement: ack-wjc
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody and K. E. Hillstrom and Henry C. {Thatcher, Jr.}
rawtitle: {Chebyshev} approximations for the {Riemann} zeta function
entry:
@Article{Cody:1971:CAR,
  author =       "W. J. Cody and K. E. Hillstrom and Henry C. {Thatcher,
                 Jr.}",
  title =        "{Chebyshev} approximations for the {Riemann} zeta
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "115",
  pages =        "537--547",
  month =        jul,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "47 2785",
  bibdate =      "Wed Jan 17 08:57:00 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 20-digit approximations for either $ \zeta
                 (s) $ or $ \zeta (s) - 1 $.",
}


bibtype: incollection
filename: elefunt.bib
label: Cody:1971:SEF
author: W. J. Cody
title: Software for the Elementary Functions
crossref: Rice:1971:MS
pages: 171--186
year: 1971
bibdate: Thu Sep 15 18:56:47 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.15 18:56:47 ???
acknowledgement: ack-nj
rawauthor: W. J. Cody
rawtitle: Software for the Elementary Functions
entry:
@InCollection{Cody:1971:SEF,
  author =       "W. J. Cody",
  title =        "Software for the Elementary Functions",
  crossref =     "Rice:1971:MS",
  pages =        "171--186",
  year =         "1971",
  bibdate =      "Thu Sep 15 18:56:47 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Glasser:1971:CFE
author: M. L. Glasser and V. E. Wood
title: A Closed Form Evaluation of the Elliptic Integral
journal: j-MATH-COMPUT
volume: 25
number: 115
pages: 535--536
month: jul
monthnumber: 7
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: M. L. Glasser and V. E. Wood
rawtitle: A Closed Form Evaluation of the Elliptic Integral
entry:
@Article{Glasser:1971:CFE,
  author =       "M. L. Glasser and V. E. Wood",
  title =        "A Closed Form Evaluation of the Elliptic Integral",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "115",
  pages =        "535--536",
  month =        jul,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Glasser:1971:EII
author: M. L. Glasser
title: An Elliptic Integral Identity
journal: j-MATH-COMPUT
volume: 25
number: 115
pages: 533--534
month: jul
monthnumber: 7
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: M. L. Glasser
rawtitle: An Elliptic Integral Identity
entry:
@Article{Glasser:1971:EII,
  author =       "M. L. Glasser",
  title =        "An Elliptic Integral Identity",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "115",
  pages =        "533--534",
  month =        jul,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Herman:1971:EDH
author: G. T. Herman
title: The equivalence of different hierarchies of elementary functions
journal: Z. Math. Logik Grundlagen Math.
volume: 17
pages: 219--224
year: 1971
MRclass: 02.77 (68.00)
MRnumber: 44 \#6494
MRreviewer: D. A. Clarke
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: G. T. Herman
rawtitle: The equivalence of different hierarchies of elementary functions
entry:
@Article{Herman:1971:EDH,
  author =       "G. T. Herman",
  title =        "The equivalence of different hierarchies of elementary
                 functions",
  journal =      "Z. Math. Logik Grundlagen Math.",
  volume =       "17",
  pages =        "219--224",
  year =         "1971",
  MRclass =      "02.77 (68.00)",
  MRnumber =     "44 \#6494",
  MRreviewer =   "D. A. Clarke",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Hochstadt:1971:FMP
author: Harry Hochstadt
title: The Functions of Mathematical Physics
volume: XXIII
publisher: pub-WI
address: pub-WI:adr
pages: xi + 322
year: 1971
ISBN: 0-471-40170-6 (hardcover) OR 0471401706 (hardcover)
ISBN13: 978-0-471-40170-4 (hardcover) OR 9780471401704 (hardcover)
LCCN: QA351 .H68
bibdate: Tue Dec 5 10:48:41 MST 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.12.05 10:48:41 MST
series: Pure and applied mathematics: a series of texts and monographs
subject: Functions, Special; Fonctions speciales; Fonctions (mathematiques)
acknowledgement: ack-nhfb
rawauthor: Harry Hochstadt
rawtitle: The Functions of Mathematical Physics
TOC:
1: Orthogonal Polynomials 1 Linear Spaces / 1 2 Orthogonal Polynomials / 6 3 The Recurrence Formula / 8 4 The Christoffel--Darboux Formula / 9 5 The Weierstrass Approximation Theorem / 11 6 The Zeros of the Orthogonal Polynomials / 14 7 Approximation Theory / 16 8 More about the Zeros of the Orthonormal Polynomials / 23 9 The completeness of the Orthonormal Polynomials in the Space of Square-Integrable Functions / 27 10 Generalizations and an Application to Conformal Mappings / 32 2: The Classical Orthogonal Polynomials 1 Rodrigues' Formula and the Classical Orthogonal Polynomials / 39 2 The Differential Equations Satisfied by the Classical Orthogonal Polynomials / 43 3 On the Zeros of the Jacobi Polynomials / 45 4 An Alternative Approach to the Tchebicheff Polynomials / 46 5 An Application of the Hermite Polynomials to Quantum Mechanics / 49 6 The Completeness of the Hermite and Laguerre Polynomials / 53 7 Generating Functions / 57 3: The Gamma Function 1 Definitions and Basic Properties / 61 2 Analytic Continuation and Integral Representations / 65 3 Asymptotic Expansions / 69 4 Beta Functions / 75 5 The Logarithmic Derivative of the Gamma Function / 77 6 Mellin--Barnes Integrals / 78 7 Mellin Transforms / 80 8 Applications to Algebraic Equations / 81 4: Hypergeometric Functions 1 Review of Linear Differential Equations with Regular Singular Points / 88 2 The Hypergeometric Differential Equation / 90 3 The Hypergeometric Function / 93 4 A General Method for Finding Integral Representations / 100 5 Integral Representations for the Hypergeometric Function / 105 6 The Twenty-four Solutions of the Hypergeometric / Equation / 106 7 The Schwarz--Christoffel Transformation / 112 8 Mappings of Curvilinear Triangles / 119 9 Group Theoretic Discussion of the Case $ pi (alpha _1 + alpha _2 + alpha _3) > pi $ / 130 10 Nonlinear Transformations of Hypergeometric Functions / 132 5: The Legendre Functions 1 Laplace's Differential Equation / 138 2 Maxwell's Theory of Poles / 140 3 Relationship to the Hypergeometric Functions / 141 4 Expansion Formulas / 147 5 The Addition Theorem / 149 6 Green's Functions / 153 7 The Complete Solution of Legendre's Differential Equation / 156 8 Asymptotic Formulas / 161 6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous Polynomials / 168 2 Orthogonality of Spherical Harmonics / 171 3 Legendre Polynomials / 175 4 Applications to Boundary Value Problems / 183 7: Confluent Hypergeometric Functions 1 Relationship to the Hypergeometric Functions / 189 2 Applications of These Functions in Mathematical Physics / 191 3 Integral Representations / 195 4 Asymptotic Representations / 198 8: Bessel Functions 1 Basic Definitions / 200 2 Integral Representations / 203 3 Relationship to the Legendre Functions / 205 4 The Generating Function of the Bessel Function / 207 5 More Integral Representations / 210 6 Addition Theorems / 216 7 The Complete Solution of Bessel's Equation / 223 8 Asymptotic Expansions for Large Argument / 225 9 Airy Functions / 230 10 Asymptotic Expansions for Large Indices and Large Arguments / 235 11 Some Applications of Bessel Functions in Physical Optics / 241 12 The Zeros of Bessel Functions / 249 13 Fourier--Bessel Expansions / 257 14 Applications in Mathematical Physics / 266 15 Discontinuous Integrals / 269 9: Hill's Equation 1 Mathieu's Equation / 281 2 Hill's Equation / 282 3 The Discriminant / 287 4 Expansion Theorems / 299 5 Inverse Problems / 305 6 Hill's Equations with Even Coefficients / 309 7 Mathieu's Equation Revisited / 310 8 Energy Bands in Crystals / 313 Appendix / 314 Bibliography / 318 Index / 321

