# bibtab

bibtype: article
filename: elefunt.bib
label: Wong:1994:FHB
author: W. F. Wong and E. Goto
title: Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers
journal: j-IEEE-TRANS-COMPUT
volume: 43
number: 3
pages: 278--294
month: mar
monthnumber: 3
year: 1994
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.272429
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 07:13:54 MDT 2011
bibtimestamp: 2011.07.07 07:13:54 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
affiliation: Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Error analysis
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

abstract:
As the name suggests, elementary functions play a vital role in scientific computations. Yet due to their inherent nature, they are a considerable computing task by themselves. Not surprisingly, since the dawn of computing, the goal of speeding up elementary function computation has been pursued. This paper describes new hardware based algorithms for the computation of the common elementary functions, namely division, logarithm, reciprocal square root, arc tangent, sine and cosine. These algorithms exploit microscopic parallelism using specialized hardware with heavy use of truncation based on detailed accuracy analysis. The contribution of this work lies in the fact that these algorithms are very fast and yet are accurate. If we let the time to perform an IEEE Standard 754 double precision floating point multiplication be $ tau _times $, our algorithms to achieve roughly $ 3.68 tau _times $, $ 4.56 tau _times $, $ 5.25 tau _times $, $ 3.69 tau _times $, $ 7.06 tau _times $, and $ 6.5 tau _times $, for division, logarithm, square root, exponential, are tangent and complex exponential (sine and cosine) respectively. The trade-off is the need for tables and some specialized hardware. The total amount of tables required, however, is less than 128 Kbytes. We discuss the hardware, algorithmic and accuracy aspects of these algorithms.

keywords:
Arc tangent; Common elementary functions; Cosine; Elementary function computations; Floating point multiplication; Hardware-based algorithms; Microscopic parallelism; Reciprocal square root; Rectangular multipliers; Scientific computations; Sine

rawabstract:
As the name suggests, elementary functions play a vital role in scientific computations. Yet due to their inherent nature, they are a considerable computing task by themselves. Not surprisingly, since the dawn of computing, the goal of speeding up elementary function computation has been pursued. This paper describes new hardware based algorithms for the computation of the common elementary functions, namely division, logarithm, reciprocal square root, arc tangent, sine and cosine. These algorithms exploit microscopic parallelism using specialized hardware with heavy use of truncation based on detailed accuracy analysis. The contribution of this work lies in the fact that these algorithms are very fast and yet are accurate. If we let the time to perform an IEEE Standard 754 double precision floating point multiplication be $ \tau_\times $, our algorithms to achieve roughly $ 3.68 \tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times $, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $ 6.5 \tau_\times $, for division, logarithm, square root, exponential, are tangent and complex exponential (sine and cosine) respectively. The trade-off is the need for tables and some specialized hardware. The total amount of tables required, however, is less than 128 Kbytes. We discuss the hardware, algorithmic and accuracy aspects of these algorithms.

entry:
@Article{Wong:1994:FHB,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-Based Algorithms for Elementary Function
                 Computations Using Rectangular Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "3",
  pages =        "278--294",
  month =        mar,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.272429",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:54 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429",
  abstract =     "As the name suggests, elementary functions play a
                 vital role in scientific computations. Yet due to their
                 inherent nature, they are a considerable computing task
                 by themselves. Not surprisingly, since the dawn of
                 computing, the goal of speeding up elementary function
                 computation has been pursued. This paper describes new
                 hardware based algorithms for the computation of the
                 common elementary functions, namely division,
                 logarithm, reciprocal square root, arc tangent, sine
                 and cosine. These algorithms exploit microscopic
                 parallelism using specialized hardware with heavy use
                 of truncation based on detailed accuracy analysis. The
                 contribution of this work lies in the fact that these
                 algorithms are very fast and yet are accurate. If we
                 let the time to perform an IEEE Standard 754 double
                 precision floating point multiplication be $
                 \tau_\times $, our algorithms to achieve roughly $ 3.68
                 \tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times
                 $, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $
                 6.5 \tau_\times $, for division, logarithm, square
                 root, exponential, are tangent and complex exponential
                 (sine and cosine) respectively. The trade-off is the
                 need for tables and some specialized hardware. The
                 total amount of tables required, however, is less than
                 128 Kbytes. We discuss the hardware, algorithmic and
                 accuracy aspects of these algorithms.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arc tangent; Common elementary functions; Cosine;
                 Elementary function computations; Floating point
                 multiplication; Hardware-based algorithms; Microscopic
                 parallelism; Reciprocal square root; Rectangular
                 multipliers; Scientific computations; Sine",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Error analysis",
}