rawTOC:
1: Orthogonal Polynomials \\ 1 Linear Spaces / 1 \\ 2 Orthogonal Polynomials / 6 \\ 3 The Recurrence Formula / 8 \\ 4 The Christoffel--Darboux Formula / 9 \\ 5 The Weierstrass Approximation Theorem / 11 \\ 6 The Zeros of the Orthogonal Polynomials / 14 \\ 7 Approximation Theory / 16 \\ 8 More about the Zeros of the Orthonormal Polynomials / 23 \\ 9 The completeness of the Orthonormal Polynomials in the Space of Square-Integrable Functions / 27 \\ 10 Generalizations and an Application to Conformal Mappings / 32 \\ \\ 2: The Classical Orthogonal Polynomials 1 Rodrigues' Formula and the Classical Orthogonal Polynomials / 39 \\ 2 The Differential Equations Satisfied by the Classical Orthogonal Polynomials / 43 \\ 3 On the Zeros of the Jacobi Polynomials / 45 \\ 4 An Alternative Approach to the Tchebicheff Polynomials / 46 \\ 5 An Application of the Hermite Polynomials to Quantum Mechanics / 49 \\ 6 The Completeness of the Hermite and Laguerre Polynomials / 53 \\ 7 Generating Functions / 57 \\ \\ 3: The Gamma Function 1 Definitions and Basic Properties / 61 \\ 2 Analytic Continuation and Integral Representations / 65 \\ 3 Asymptotic Expansions / 69 \\ 4 Beta Functions / 75 \\ 5 The Logarithmic Derivative of the Gamma Function / 77 \\ 6 Mellin--Barnes Integrals / 78 \\ 7 Mellin Transforms / 80 \\ 8 Applications to Algebraic Equations / 81 \\ \\ 4: Hypergeometric Functions 1 Review of Linear Differential Equations with Regular Singular Points / 88 \\ 2 The Hypergeometric Differential Equation / 90 \\ 3 The Hypergeometric Function / 93 \\ 4 A General Method for Finding Integral Representations / 100 \\ 5 Integral Representations for the Hypergeometric Function / 105 \\ 6 The Twenty-four Solutions of the Hypergeometric / Equation / 106 \\ 7 The Schwarz--Christoffel Transformation / 112 \\ 8 Mappings of Curvilinear Triangles / 119 \\ 9 Group Theoretic Discussion of the Case $ \pi(\alpha_1 + \alpha_2 + \alpha_3) > \pi$ / 130 \\ 10 Nonlinear Transformations of Hypergeometric Functions / 132 \\ \\ 5: The Legendre Functions 1 Laplace's Differential Equation / 138 \\ 2 Maxwell's Theory of Poles / 140 \\ 3 Relationship to the Hypergeometric Functions / 141 \\ 4 Expansion Formulas / 147 \\ 5 The Addition Theorem / 149 \\ 6 Green's Functions / 153 \\ 7 The Complete Solution of Legendre's Differential Equation / 156 \\ 8 Asymptotic Formulas / 161 \\ \\ 6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous Polynomials / 168 \\ 2 Orthogonality of Spherical Harmonics / 171 \\ 3 Legendre Polynomials / 175 \\ 4 Applications to Boundary Value Problems / 183 \\ \\ 7: Confluent Hypergeometric Functions 1 Relationship to the Hypergeometric Functions / 189 \\ 2 Applications of These Functions in Mathematical Physics / 191 \\ 3 Integral Representations / 195 \\ 4 Asymptotic Representations / 198 \\ \\ 8: Bessel Functions 1 Basic Definitions / 200 \\ 2 Integral Representations / 203 \\ 3 Relationship to the Legendre Functions / 205 \\ 4 The Generating Function of the Bessel Function / 207 \\ 5 More Integral Representations / 210 \\ 6 Addition Theorems / 216 \\ 7 The Complete Solution of Bessel's Equation / 223 \\ 8 Asymptotic Expansions for Large Argument / 225 \\ 9 Airy Functions / 230 \\ 10 Asymptotic Expansions for Large Indices and Large Arguments / 235 \\ 11 Some Applications of Bessel Functions in Physical Optics / 241 \\ 12 The Zeros of Bessel Functions / 249 \\ 13 Fourier--Bessel Expansions / 257 \\ 14 Applications in Mathematical Physics / 266 \\ 15 Discontinuous Integrals / 269 \\ \\ 9: Hill's Equation 1 Mathieu's Equation / 281 \\ 2 Hill's Equation / 282 \\ 3 The Discriminant / 287 \\ 4 Expansion Theorems / 299 \\ 5 Inverse Problems / 305 \\ 6 Hill's Equations with Even Coefficients / 309 \\ 7 Mathieu's Equation Revisited / 310 \\ 8 Energy Bands in Crystals / 313 \\ Appendix / 314 \\ \\ Bibliography / 318 \\ \\ Index / 321