bibtype: article
filename: elefunt.bib
label: Xu:1994:VPC
author: Guo Liang Xu and Jia Kai Li
title: Variable precision computation of elementary functions. (Chinese)
journal: j-J-NUMER-METHODS-COMPUT-APPL
volume: 15
number: 3
pages: 161--171
year: 1994
ISSN: 1000-3266 OR 10003266
MRclass: 65D20 (65Y20)
MRnumber: MR1357336 (96i:65013)
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: Journal on Numerical Methods and Computer Applications. Shuzhi Jisuan yu Jisuanji Yingyong
acknowledgement: ack-nhfb
rawauthor: Guo Liang Xu and Jia Kai Li
rawtitle: Variable precision computation of elementary functions. ({Chinese})
entry:
@Article{Xu:1994:VPC,
  author =       "Guo Liang Xu and Jia Kai Li",
  title =        "Variable precision computation of elementary
                 functions. ({Chinese})",
  journal =      j-J-NUMER-METHODS-COMPUT-APPL,
  volume =       "15",
  number =       "3",
  pages =        "161--171",
  year =         "1994",
  ISSN =         "1000-3266",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "MR1357336 (96i:65013)",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal on Numerical Methods and Computer
                 Applications. Shuzhi Jisuan yu Jisuanji Yingyong",
}


bibtype: article
filename: elefunt.bib
label: Abad:1995:CRC
author: Julio Abad and Javier Sesma
title: Computation of the Regular Confluent Hypergeometric Function
journal: j-MATHEMATICA-J
volume: 5
number: 4
pages: ??--??
month: Fall
year: 1995
ISSN: 1047-5974 (print), 1097-1610 (electronic) OR 10475974 (print), 10971610 (electronic)
ISSNL: 1047-5974 OR 10475974
bibdate: Sat Nov 6 13:34:06 MDT 2010
bibsource: http://www.mathematica-journal.com/issue/v5i4/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.11.06 13:34:06 MDT
URL: http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html
fjournal: Mathematica Journal
acknowledgement: ack-nhfb
journalURL: http://www.mathematica-journal.com/
rawauthor: Julio Abad and Javier Sesma
rawtitle: Computation of the Regular Confluent Hypergeometric Function
entry:
@Article{Abad:1995:CRC,
  author =       "Julio Abad and Javier Sesma",
  title =        "Computation of the Regular Confluent Hypergeometric
                 Function",
  journal =      j-MATHEMATICA-J,
  volume =       "5",
  number =       "4",
  pages =        "??--??",
  month =        "Fall",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:06 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v5i4/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}


bibtype: article
filename: elefunt.bib
label: Amos:1995:RAP
author: D. E. Amos
journal: j-TOMS
volume: 21
number: 4
pages: 388--393
month: dec
monthnumber: 12
year: 1995
CODEN: ACMSCU
DOI: https://doi.org/10.1145/212066.212078
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:24:54 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1999.03.09 10:24:54 ???
note: See cite Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA.
URL: http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: D. E. Amos
rawnote: See \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.
title:
A Remark on Algorithm 644: a Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order

keywords:
complex Airy Functions; complex Bessel functions; derivatives of Airy functions; H, I, J, K, and Y Bessel functions; log gamma function

subject:
G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.m [Numerical Analysis]: Miscellaneous; G.m [Mathematics of Computing]: Miscellaneous

rawtitle:
A Remark on {Algorithm 644}: a Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order

entry:
@Article{Amos:1995:RAP,
  author =       "D. E. Amos",
  title =        "A Remark on {Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "388--393",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212078",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:24:54 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex Airy Functions; complex Bessel functions;
                 derivatives of Airy functions; H, I, J, K, and Y Bessel
                 functions; log gamma function",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.1.m [Numerical Analysis]: Miscellaneous;
                 G.m [Mathematics of Computing]: Miscellaneous",
}


bibtype: article
filename: elefunt.bib
label: Bagby:1995:CNP
author: Richard J. Bagby
title: Calculating normal probabilities
journal: j-AMER-MATH-MONTHLY
volume: 102
number: 1
pages: 46--48
month: jan
monthnumber: 1
year: 1995
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 65D20
MRnumber: 96f:65021
bibdate: Wed Dec 3 17:17:33 MST 1997
bibtimestamp: 1997.12.03 17:17:33 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Richard J. Bagby
rawtitle: Calculating normal probabilities
bibsource:
http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Bagby:1995:CNP,
  author =       "Richard J. Bagby",
  title =        "Calculating normal probabilities",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "1",
  pages =        "46--48",
  month =        jan,
  year =         "1995",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65D20",
  MRnumber =     "96f:65021",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: elefunt.bib
label: Baratchart:1995:RIE
author: L. Baratchart and E. B. Saff and F. Wielonsky
title: Rational interpolation of the exponential function
journal: j-CAN-J-MATH
volume: 47
pages: 1121--1147
year: 1995
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1995-058-6
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
bibdate: Sat Sep 10 15:39:05 MDT 2011
bibtimestamp: 2011.09.10 15:39:05 MDT
fjournal: Canadian Journal of Mathematics = Journal canadien de mathematiques
acknowledgement: ack-nhfb
journalURL: http://cms.math.ca/cjm/
rawauthor: L. Baratchart and E. B. Saff and F. Wielonsky
rawtitle: Rational interpolation of the exponential function
bibsource:
http://cms.math.ca/cjm/v47/; https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Baratchart:1995:RIE,
  author =       "L. Baratchart and E. B. Saff and F. Wielonsky",
  title =        "Rational interpolation of the exponential function",
  journal =      j-CAN-J-MATH,
  volume =       "47",
  number =       "??",
  pages =        "1121--1147",
  month =        "????",
  year =         "1995",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1995-058-6",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:39:05 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v47/;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
}


bibtype: techreport
filename: elefunt.bib
label: Borwein:1995:EARa
author: Peter Borwein
title: An Efficient Algorithm for the Riemann Zeta Function
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 9
day: 20
month: jan
monthnumber: 1
year: 1995
bibdate: Thu Sep 01 18:09:22 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2022.09.01 18:09:22 ???
URL: http://docserver.carma.newcastle.edu.au/107
acknowledgement: ack-nhfb
authordates: 10 May 1953--23 August 2020
rawauthor: Peter Borwein
rawtitle: An Efficient Algorithm for the {Riemann} Zeta Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
A very simple class of algorithms for the computation of the Riemann-zeta function to arbitrary precision in arbitrary domains is proposed. These algorithms out perform the standard methods based on Euler--Maclaurin summation, are easier to implement and are easier to analyse.

rawabstract:
A very simple class of algorithms for the computation of the Riemann-zeta function to arbitrary precision in arbitrary domains is proposed. These algorithms out perform the standard methods based on Euler--Maclaurin summation, are easier to implement and are easier to analyse.

entry:
@TechReport{Borwein:1995:EARa,
  author =       "Peter Borwein",
  title =        "An Efficient Algorithm for the {Riemann} Zeta
                 Function",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "9",
  day =          "20",
  month =        jan,
  year =         "1995",
  bibdate =      "Thu Sep 01 18:09:22 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/107",
  abstract =     "A very simple class of algorithms for the computation
                 of the Riemann-zeta function to arbitrary precision in
                 arbitrary domains is proposed. These algorithms out
                 perform the standard methods based on Euler--Maclaurin
                 summation, are easier to implement and are easier to
                 analyse.",
  acknowledgement = ack-nhfb,
  author-dates = "10 May 1953--23 August 2020",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: elefunt.bib
label: Borwein:1995:EARb
author: P. Borwein
booktitle: CMS Conference Proceedings
title: An efficient algorithm for the Riemann zeta function
volume: 27
publisher: Canadian Mathematical Society
address: 616 Cooper Street, Ottawa, ON, K1R 5J2, Canada
pages: 29--34
month: jan
monthnumber: 1
year: 1995
bibdate: Wed Jun 28 08:27:14 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.06.28 08:27:14 ???
URL: https://web.archive.org/web/20140602151514/http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
acknowledgement: ack-nhfb
rawauthor: P. Borwein
rawbooktitle: {CMS} Conference Proceedings
rawtitle: An efficient algorithm for the {Riemann} zeta function
entry:
@InProceedings{Borwein:1995:EARb,
  author =       "P. Borwein",
  editor =       "????",
  booktitle =    "{CMS} Conference Proceedings",
  title =        "An efficient algorithm for the {Riemann} zeta
                 function",
  volume =       "27",
  publisher =    "Canadian Mathematical Society",
  address =      "616 Cooper Street, Ottawa, ON, K1R 5J2, Canada",
  pages =        "29--34",
  month =        jan,
  year =         "1995",
  bibdate =      "Wed Jun 28 08:27:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://web.archive.org/web/20140602151514/http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
  acknowledgement = ack-nhfb,
  xxURL =        "http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1995:NCR
author: B. C. Carlson
title: Numerical computation of real or complex elliptic integrals
journal: j-NUMER-ALGORITHMS
volume: 10
number: 1--2
pages: 13--26
month: jul
monthnumber: 7
year: 1995
CODEN: NUALEG
DOI: https://doi.org/10.1007/BF02198293
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 33Exx (33-04 65D20)
MRnumber: 1 345 407
bibdate: Fri Nov 6 18:06:29 MST 1998
bibsource: http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.06 18:06:29 MST
note: Special functions (Torino, 1993)
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Ames Lab., Iowa State Univ., Ames, IA, USA
journalURL: http://link.springer.com/journal/11075
treatment: T Theoretical or Mathematical
rawauthor: B. C. Carlson
rawnote: Special functions (Torino, 1993)
rawtitle: Numerical computation of real or complex elliptic integrals
abstract:
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included.

keywords:
Bulirsch's integrals; complex elliptic integrals; complex values; consistency checks; elliptic equations; integral equations; Legendre's integrals; numerical analysis; numerical check values; numerical computation algorithms; real elliptic integrals

rawabstract:
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included.

entry:
@Article{Carlson:1995:NCR,
  author =       "B. C. Carlson",
  title =        "Numerical computation of real or complex elliptic
                 integrals",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "1--2",
  pages =        "13--26",
  month =        jul,
  year =         "1995",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/BF02198293",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "33Exx (33-04 65D20)",
  MRnumber =     "1 345 407",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Special functions (Torino, 1993)",
  abstract =     "Algorithms for numerical computation of symmetric
                 elliptic integrals of all three kinds are improved in
                 several ways and extended to complex values of the
                 variables (with some restrictions in the case of the
                 integral of the third kind). Numerical check values,
                 consistency checks, and relations to Legendre's
                 integrals and Bulirsch's integrals are included.",
  acknowledgement = ack-nhfb,
  classification = "B0290R (Integral equations); C4180 (Integral
                 equations)",
  conflocation = "Torino, Italy; 14-15 Oct. 1993",
  conftitle =    "International Joint Symposium on Special Functions and
                 Artificial Intelligence",
  corpsource =   "Ames Lab., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Bulirsch's integrals; complex elliptic integrals;
                 complex values; consistency checks; elliptic equations;
                 integral equations; Legendre's integrals; numerical
                 analysis; numerical check values; numerical computation
                 algorithms; real elliptic integrals",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Chaudhry:1995:DGI
author: M. Aslam Chaudhry and S. M. Zubair
journal: j-J-COMPUT-APPL-MATH
volume: 59
number: 3
pages: 253--284
day: 30
month: may
monthnumber: 5
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:37 MST 2017
bibtimestamp: 2017.02.25 12:24:37 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279400026W
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Aslam Chaudhry and S. M. Zubair
title:
On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms

rawtitle:
On the decomposition of generalized incomplete gamma functions with applications to {Fourier} transforms

entry:
@Article{Chaudhry:1995:DGI,
  author =       "M. Aslam Chaudhry and S. M. Zubair",
  title =        "On the decomposition of generalized incomplete gamma
                 functions with applications to {Fourier} transforms",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "59",
  number =       "3",
  pages =        "253--284",
  day =          "30",
  month =        may,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279400026W",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chen:1995:UCA
author: San-Gee Chen and Chieh-Chih Li
booktitle: IEEE Signal Processing Society Workshop on VLSI Signal Processing, VIII, 1995
title: A unified cellular array for multiplication, division and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 533--541
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: San-Gee Chen and Chieh-Chih Li
rawbooktitle: {IEEE} Signal Processing Society Workshop on {VLSI} Signal Processing, {VIII, 1995}
rawtitle: A unified cellular array for multiplication, division and square root
entry:
@InProceedings{Chen:1995:UCA,
  author =       "San-Gee Chen and Chieh-Chih Li",
  booktitle =    "{IEEE} Signal Processing Society Workshop on {VLSI}
                 Signal Processing, {VIII, 1995}",
  title =        "A unified cellular array for multiplication, division
                 and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "533--541",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A unified fast, small-area processor capable of
                 executing multiplication, division and square-root
                 operations, all starting from MSD is proposed. Unlike
                 the existing designs which require both addition and
                 subtraction operations, and complicated \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Das:1995:IFC
author: D. Das and K. Mukhopadhyaya and B. P. Sinha
title: Implementation of four common functions on an LNS co-processor
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 1
pages: 155--161
month: jan
monthnumber: 1
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.367997
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 16:14:38 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 16:14:38 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Das and K. Mukhopadhyaya and B. P. Sinha
rawtitle: Implementation of four common functions on an {LNS} co-processor
entry:
@Article{Das:1995:IFC,
  author =       "D. Das and K. Mukhopadhyaya and B. P. Sinha",
  title =        "Implementation of four common functions on an {LNS}
                 co-processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "155--161",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.367997",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We propose a scheme for evaluating four commonly used
                 functions namely, (1) inverse trigonometric functions,
                 (2) trigonometric functions, (3) the exponential
                 function, and (4) the logarithmic function with the
                 help of a logarithmic number system (\ldots{}).",
}


bibtype: article
filename: elefunt.bib
label: Daumas:1995:MRR
author: Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
journal: j-J-UCS
volume: 1
number: 3
pages: 162--175 (electronic)
year: 1995
ISSN: 0948-6968 OR 09486968
ISSNL: 0948-6968 OR 09486968
MRclass: 68M07 (68Q20)
MRnumber: 1 390 003
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: J.UCS: Journal of Universal Computer Science
acknowledgement: ack-nhfb
journalURL: http://www.jucs.org/jucs
rawauthor: Marc Daumas and Christophe Mazenc and Xavier Merrheim and Jean-Michel Muller
title:
Modular range reduction: a new algorithm for fast and accurate computation of the elementary functions

rawtitle:
Modular range reduction: a new algorithm for fast and accurate computation of the elementary functions

entry:
@Article{Daumas:1995:MRR,
  author =       "Marc Daumas and Christophe Mazenc and Xavier Merrheim
                 and Jean-Michel Muller",
  title =        "Modular range reduction: a new algorithm for fast and
                 accurate computation of the elementary functions",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "3",
  pages =        "162--175 (electronic)",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07 (68Q20)",
  MRnumber =     "1 390 003",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}


bibtype: article
filename: elefunt.bib
label: Doman:1995:SAP
author: B. G. S. Doman and C. J. Pursglove and W. M. Coen
title: A Set of Ada Packages for High Precision Calculations
journal: j-TOMS
volume: 21
number: 4
pages: 416--431
month: dec
monthnumber: 12
year: 1995
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Nov 14 09:57:55 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.11.14 09:57:55 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: B. G. S. Doman and C. J. Pursglove and W. M. Coen
rawtitle: A Set of {Ada} Packages for High Precision Calculations
keywords:
accuracy; Ada; arithmetic elementary-function evaluation; floating-point; multiple-precision portable software

subject:
G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; portability

entry:
@Article{Doman:1995:SAP,
  author =       "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
  title =        "A Set of {Ada} Packages for High Precision
                 Calculations",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "416--431",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:57:55 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accuracy; Ada; arithmetic elementary-function
                 evaluation; floating-point; multiple-precision portable
                 software",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic; G.1.2 [Numerical Analysis]: Approximation
                 -- elementary function approximation; G.4 [Mathematics
                 of Computing]: Mathematical Software -- algorithm
                 analysis; efficiency; portability",
}