entry:
@Book{Hochstadt:1971:FMP,
  author =       "Harry Hochstadt",
  title =        "The Functions of Mathematical Physics",
  volume =       "XXIII",
  publisher =    pub-WI,
  address =      pub-WI:adr,
  pages =        "xi + 322",
  year =         "1971",
  ISBN =         "0-471-40170-6 (hardcover)",
  ISBN-13 =      "978-0-471-40170-4 (hardcover)",
  LCCN =         "QA351 .H68",
  bibdate =      "Tue Dec 5 10:48:41 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Pure and applied mathematics: a series of texts and
                 monographs",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Fonctions sp{\'e}ciales; Fonctions
                 (math{\'e}matiques)",
  tableofcontents = "1: Orthogonal Polynomials \\
                 1 Linear Spaces / 1 \\
                 2 Orthogonal Polynomials / 6 \\
                 3 The Recurrence Formula / 8 \\
                 4 The Christoffel--Darboux Formula / 9 \\
                 5 The Weierstrass Approximation Theorem / 11 \\
                 6 The Zeros of the Orthogonal Polynomials / 14 \\
                 7 Approximation Theory / 16 \\
                 8 More about the Zeros of the Orthonormal Polynomials /
                 23 \\
                 9 The completeness of the Orthonormal Polynomials in
                 the Space of Square-Integrable Functions / 27 \\
                 10 Generalizations and an Application to Conformal
                 Mappings / 32 \\
                 \\
                 2: The Classical Orthogonal Polynomials 1 Rodrigues'
                 Formula and the Classical Orthogonal Polynomials / 39
                 \\
                 2 The Differential Equations Satisfied by the Classical
                 Orthogonal Polynomials / 43 \\
                 3 On the Zeros of the Jacobi Polynomials / 45 \\
                 4 An Alternative Approach to the Tchebicheff
                 Polynomials / 46 \\
                 5 An Application of the Hermite Polynomials to Quantum
                 Mechanics / 49 \\
                 6 The Completeness of the Hermite and Laguerre
                 Polynomials / 53 \\
                 7 Generating Functions / 57 \\
                 \\
                 3: The Gamma Function 1 Definitions and Basic
                 Properties / 61 \\
                 2 Analytic Continuation and Integral Representations /
                 65 \\
                 3 Asymptotic Expansions / 69 \\
                 4 Beta Functions / 75 \\
                 5 The Logarithmic Derivative of the Gamma Function / 77
                 \\
                 6 Mellin--Barnes Integrals / 78 \\
                 7 Mellin Transforms / 80 \\
                 8 Applications to Algebraic Equations / 81 \\
                 \\
                 4: Hypergeometric Functions 1 Review of Linear
                 Differential Equations with Regular Singular Points /
                 88 \\
                 2 The Hypergeometric Differential Equation / 90 \\
                 3 The Hypergeometric Function / 93 \\
                 4 A General Method for Finding Integral Representations
                 / 100 \\
                 5 Integral Representations for the Hypergeometric
                 Function / 105 \\
                 6 The Twenty-four Solutions of the Hypergeometric /
                 Equation / 106 \\
                 7 The Schwarz--Christoffel Transformation / 112 \\
                 8 Mappings of Curvilinear Triangles / 119 \\
                 9 Group Theoretic Discussion of the Case $ \pi(\alpha_1
                 + \alpha_2 + \alpha_3) > \pi$ / 130 \\
                 10 Nonlinear Transformations of Hypergeometric
                 Functions / 132 \\
                 \\
                 5: The Legendre Functions 1 Laplace's Differential
                 Equation / 138 \\
                 2 Maxwell's Theory of Poles / 140 \\
                 3 Relationship to the Hypergeometric Functions / 141
                 \\
                 4 Expansion Formulas / 147 \\
                 5 The Addition Theorem / 149 \\
                 6 Green's Functions / 153 \\
                 7 The Complete Solution of Legendre's Differential
                 Equation / 156 \\
                 8 Asymptotic Formulas / 161 \\
                 \\
                 6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous
                 Polynomials / 168 \\
                 2 Orthogonality of Spherical Harmonics / 171 \\
                 3 Legendre Polynomials / 175 \\
                 4 Applications to Boundary Value Problems / 183 \\
                 \\
                 7: Confluent Hypergeometric Functions 1 Relationship to
                 the Hypergeometric Functions / 189 \\
                 2 Applications of These Functions in Mathematical
                 Physics / 191 \\
                 3 Integral Representations / 195 \\
                 4 Asymptotic Representations / 198 \\
                 \\
                 8: Bessel Functions 1 Basic Definitions / 200 \\
                 2 Integral Representations / 203 \\
                 3 Relationship to the Legendre Functions / 205 \\
                 4 The Generating Function of the Bessel Function / 207
                 \\
                 5 More Integral Representations / 210 \\
                 6 Addition Theorems / 216 \\
                 7 The Complete Solution of Bessel's Equation / 223 \\
                 8 Asymptotic Expansions for Large Argument / 225 \\
                 9 Airy Functions / 230 \\
                 10 Asymptotic Expansions for Large Indices and Large
                 Arguments / 235 \\
                 11 Some Applications of Bessel Functions in Physical
                 Optics / 241 \\
                 12 The Zeros of Bessel Functions / 249 \\
                 13 Fourier--Bessel Expansions / 257 \\
                 14 Applications in Mathematical Physics / 266 \\
                 15 Discontinuous Integrals / 269 \\
                 \\
                 9: Hill's Equation 1 Mathieu's Equation / 281 \\
                 2 Hill's Equation / 282 \\
                 3 The Discriminant / 287 \\
                 4 Expansion Theorems / 299 \\
                 5 Inverse Problems / 305 \\
                 6 Hill's Equations with Even Coefficients / 309 \\
                 7 Mathieu's Equation Revisited / 310 \\
                 8 Energy Bands in Crystals / 313 \\
                 Appendix / 314 \\
                 \\
                 Bibliography / 318 \\
                 \\
                 Index / 321",
}


bibtype: article
filename: elefunt.bib
label: Honey:1971:CCD
author: D. W. Honey
journal: j-COMP-J
volume: 14
number: 4
pages: 443--443
month: nov
monthnumber: 11
year: 1971
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:51:58 MDT 2000
bibtimestamp: 2000.09.29 08:51:58 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: D. W. Honey
title:
Correspondence: Calculation of a double-length square root from a double length number using single precision techniques

bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/; https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif

rawtitle:
Correspondence: Calculation of a double-length square root from a double length number using single precision techniques