bibtype: article
filename: elefunt.bib
label: Driver:1995:NQH
author: Kathy Driver
title: Nondiagonal quadratic Hermite--Pade approximation to the exponential function
journal: j-J-COMPUT-APPL-MATH
volume: 65
number: 1--3
pages: 125--134
day: 29
month: dec
monthnumber: 12
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:25 MST 2017
bibtimestamp: 2017.02.25 13:02:25 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795001069
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Kathy Driver
rawtitle: Nondiagonal quadratic {Hermite--Pad{\'e}} approximation to the exponential function
entry:
@Article{Driver:1995:NQH,
  author =       "Kathy Driver",
  title =        "Nondiagonal quadratic {Hermite--Pad{\'e}}
                 approximation to the exponential function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "65",
  number =       "1--3",
  pages =        "125--134",
  day =          "29",
  month =        dec,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001069",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Goano:1995:ACC
author: Michele Goano
title: Algorithm 745: Computation of the Complete and Incomplete Fermi--Dirac Integral
journal: j-TOMS
volume: 21
number: 3
pages: 221--232
month: sep
monthnumber: 9
year: 1995
CODEN: ACMSCU
DOI: https://doi.org/10.1145/210089.210090
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:19:43 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.03.09 10:19:43 ???
note: See remark cite Goano:1997:RA7
URL: http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Michele Goano
rawnote: See remark \cite{Goano:1997:RA7}
rawtitle: {Algorithm 745}: Computation of the Complete and Incomplete {Fermi--Dirac} Integral
keywords:
asymptotic expansions; confluent hypergeometric functions; convergence acceleration; e[k] transforms; epsilon algorithm; Euler transformation; Fermi--Dirac integral; incomplete Fermi--Dirac integral; incomplete gamma function; Levin's u transform; Riemann's zeta function

subject:
G.1.2 [Mathematics of Computing]: Approximation; G.4 [Mathematics of Computing]: Mathematical Software; J.2 [Computer Applications]: Physical Sciences and Engineering

entry:
@Article{Goano:1995:ACC,
  author =       "Michele Goano",
  title =        "{Algorithm 745}: Computation of the Complete and
                 Incomplete {Fermi--Dirac} Integral",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210090",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:19:43 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Goano:1997:RA7}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "asymptotic expansions; confluent hypergeometric
                 functions; convergence acceleration; e[k] transforms;
                 epsilon algorithm; Euler transformation; Fermi--Dirac
                 integral; incomplete Fermi--Dirac integral; incomplete
                 gamma function; Levin's u transform; Riemann's zeta
                 function",
  subject =      "G.1.2 [Mathematics of Computing]: Approximation; G.4
                 [Mathematics of Computing]: Mathematical Software; J.2
                 [Computer Applications]: Physical Sciences and
                 Engineering",
}


bibtype: article
filename: elefunt.bib
label: Hobson:1995:EMR
author: R. F. Hobson and M. W. Fraser
title: An efficient maximum-redundancy radix-$8$ SRT division and square-root method
journal: j-IEEE-J-SOLID-STATE-CIRCUITS
volume: 30
number: 1
pages: 29--38
month: jan
monthnumber: 1
year: 1995
CODEN: IJSCBC
DOI: https://doi.org/10.1109/4.350197
ISSN: 0018-9200 (print), 1558-173X (electronic) OR 00189200 (print), 1558173X (electronic)
ISSNL: 0018-9200 OR 00189200
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Journal of Solid-State Circuits
acknowledgement: ack-nhfb
affiliation: Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC, Canada
rawauthor: R. F. Hobson and M. W. Fraser
rawtitle: An efficient maximum-redundancy radix-$8$ {SRT} division and square-root method
abstract:
A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the next quotient or square-root digit by the divisor or square-root value. A separate (parallel) full precision iterative multiplier is used for partial remainder production. Strategic details of a radix-8 implementation are discussed. It is shown that a maximally redundant digit set is a viable choice for high performance in this case.

keywords:
1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE floating point algorithm; Integrated control path; Maximally redundant digit set; Maximum-redundancy radix-8 SRT algorithm; Multiplication; Parallel iterative multiplier; Partial remainder production; Redundant partial-remainder; Square-root method; Table lookup

thesaurus:
Adders; CMOS digital integrated circuits; Digital arithmetic; Dividing circuits; Floating point arithmetic; Multiplying circuits

rawabstract:
A new approach to integrating hardware multiplication, division, and square-root is presented. We use a fully integrated control path which simultaneously reduces part of the redundant partial-remainder and performs a truncated multiplication of the next quotient or square-root digit by the divisor or square-root value. A separate (parallel) full precision iterative multiplier is used for partial remainder production. Strategic details of a radix-8 implementation are discussed. It is shown that a maximally redundant digit set is a viable choice for high performance in this case.