entry:
@Article{Honey:1971:CCD,
  author =       "D. W. Honey",
  title =        "Correspondence: Calculation of a double-length square
                 root from a double length number using single precision
                 techniques",
  journal =      j-COMP-J,
  volume =       "14",
  number =       "4",
  pages =        "443--443",
  month =        nov,
  year =         "1971",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:58 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: elefunt.bib
label: Kuki:1971:FEP
author: H. Kuki and J. Ascoly
title: FORTRAN extended-precision library
journal: j-IBM-SYS-J
volume: 10
number: 1
pages: 39--61
year: 1971
CODEN: IBMSA7
ISSN: 0018-8670 OR 00188670
bibdate: Thu Sep 15 18:51:32 1994
bibtimestamp: 1994.09.15 18:51:32 ???
fjournal: IBM Systems Journal
acknowledgement: ack-nj
rawauthor: H. Kuki and J. Ascoly
rawtitle: {FORTRAN} extended-precision library
bibsource:
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib

entry:
@Article{Kuki:1971:FEP,
  author =       "H. Kuki and J. Ascoly",
  title =        "{FORTRAN} extended-precision library",
  journal =      j-IBM-SYS-J,
  volume =       "10",
  number =       "1",
  pages =        "39--61",
  year =         "1971",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:51:32 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Systems Journal",
  xxmonth =      "(none)",
}


bibtype: incollection
filename: elefunt.bib
label: Kuki:1971:MFS
author: H. Kuki
crossref: Rice:1971:MS
pages: 187--199
year: 1971
bibdate: Fri Sep 16 16:27:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 16:27:40 ???
acknowledgement: ack-nj
rawauthor: H. Kuki
title:
Mathematical Function Subprograms for Basic System Libraries --- Objectives, Constraints, and Trade-Off

rawtitle:
Mathematical Function Subprograms for Basic System Libraries{}\emdash Objectives, Constraints, and Trade-Off

entry:
@InCollection{Kuki:1971:MFS,
  author =       "H. Kuki",
  title =        "Mathematical Function Subprograms for Basic System
                 Libraries{}\emdash Objectives, Constraints, and
                 Trade-Off",
  crossref =     "Rice:1971:MS",
  pages =        "187--199",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:27:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Lehmer:1971:CCM
author: D. H. Lehmer
title: On the compounding of certain means
journal: j-J-MATH-ANAL-APPL
volume: 36
number: 1
pages: 183--200
month: oct
monthnumber: 10
year: 1971
CODEN: JMANAK
DOI: https://doi.org/10.1016/0022-247x(71)90029-1
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
bibdate: Tue Mar 14 18:52:11 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.14 18:52:11 ???
fjournal: Journal of Mathematical Analysis and Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/0022247X
rawauthor: D. H. Lehmer
rawtitle: On the compounding of certain means
keywords:
arithmetic--geometric mean (AGM) iteration; complete elliptic integrals of the first and second kinds. Landen s transformation

entry:
@Article{Lehmer:1971:CCM,
  author =       "D. H. Lehmer",
  title =        "On the compounding of certain means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "36",
  number =       "1",
  pages =        "183--200",
  month =        oct,
  year =         "1971",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/0022-247x(71)90029-1",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 18:52:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "arithmetic--geometric mean (AGM) iteration; complete
                 elliptic integrals of the first and second kinds.
                 Landen s transformation",
}


bibtype: article
filename: elefunt.bib
label: Liron:1971:ISR
author: N. Liron
journal: j-MATH-COMPUT
volume: 25
number: 116
pages: 769--781
month: oct
monthnumber: 10
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: N. Liron
title:
Infinite Sums of Roots for a Class of Transcendental Equations and Bessel Functions of Order One-Half

rawtitle:
Infinite Sums of Roots for a Class of Transcendental Equations and {Bessel} Functions of Order One-Half

entry:
@Article{Liron:1971:ISR,
  author =       "N. Liron",
  title =        "Infinite Sums of Roots for a Class of Transcendental
                 Equations and {Bessel} Functions of Order One-Half",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "769--781",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Lucas:1971:AAC
author: C. W. Lucas, Jr. and C. W. Terrill
title: ACM Algorithm 404: Complex Gamma Function [S14]
journal: j-CACM
volume: 14
number: 1
pages: 48--49
month: jan
monthnumber: 1
year: 1971
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:00:03 MST 2001
bibtimestamp: 2001.01.22 07:00:03 MST
fjournal: Communications of the ACM
remark: Fullerton: Fortran routine with machine-dependent constants.
acknowledgement: ack-nhfb
classcodes: C4120 (Functional analysis); C7310 (Mathematics computing)
corpsource: Coll. William and Mary, Williamsburg, VA, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: C. W. {Lucas, Jr.} and C. W. Terrill
rawtitle: {ACM Algorithm 404}: Complex Gamma Function [{S14}]
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#LucasT71; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
algorithm; CGAMMA; complex gamma function evaluation; formula; function evaluation; poles of gamma function; recursion formula; reflection; Stirling's asymptotic series; subroutine in ALGOL; subroutines

entry:
@Article{Lucas:1971:AAC,
  author =       "C. W. {Lucas, Jr.} and C. W. Terrill",
  title =        "{ACM Algorithm 404}: Complex Gamma Function [{S14}]",
  journal =      j-CACM,
  volume =       "14",
  number =       "1",
  pages =        "48--49",
  month =        jan,
  year =         "1971",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:00:03 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#LucasT71;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4120 (Functional analysis); C7310 (Mathematics
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  corpsource =   "Coll. William and Mary, Williamsburg, VA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; CGAMMA; complex gamma function evaluation;
                 formula; function evaluation; poles of gamma function;
                 recursion formula; reflection; Stirling's asymptotic
                 series; subroutine in ALGOL; subroutines",
  oldlabel =     "LucasT71",
  remark =       "Fullerton: Fortran routine with machine-dependent
                 constants.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/LucasT71",
}


bibtype: article
filename: elefunt.bib
label: Luke:1971:MTBa
author: Yudell L. Luke
title: Miniaturized Tables of Bessel Functions
journal: j-MATH-COMPUT
volume: 25
number: 114
pages: 323--330
month: apr
monthnumber: 4
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Yudell L. Luke
rawtitle: Miniaturized Tables of {Bessel} Functions
entry:
@Article{Luke:1971:MTBa,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "323--330",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Luke:1971:MTBb
author: Yudell L. Luke
title: Miniaturized Tables of Bessel Functions, II
journal: j-MATH-COMPUT
volume: 25
number: 116
pages: 789--795
month: oct
monthnumber: 10
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Yudell L. Luke
rawtitle: Miniaturized Tables of {Bessel} Functions, {II}
entry:
@Article{Luke:1971:MTBb,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions, {II}",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "789--795",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Majithia:1971:CAN
author: J. C. Majithia and R. Kitai
title: A Cellular Array for the Nonrestoring Extraction of Square Roots
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 12
pages: 1617--1618
month: dec
monthnumber: 12
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223191
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 06:38:22 MDT 2011
bibtimestamp: 2011.07.13 06:38:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. C. Majithia and R. Kitai
rawtitle: A Cellular Array for the Nonrestoring Extraction of Square Roots
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