entry:
@Article{Hobson:1995:EMR,
  author =       "R. F. Hobson and M. W. Fraser",
  title =        "An efficient maximum-redundancy radix-$8$ {SRT}
                 division and square-root method",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "1",
  pages =        "29--38",
  month =        jan,
  year =         "1995",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.350197",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the next quotient or
                 square-root digit by the divisor or square-root value.
                 A separate (parallel) full precision iterative
                 multiplier is used for partial remainder production.
                 Strategic details of a radix-8 implementation are
                 discussed. It is shown that a maximally redundant digit
                 set is a viable choice for high performance in this
                 case.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC,
                 Canada",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
                 floating point algorithm; Integrated control path;
                 Maximally redundant digit set; Maximum-redundancy
                 radix-8 SRT algorithm; Multiplication; Parallel
                 iterative multiplier; Partial remainder production;
                 Redundant partial-remainder; Square-root method; Table
                 lookup",
  numericalindex = "Size 1.2E-06 m",
  pubcountry =   "USA",
  summary =      "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the \ldots{}",
  thesaurus =    "Adders; CMOS digital integrated circuits; Digital
                 arithmetic; Dividing circuits; Floating point
                 arithmetic; Multiplying circuits",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ito:1995:EIA
author: M. Ito and N. Takagi and S. Yajima
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 2--9
month: jul
monthnumber: 7
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-sfo
rawauthor: M. Ito and N. Takagi and S. Yajima
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
entry:
@InProceedings{Ito:1995:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Efficient Initial Approximation and Fast Converging
                 Methods for Division and Square Root",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2--9",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Efficient initial approximations and fast converging
                 algorithms are important to achieve the desired
                 precision faster at lower hardware cost in
                 multiplicative division and square root. In this paper,
                 a new initial approximation method for division,
                 \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Jeffrey:1995:HMF
author: Alan Jeffrey
title: Handbook of Mathematical Formulas and Integrals
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xxiv + 410
year: 1995
LCCN: QA47 .J38 1995
bibdate: Wed Jun 12 14:33:38 MDT 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.06.12 14:33:38 MDT
URL: http://www.sciencedirect.com/science/book/9780123825803
subject: Mathematics; Tables; Formulae; Mathematiques; Formules; formulas (algorithms); Mathematics.
acknowledgement: ack-nhfb
rawauthor: Alan Jeffrey
rawtitle: Handbook of Mathematical Formulas and Integrals
ISBN:
0-08-052301-3, 0-12-382580-6 (e-book), 1-4832-9514-1 (e-book) OR 0080523013, 0123825806 (ebook), 1483295141 (ebook)

ISBN13:
978-0-08-052301-9, 978-0-12-382580-3 (e-book), 978-1-4832-9514-5 (e-book) OR 9780080523019, 9780123825803 (ebook), 9781483295145 (ebook)

abstract:
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's booktitle Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse.