entry:
@Article{Majithia:1971:CAN,
  author =       "J. C. Majithia and R. Kitai",
  title =        "A Cellular Array for the Nonrestoring Extraction of
                 Square Roots",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1617--1618",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223191",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Matta:1971:UCE
author: F. Matta and A. Reichel
title: Uniform Computation of the Error Function and Other Related Functions
journal: j-MATH-COMPUT
volume: 25
number: 114
pages: 339--344
month: apr
monthnumber: 4
year: 1971
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1971-0295538-4
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0295538-4
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: F. Matta and A. Reichel
rawtitle: Uniform Computation of the Error Function and Other Related Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database

entry:
@Article{Matta:1971:UCE,
  author =       "F. Matta and A. Reichel",
  title =        "Uniform Computation of the Error Function and Other
                 Related Functions",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "339--344",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1971-0295538-4",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  URL =          "http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0295538-4",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: phdthesis
filename: elefunt.bib
label: Rothmaier:1971:BEF
author: B. Rothmaier
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1971
bibdate: Fri Sep 16 16:30:40 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 16:30:40 ???
acknowledgement: ack-nj
rawauthor: B. Rothmaier
title:
Die Berechnung der elementaren Funktionen mit beliebiger Genauigkeit toenglish The Computation of Elementary Functions with Arbitrary Accuracy endtoenglish 

rawtitle:
{Die Berechnung der elementaren Funktionen mit beliebiger Genauigkeit} \toenglish {The Computation of Elementary Functions with Arbitrary Accuracy} \endtoenglish

entry:
@PhdThesis{Rothmaier:1971:BEF,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der elementaren Funktionen mit
                 beliebiger Genauigkeit} \toenglish {The Computation of
                 Elementary Functions with Arbitrary Accuracy}
                 \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Sarkar:1971:EPP
author: B. P. Sarkar and E. V. Krishnamurthy
title: Economic Pseudodivision Processes for Obtaining Square Root, Logarithm, and Arctan
journal: j-IEEE-TRANS-COMPUT
volume: C-20
number: 12
pages: 1589--1593
month: dec
monthnumber: 12
year: 1971
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1971.223178
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 01 10:32:36 1994
bibtimestamp: 1994.09.01 10:32:36 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: B. P. Sarkar and E. V. Krishnamurthy
rawtitle: Economic Pseudodivision Processes for Obtaining Square Root, Logarithm, and Arctan
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

entry:
@Article{Sarkar:1971:EPP,
  author =       "B. P. Sarkar and E. V. Krishnamurthy",
  title =        "Economic Pseudodivision Processes for Obtaining Square
                 Root, Logarithm, and Arctan",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1589--1593",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223178",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 01 10:32:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Scarton:1971:DPF
author: Henry A. Scarton
journal: j-J-COMPUT-PHYS
volume: 8
number: 2
pages: 295--299
month: oct
monthnumber: 10
year: 1971
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(71)90010-6
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:04 MST 2012
bibtimestamp: 2012.01.01 09:15:04 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999171900106
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Henry A. Scarton
title:
Double precision FORTRAN subroutines to compute both ordinary and modified Bessel functions of the first kind and of integer order with arbitrary complex argument: $ J_n(x + j y) $ and $ I_n(x + j y) $

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib

rawtitle:
Double precision {FORTRAN} subroutines to compute both ordinary and modified {Bessel} functions of the first kind and of integer order with arbitrary complex argument: {$ J_n(x + j y) $} and {$ I_n(x + j y) $}

entry:
@Article{Scarton:1971:DPF,
  author =       "Henry A. Scarton",
  title =        "Double precision {FORTRAN} subroutines to compute both
                 ordinary and modified {Bessel} functions of the first
                 kind and of integer order with arbitrary complex
                 argument: {$ J_n(x + j y) $} and {$ I_n(x + j y) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "8",
  number =       "2",
  pages =        "295--299",
  month =        oct,
  year =         "1971",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(71)90010-6",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999171900106",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Shenton:1971:CFP
author: L. R. Shenton and K. O. Bowman
title: Continued Fractions for the Psi Function and its Derivatives
journal: j-SIAM-J-APPL-MATH
volume: 20
number: 4
pages: 547--554
month: jun
monthnumber: 6
year: 1971
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Thu Oct 15 18:16:06 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.15 18:16:06 MDT
URL: http://www.jstor.org/stable/2099856
fjournal: SIAM Journal on Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siap
rawauthor: L. R. Shenton and K. O. Bowman
rawtitle: Continued Fractions for the Psi Function and its Derivatives
entry:
@Article{Shenton:1971:CFP,
  author =       "L. R. Shenton and K. O. Bowman",
  title =        "Continued Fractions for the Psi Function and its
                 Derivatives",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "20",
  number =       "4",
  pages =        "547--554",
  month =        jun,
  year =         "1971",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2099856",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
}


bibtype: article
filename: elefunt.bib
label: Shipman:1971:HSE
author: L. L. Shipman and R. E. Christoffersen
title: High Speed Evaluation of $ F_0 (x) $
journal: j-COMP-PHYS-COMM
volume: 2
number: 4
pages: 201--206
month: may
monthnumber: 5
year: 1971
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(71)90053-1
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Oct 30 10:40:08 2010
bibtimestamp: 2010.10.30 10:40:08 ???
URL: http://www.sciencedirect.com/science/article/pii/0010465571900531
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: L. L. Shipman and R. E. Christoffersen
rawtitle: High Speed Evaluation of {$ F_0 (x) $}
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
Fullerton: $ F_0 (x) = int _0^1 exp ( - x u^2) d u $, which is simply related to $ erf $ for $ x > 0 $ and to Dawson's function for $ x < 0 $.

entry:
@Article{Shipman:1971:HSE,
  author =       "L. L. Shipman and R. E. Christoffersen",
  title =        "High Speed Evaluation of {$ F_0 (x) $}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "2",
  number =       "4",
  pages =        "201--206",
  month =        may # "\slash " # jun,
  year =         "1971",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(71)90053-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:40:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465571900531",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: $ F_0 (x) = \int_0^1 \exp ( - x u^2) \, d u
                 $, which is simply related to $ \erf $ for $ x > 0 $
                 and to Dawson's function for $ x < 0 $.",
}


bibtype: article
filename: elefunt.bib
label: Spellucci:1971:DPA
author: P. Spellucci
title: Double precision approximations to the elementary functions using Jacobi-fractions
journal: j-NUM-MATH
volume: 18
pages: 127--143
year: 1971/1972
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65D20
MRnumber: 45 \#7938
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: P. Spellucci
rawtitle: Double precision approximations to the elementary functions using {Jacobi-fractions}
entry:
@Article{Spellucci:1971:DPA,
  author =       "P. Spellucci",
  title =        "Double precision approximations to the elementary
                 functions using {Jacobi-fractions}",
  journal =      j-NUM-MATH,
  volume =       "18",
  pages =        "127--143",
  year =         "1971/1972",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20",
  MRnumber =     "45 \#7938",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Spira:1971:CGF
author: Robert Spira
title: Calculation of the Gamma Function by Stirling's Formula
journal: j-MATH-COMPUT
volume: 25
number: 114
pages: 317--322
month: apr
monthnumber: 4
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Robert Spira
rawtitle: Calculation of the Gamma Function by {Stirling}'s Formula
entry:
@Article{Spira:1971:CGF,
  author =       "Robert Spira",
  title =        "Calculation of the Gamma Function by {Stirling}'s
                 Formula",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "317--322",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Sundblad:1971:AFT
author: Y. Sundblad
title: The Ackermann Function. A Theoretical, Computational, and Formula Manipulative Study
journal: j-BIT
volume: 11
number: 1
pages: 107--119
month: mar
monthnumber: 3
year: 1971
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01935330
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:11 MST 2006
bibtimestamp: 2006.01.04 18:52:11 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=1&spage=107
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Y. Sundblad
rawtitle: The {Ackermann} Function. {A} Theoretical, Computational, and Formula Manipulative Study
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
Fullerton: Ackermann's function is a recursively defined function of importance to computer science theorists.

entry:
@Article{Sundblad:1971:AFT,
  author =       "Y. Sundblad",
  title =        "The {Ackermann} Function. {A} Theoretical,
                 Computational, and Formula Manipulative Study",
  journal =      j-BIT,
  volume =       "11",
  number =       "1",
  pages =        "107--119",
  month =        mar,
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01935330",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:11 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=1&spage=107",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: Ackermann's function is a recursively
                 defined function of importance to computer science
                 theorists.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Walther:1971:UAE
author: J. S. Walther
title: A unified algorithm for elementary functions
crossref: AFIPS:1971:ACP
volume: 38
pages: 379--385
year: 1971
bibdate: Thu Sep 1 10:15:31 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:15:31 ???
acknowledgement: ack-nj
rawauthor: J. S. Walther
rawtitle: A unified algorithm for elementary functions
entry:
@InProceedings{Walther:1971:UAE,
  author =       "J. S. Walther",
  title =        "A unified algorithm for elementary functions",
  crossref =     "AFIPS:1971:ACP",
  volume =       "38",
  pages =        "379--385",
  year =         "1971",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Wills:1971:URR
author: John G. Wills
journal: j-J-COMPUT-PHYS
volume: 8
number: 1
pages: 162--166
month: aug
monthnumber: 8
year: 1971
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(71)90043-X
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:04 MST 2012
bibtimestamp: 2012.01.01 09:15:04 MST
URL: http://www.sciencedirect.com/science/article/pii/002199917190043X
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: John G. Wills
title:
On the use of recursion relations in the numerical evaluation of spherical Bessel functions and Coulomb functions

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib

rawtitle:
On the use of recursion relations in the numerical evaluation of spherical {Bessel} functions and {Coulomb} functions

entry:
@Article{Wills:1971:URR,
  author =       "John G. Wills",
  title =        "On the use of recursion relations in the numerical
                 evaluation of spherical {Bessel} functions and
                 {Coulomb} functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "8",
  number =       "1",
  pages =        "162--166",
  month =        aug,
  year =         "1971",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(71)90043-X",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199917190043X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Wong:1971:SEI
author: R. Wong and E. Rosenbloom
title: Series Expansions of $ W_k, m(z) $ Involving Parabolic Cylinder Functions
journal: j-MATH-COMPUT
volume: 25
number: 116
pages: 783--787
month: oct
monthnumber: 10
year: 1971
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: R. Wong and E. Rosenbloom
rawtitle: Series Expansions of $ {W}_{k, m}(z) $ Involving Parabolic Cylinder Functions
entry:
@Article{Wong:1971:SEI,
  author =       "R. Wong and E. Rosenbloom",
  title =        "Series Expansions of $ {W}_{k, m}(z) $ Involving
                 Parabolic Cylinder Functions",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "783--787",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Bardin:1972:CFE
title: Coulomb Functions in Entire $ (eta , rho ) $ Plane
journal: j-COMP-PHYS-COMM
volume: 3
number: 2
pages: 73--87
month: mar
monthnumber: 3
year: 1972
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(72)90057-4
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Fri Oct 29 21:09:33 2010
bibtimestamp: 2010.10.29 21:09:33 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawtitle: {Coulomb} Functions in Entire $ (\eta, \rho) $ Plane
author:
C. Bardin and Y. Dandeu and L. Gauthier and J. Guillermin. T. Lena. J.-M. Pernet and H. H. Wolter and T. Tamura

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawauthor:
C. Bardin and Y. Dandeu and L. Gauthier and J. Guillermin. T. Lena. J.-M. Pernet and H. H. Wolter and T. Tamura

entry:
@Article{Bardin:1972:CFE,
  author =       "C. Bardin and Y. Dandeu and L. Gauthier and J.
                 Guillermin. T. Lena. J.-M. Pernet and H. H. Wolter and
                 T. Tamura",
  title =        "{Coulomb} Functions in Entire $ (\eta, \rho) $ Plane",
  journal =      j-COMP-PHYS-COMM,
  volume =       "3",
  number =       "2",
  pages =        "73--87",
  month =        mar,
  year =         "1972",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(72)90057-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Oct 29 21:09:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Bark:1972:MTF
author: L. S. Bark
publisher: Vycisl. Centr Akad. Nauk SSSR
address: Moscow, USSR
edition: Second, unrevised
pages: 134
year: 1972
MRclass: 65A05
MRnumber: 50 \#6100
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: L. S. Bark
title:
cyr Mnogoznachnye tablitsy elementarnykh funktsiui ($ operatorname sin x $, $ operatorname cos x $, $ e^x $ cyr i $ e^-x $). (Russian) [Multiplace tables of the elementary functions ($ operatorname sin x $, $ operatorname cos x $, $ e^x $ and $ e^-x $ )]