TOC:
0: Quick Reference List of Frequently Used Data 0.1: Useful Identities / 1 0.2: Complex Relationships / 2 0.3: Constants / 2 0.4: Derivatives of Elementary Functions / 3 0.5: Rules of Differentiation and Integration / 3 0.6: Standard Integrals / 4 0.7: Standard Series / 11 0.8: Geometry / 13 1: Numerical, Algebraic, and Analytical Results for Series and Calculus 1.1: Algebraic Results Involving Real and Complex Numbers / 25 1.2: Finite Sums / 29 1.3: Bernoulli and Euler Numbers and Polynomials 37 1.4: Determinants / 47 1.5: Matrices / 55 1.6: Permutations and Combinations / 62 1.7: Partial Fraction Decomposition / 63 1.8: Convergence of Series / 66 1.9: Infinite Products / 71 1.10: Functional Series / 73 1.11: Power Series / 74 1.12: Taylor Series / 79 1.13: Fourier Series / 81 1.14: Asymptotic Expansions / 85 1.15: Basic Results from the Calculus / 86 2: Functions and Identities 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 2.2: Logarithms and Exponentials / 112 2.3: The Exponential Function / 114 2.4: Trigonometric Identities / 115 2.5: Hyperbolic Identities / 121 2.6: The Logarithm / 126 2.7: Inverse Trigonometric and Hyperbolic Functions / 128 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 3: Derivatives of Elementary Functions 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 3.2: Derivatives of Trigonometric Functions / 140 3.3: Derivatives of Inverse Trigonometric Functions / 140 3.4: Derivatives of Hyperbolic Functions / 141 3.5: Derivatives of Inverse Hyperbolic Functions 142 4: Indefinite Integrals of Algebraic Functions 4.1: Algebraic and Transcendental Functions / 145 4.2: Indefinite Integrals of Rational Functions 146 4.3: Nonrational Algebraic Functions / 158 5: Indefinite Integrals of Exponential Functions 5.1: Basic Results / 167 6: Indefinite Integrals of Logarithmic Functions 6.1: Combinations of Logarithms and Polynomials 173 7: Indefinite Integrals of Hyperbolic Functions 7.1: Basic Results / 179 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 7.9: Integrands Involving tanh kx and coth kx 188 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 8: Indefinite Integrals Involving Inverse Hyperbolic Functions 8.1: Basic Results / 191 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) 194 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 9: Indefinite Integrals of Trigonometric Functions 9.1: Basic Results / 197 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 9.3: Integrands Involving tan x and/or cot x 205 9.4: Integrands Involving sin x and cos x / 207 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 10: Indefinite Integrals of Inverse Trigonometric Functions 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions / 215 11: The Gamma, Beta, Pi, and Psi Functions 11.1: The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 12: Elliptic Integrals and Functions 12.1: Elliptic Integrals / 229 12.2: Jacobian Elliptic Functions / 235 12.3: Derivatives and Integrals / 237 12.4: Inverse Jacobian Elliptic Functions / 237 13: Probability Integrals and the Error Function 13.1: Normal Distribution / 239 13.2: The Error Function / 242 14: Fresnel Integrals, Sine and Cosine Integrals 14.1: Definitions, Series Representations, and Values at Infinity / 245 14.2: Definitions, Series Representations, and Values at Infinity / 247 15: Definite Integrals 15.1: Integrands Involving Powers of x / 249 15.2: Integrands Involving Trigonometric Functions 251 15.3: Integrands Involving the Exponential Function / 254 15.4: Integrands Involving the Hyperbolic Function 256 15.5: Integrands Involving the Logarithmic Function / 256 16: Different Forms of Fourier Series 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L 259 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L 260 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 16.10: Representative Examples of Fourier Series 261 16.11: Fourier Series and Discontinuous Functions 265 17: Bessel Functions 17.1: Bessel's Differential Equation / 269 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 17.3: Bessel Functions of Fractional Order / 272 17.4: Asymptotic Representations for Bessel Functions / 273 17.5: Zeros of Bessel Functions / 273 17.6: Bessel's Modified Equation / 274 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 17.8: Modified Bessel Functions of Fractional Order / 277 17.9: Asymptotic Representations of Modified Bessel Functions / 278 17.10: Relationships between Bessel Functions 278 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 17.12: Indefinite Integrals of Bessel Functions 281 17.13: Definite Integrals Involving Bessel Functions / 282 17.14: Spherical Bessel Functions / 283 18: Orthogonal Polynomials 18.2: Legendre Polynomials P[subscript n](x) 286 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 18.4: Laguerre Polynomials L[subscript n](x) 294 18.5: Hermite Polynomials H[subscript n](x) / 296 19: Laplace Transformation 20: Fourier Transforms 21: Numerical Integration 21.1: Classical Methods / 315 22: Solutions of Standard Ordinary Differential Equations 22.2: Separation of Variables / 323 22.3: Linear First-Order Equations / 323 22.4: Bernoulli's Equation / 324 22.5: Exact Equations / 325 22.6: Homogeneous Equations / 325 22.7: Linear Differential Equations / 326 22.8: Constant Coefficient Linear Differential Equations Homogeneous Case / 327 22.9: Linear Homogeneous Second-Order Equation 330 22.10: Constant Coefficient Linear Differential Equations Inhomogeneous Case / 331 22.11: Linear Inhomogeneous Second-Order Equation 333 22.12: Determination of Particular Integrals by the Method of Undetermined Coefficients / 334 22.13: The Cauchy-Euler Equation / 336 22.14: Legendre's Equation / 337 22.15: Bessel's Equations / 337 22.16: Power Series and Frobenius Methods / 339 22.17: The Hypergeometric Equation / 344 22.18: Numerical Methods / 345 23: Vector Analysis 23.1: Scalars and Vectors / 353 23.2: Scalar Products / 358 23.3: Vector Products / 359 23.4: Triple Products / 360 23.5: Products of Four Vectors / 361 23.6: Derivatives of Vector Functions of a Scalar t / 361 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 23.9: Line Integrals / 364 23.10: Vector Integral Theorems / 366 23.11: A Vector Rate of Change Theorem / 368 23.12: Useful Vector Identities and Results / 368 24: Systems of Orthogonal Coordinates 24.1: Curvilinear Coordinates / 369 24.2: Vector Operators in Orthogonal Coordinates 371 24.3: Systems of Orthogonal Coordinates / 371 25: Partial Differential Equations and Special Functions 25.1: Fundamental Ideas / 381 25.2: Method of Separation of Variables / 385 25.3: The Sturm--Liouville Problem and Special Functions / 387 25.4: A First-Order System and the Wave Equation 390 25.5: Conservation Equations (Laws) / 391 25.6: The Method of Characteristics / 392 25.7: Discontinuous Solutions (Shocks) / 396 25.8: Similarity Solutions / 398 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 26: The z-Transform 26.1: The z-Transform and Transform Pairs / 403 27: Numerical Approximation 27.2: Economization of Series / 411 27.3: Pade Approximation / 413 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

rawabstract:
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's \booktitle{Handbook of Mathematical Formulas and Integrals}. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse.