note:
Tables processed and text translated from the English by L. S. Bark. Library of Mathematical Tables, No. 9. 1972

rawnote:
Tables processed and text translated from the English by L. S. Bark. Library of Mathematical Tables, No. 9. 1972

rawtitle:
{{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh funktsi{\u\i}}} ($ \operatorname {sin} x $, $ \operatorname {cos} x $, $ e^x $ {\cyr i} $ e^{-x} $). ({Russian}) [Multiplace tables of the elementary functions ($ \operatorname {sin} \ x $, $ \operatorname {cos} \ x $, $ e^x $ and $ e^{-x} $ )]

entry:
@Book{Bark:1972:MTF,
  author =       "L. S. Bark",
  title =        "{{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh
                 funktsi{\u\i}}} ($ \operatorname {sin} x $, $
                 \operatorname {cos} x $, $ e^x $ {\cyr i} $ e^{-x} $).
                 ({Russian}) [Multiplace tables of the elementary
                 functions ($ \operatorname {sin} \ x $, $ \operatorname
                 {cos} \ x $, $ e^x $ and $ e^{-x} $ )]",
  publisher =    "Vy{\v{c}}isl. Centr Akad. Nauk SSSR",
  address =      "Moscow, USSR",
  edition =      "Second, unrevised",
  pages =        "134",
  year =         "1972",
  MRclass =      "65A05",
  MRnumber =     "50 \#6100",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Tables processed and text translated from the English
                 by L. S. Bark. Library of Mathematical Tables, No. 9.
                 1972",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1972:ACL
author: B. C. Carlson
title: An algorithm for computing logarithms and arctangents
journal: j-MATH-COMPUT
volume: 26
number: 118
pages: 543--549
month: apr
monthnumber: 4
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Iowa State Univ., Ames, IA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: B. C. Carlson
rawtitle: An algorithm for computing logarithms and arctangents
keywords:
acceleration; arctangents; auxiliary; Borchardt's algorithm; convergence; fast; function approximation; functions; inverse circular functions; inverse hyperbolic; iterative algorithm; logarithms; numerical methods; rational operations; recurrence relation; square roots

entry:
@Article{Carlson:1972:ACL,
  author =       "B. C. Carlson",
  title =        "An algorithm for computing logarithms and
                 arctangents",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "543--549",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "acceleration; arctangents; auxiliary; Borchardt's
                 algorithm; convergence; fast; function approximation;
                 functions; inverse circular functions; inverse
                 hyperbolic; iterative algorithm; logarithms; numerical
                 methods; rational operations; recurrence relation;
                 square roots",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Chen:1972:ACE
author: Tien Chi Chen
title: Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots
journal: j-IBM-JRD
volume: 16
number: 4
pages: 380--388
month: jul
monthnumber: 7
year: 1972
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65D20
MRnumber: 49 \#1738
bibdate: Tue Mar 25 14:26:59 MST 1997
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.03.25 14:26:59 MST
URL: http://www.research.ibm.com/journal/rd/164/chen.pdf
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: IBM, San Jose, CA, USA
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: F. Gotze
treatment: P Practical
rawauthor: Tien Chi Chen
rawtitle: Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots
abstract:
It is shown how a relatively simple device can evaluate exponentials, logarithms, ratios and square roots for fraction arguments, employing only shifts, adds, high-speed table lookups, and bit counting. The scheme is based on the cotransformation of a number pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is invariant; when $x$ is driven towards a known value $ x_w $, $y$ is driven towards the result. For an $N$-bit fraction about $ N / 4 $ iterations are required, each involving two or three adds; then a termination algorithm, based on an add and an abbreviated multiply, completes the process, for a total cost of about one conventional multiply time. Convergence, errors and simulation using APL are discussed.

keywords:
adds; APL; bit counting; convergence; cotransformation; digital arithmetic; errors; exponentials; high speed table; iteration; logarithms; lookups; ratios; shifts; simulation; square roots; termination algorithm

rawabstract:
It is shown how a relatively simple device can evaluate exponentials, logarithms, ratios and square roots for fraction arguments, employing only shifts, adds, high-speed table lookups, and bit counting. The scheme is based on the cotransformation of a number pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is invariant; when $x$ is driven towards a known value $ x_w $, $y$ is driven towards the result. For an $N$-bit fraction about $ N / 4 $ iterations are required, each involving two or three adds; then a termination algorithm, based on an add and an abbreviated multiply, completes the process, for a total cost of about one conventional multiply time. Convergence, errors and simulation using APL are discussed.

entry:
@Article{Chen:1972:ACE,
  author =       "Tien Chi Chen",
  title =        "Automatic Computation of Exponentials, Logarithms,
                 Ratios and Square Roots",
  journal =      j-IBM-JRD,
  volume =       "16",
  number =       "4",
  pages =        "380--388",
  month =        jul,
  year =         "1972",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65D20",
  MRnumber =     "49 \#1738",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.research.ibm.com/journal/rd/164/chen.pdf",
  abstract =     "It is shown how a relatively simple device can
                 evaluate exponentials, logarithms, ratios and square
                 roots for fraction arguments, employing only shifts,
                 adds, high-speed table lookups, and bit counting. The
                 scheme is based on the cotransformation of a number
                 pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
                 invariant; when $x$ is driven towards a known value $
                 x_w $, $y$ is driven towards the result. For an $N$-bit
                 fraction about $ N / 4 $ iterations are required, each
                 involving two or three adds; then a termination
                 algorithm, based on an add and an abbreviated multiply,
                 completes the process, for a total cost of about one
                 conventional multiply time. Convergence, errors and
                 simulation using APL are discussed.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, San Jose, CA, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "adds; APL; bit counting; convergence;
                 cotransformation; digital arithmetic; errors;
                 exponentials; high speed table; iteration; logarithms;
                 lookups; ratios; shifts; simulation; square roots;
                 termination algorithm",
  reviewer =     "F. Gotze",
  treatment =    "P Practical",
}


bibtype: techreport
filename: elefunt.bib
label: Ercegovac:1972:RES
author: Milos D. Ercegovac
title: Radix 16 Evaluation of Some Elementary Functions
number: 540
institution: Department of Computer Science, University of Illinois at Urbana-Champaign
address: Urbana, Illinois
pages: 30
year: 1972
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
acknowledgement: ack-nhfb
rawauthor: Milos D. Ercegovac
rawtitle: Radix 16 Evaluation of Some Elementary Functions
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{Ercegovac:1972:RES,
  author =       "Milos D. Ercegovac",
  title =        "Radix 16 Evaluation of Some Elementary Functions",
  number =       "540",
  institution =  "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, Illinois",
  pages =        "30",
  year =         "1972",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Frisch:1972:RAR
author: Michael J. Frisch
journal: j-CACM
volume: 15
number: 12
pages: 1074--??
year: 1972
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:42:24 MST 2001
bibtimestamp: 2001.01.22 06:42:24 MST
note: See cite Clemm:1969:ACV,Paciorek:1970:AEI,Smith:1970:ASH.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Michael J. Frisch
rawnote: See \cite{Clemm:1969:ACV,Paciorek:1970:AEI,Smith:1970:ASH}.
title:
Remark on ``Algorithms 352, 385, 392: Remarks on Characteristic Values and Associated Solutions of Mathieu's Differential Equation, Exponential Integral, and Systems of Hyperbolic P.D.E.''

bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Frisch72; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Remark on ``{Algorithms 352, 385, 392}: Remarks on Characteristic Values and Associated Solutions of {Mathieu}'s Differential Equation, Exponential Integral, and Systems of Hyperbolic {P.D.E.}''

entry:
@Article{Frisch:1972:RAR,
  author =       "Michael J. Frisch",
  title =        "Remark on ``{Algorithms 352, 385, 392}: Remarks on
                 Characteristic Values and Associated Solutions of
                 {Mathieu}'s Differential Equation, Exponential
                 Integral, and Systems of Hyperbolic {P.D.E.}''",
  journal =      j-CACM,
  volume =       "15",
  number =       "12",
  pages =        "1074--??",
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:42:24 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Frisch72;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Clemm:1969:ACV,Paciorek:1970:AEI,Smith:1970:ASH}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Frisch72",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Frisch72",
}


bibtype: article
filename: elefunt.bib
label: Fullerton:1972:MIG
author: W. Fullerton
title: ACM Algorithm 435: Modified Incomplete Gamma Function
journal: j-CACM
volume: 15
number: 11
pages: 993--995
month: nov
monthnumber: 11
year: 1972
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 08 09:47:55 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 09:47:55 ???
note: See also cite Schoene:1978:RMI.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. Fullerton
rawnote: See also \cite{Schoene:1978:RMI}.
rawtitle: {ACM Algorithm 435}: Modified Incomplete Gamma Function
remark:
Fullerton: Fortran subprogram for evaluating $ e^x_1 int _x_1^x_2 |y|^a - 1 e^-y d y $ for $a$ roughly between $1$ and $2$.

entry:
@Article{Fullerton:1972:MIG,
  author =       "W. Fullerton",
  title =        "{ACM Algorithm 435}: Modified Incomplete Gamma
                 Function",
  journal =      j-CACM,
  volume =       "15",
  number =       "11",
  pages =        "993--995",
  month =        nov,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Schoene:1978:RMI}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Fortran subprogram for evaluating $ e^{x_1}
                 \int_{x_1}^{x_2} |y|^{a - 1} e^{-y} \, d y $ for $a$
                 roughly between $1$ and $2$.",
}


bibtype: article
filename: elefunt.bib
label: Hunter:1972:NEC
author: D. B. Hunter and T. Regan
title: A note on the evaluation of the complementary error function
journal: j-MATH-COMPUT
volume: 26
number: 118
pages: 539--541
month: apr
monthnumber: 4
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4160 (Numerical integration and differentiation)
corpsource: Univ. Bradford, UK
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: D. B. Hunter and T. Regan
rawtitle: A note on the evaluation of the complementary error function
keywords:
complementary error function; complex variable; evaluation; integration; method of Matta and Reichel; modification; numerical; stability

entry:
@Article{Hunter:1972:NEC,
  author =       "D. B. Hunter and T. Regan",
  title =        "A note on the evaluation of the complementary error
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "539--541",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. Bradford, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "complementary error function; complex variable;
                 evaluation; integration; method of Matta and Reichel;
                 modification; numerical; stability",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Kim:1972:AEH
author: Shoon K. Kim
title: The Asymptotic Expansion of a Hypergeometric Function $_2 F_2 (1, alpha ; rho _1, rho _2; z)$
journal: j-MATH-COMPUT
volume: 26
number: 120
pages: 963--963
month: oct
monthnumber: 10
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Shoon K. Kim
rawtitle: The Asymptotic Expansion of a Hypergeometric Function $_2 {F}_2 (1, \alpha; \rho_1, \rho_2; z)$
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database

entry:
@Article{Kim:1972:AEH,
  author =       "Shoon K. Kim",
  title =        "The Asymptotic Expansion of a Hypergeometric Function
                 $_2 {F}_2 (1, \alpha; \rho_1, \rho_2; z)$",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "963--963",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1972:CAC
author: K. S. Kolbig
title: Certification of ``Algorithm 363: Complex error function''
journal: j-CACM
volume: 15
number: 6
pages: 465--466
month: jun
monthnumber: 6
year: 1972
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:55:38 MST 2001
bibtimestamp: 2001.01.22 06:55:38 MST
note: See cite Gautschi:1969:ACE.
fjournal: Communications of the ACM
remark: Fullerton: Corrections and tests of an Algol procedure.
acknowledgement: ack-nhfb
classcodes: C4120 (Functional analysis); C7310 (Mathematics computing)
corpsource: CERN, Geneva, Switzerland
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: K. S. K{\"o}lbig
rawnote: See \cite{Gautschi:1969:ACE}.
rawtitle: Certification of ``{Algorithm 363}: {Complex} error function''
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kolbig72; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
$erf (z)$; complex error function; function evaluation; special functions; subroutines; Voigt function

entry:
@Article{Kolbig:1972:CAC,
  author =       "K. S. K{\"o}lbig",
  title =        "Certification of ``{Algorithm 363}: {Complex} error
                 function''",
  journal =      j-CACM,
  volume =       "15",
  number =       "6",
  pages =        "465--466",
  month =        jun,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:55:38 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kolbig72;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1969:ACE}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4120 (Functional analysis); C7310 (Mathematics
                 computing)",
  corpsource =   "CERN, Geneva, Switzerland",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\erf(z)$; complex error function; function
                 evaluation; special functions; subroutines; Voigt
                 function",
  oldlabel =     "Kolbig72",
  remark =       "Fullerton: Corrections and tests of an Algol
                 procedure.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kolbig72",
}