rawTOC:
0: Quick Reference List of Frequently Used Data \\ 0.1: Useful Identities / 1 \\ 0.2: Complex Relationships / 2 \\ 0.3: Constants / 2 \\ 0.4: Derivatives of Elementary Functions / 3 \\ 0.5: Rules of Differentiation and Integration / 3 \\ 0.6: Standard Integrals / 4 \\ 0.7: Standard Series / 11 \\ 0.8: Geometry / 13 \\ 1: Numerical, Algebraic, and Analytical Results for Series and Calculus \\ 1.1: Algebraic Results Involving Real and Complex Numbers / 25 \\ 1.2: Finite Sums / 29 \\ 1.3: Bernoulli and Euler Numbers and Polynomials 37 \\ 1.4: Determinants / 47 \\ 1.5: Matrices / 55 \\ 1.6: Permutations and Combinations / 62 \\ 1.7: Partial Fraction Decomposition / 63 \\ 1.8: Convergence of Series / 66 \\ 1.9: Infinite Products / 71 \\ 1.10: Functional Series / 73 \\ 1.11: Power Series / 74 \\ 1.12: Taylor Series / 79 \\ 1.13: Fourier Series / 81 \\ 1.14: Asymptotic Expansions / 85 \\ 1.15: Basic Results from the Calculus / 86 \\ 2: Functions and Identities \\ 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 \\ 2.2: Logarithms and Exponentials / 112 \\ 2.3: The Exponential Function / 114 \\ 2.4: Trigonometric Identities / 115 \\ 2.5: Hyperbolic Identities / 121 \\ 2.6: The Logarithm / 126 \\ 2.7: Inverse Trigonometric and Hyperbolic Functions / 128 \\ 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 \\ 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 \\ 3: Derivatives of Elementary Functions \\ 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 \\ 3.2: Derivatives of Trigonometric Functions / 140 \\ 3.3: Derivatives of Inverse Trigonometric Functions / 140 \\ 3.4: Derivatives of Hyperbolic Functions / 141 \\ 3.5: Derivatives of Inverse Hyperbolic Functions 142 \\ 4: Indefinite Integrals of Algebraic Functions \\ 4.1: Algebraic and Transcendental Functions / 145 \\ 4.2: Indefinite Integrals of Rational Functions 146 \\ 4.3: Nonrational Algebraic Functions / 158 \\ 5: Indefinite Integrals of Exponential Functions \\ 5.1: Basic Results / 167 \\ 6: Indefinite Integrals of Logarithmic Functions \\ 6.1: Combinations of Logarithms and Polynomials 173 \\ 7: Indefinite Integrals of Hyperbolic Functions \\ 7.1: Basic Results / 179 \\ 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 \\ 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 \\ 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 \\ 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 \\ 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 \\ 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 \\ 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 \\ 7.9: Integrands Involving tanh kx and coth kx 188 \\ 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 \\ 8: Indefinite Integrals Involving Inverse Hyperbolic Functions \\ 8.1: Basic Results / 191 \\ 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 \\ 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) 194 \\ 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 \\ 9: Indefinite Integrals of Trigonometric Functions \\ 9.1: Basic Results / 197 \\ 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 \\ 9.3: Integrands Involving tan x and/or cot x 205 \\ 9.4: Integrands Involving sin x and cos x / 207 \\ 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 \\ 10: Indefinite Integrals of Inverse Trigonometric Functions \\ 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions / 215 \\ 11: The Gamma, Beta, Pi, and Psi Functions \\ 11.1: The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 \\ 12: Elliptic Integrals and Functions \\ 12.1: Elliptic Integrals / 229 \\ 12.2: Jacobian Elliptic Functions / 235 \\ 12.3: Derivatives and Integrals / 237 \\ 12.4: Inverse Jacobian Elliptic Functions / 237 \\ 13: Probability Integrals and the Error Function \\ 13.1: Normal Distribution / 239 \\ 13.2: The Error Function / 242 \\ 14: Fresnel Integrals, Sine and Cosine Integrals \\ 14.1: Definitions, Series Representations, and Values at Infinity / 245 \\ 14.2: Definitions, Series Representations, and Values at Infinity / 247 \\ 15: Definite Integrals \\ 15.1: Integrands Involving Powers of x / 249 \\ 15.2: Integrands Involving Trigonometric Functions 251 \\ 15.3: Integrands Involving the Exponential Function / 254 \\ 15.4: Integrands Involving the Hyperbolic Function 256 \\ 15.5: Integrands Involving the Logarithmic Function / 256 \\ 16: Different Forms of Fourier Series \\ 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 \\ 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 \\ 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 \\ 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 \\ 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L 259 \\ 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 \\ 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L 260 \\ 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 \\ 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 \\ 16.10: Representative Examples of Fourier Series 261 \\ 16.11: Fourier Series and Discontinuous Functions 265 \\ 17: Bessel Functions \\ 17.1: Bessel's Differential Equation / 269 \\ 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 \\ 17.3: Bessel Functions of Fractional Order / 272 \\ 17.4: Asymptotic Representations for Bessel Functions / 273 \\ 17.5: Zeros of Bessel Functions / 273 \\ 17.6: Bessel's Modified Equation / 274 \\ 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 \\ 17.8: Modified Bessel Functions of Fractional Order / 277 \\ 17.9: Asymptotic Representations of Modified Bessel Functions / 278 \\ 17.10: Relationships between Bessel Functions 278 \\ 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 \\ 17.12: Indefinite Integrals of Bessel Functions 281 \\ 17.13: Definite Integrals Involving Bessel Functions / 282 \\ 17.14: Spherical Bessel Functions / 283 \\ 18: Orthogonal Polynomials \\ 18.2: Legendre Polynomials P[subscript n](x) 286 \\ 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 \\ 18.4: Laguerre Polynomials L[subscript n](x) 294 \\ 18.5: Hermite Polynomials H[subscript n](x) / 296 \\ 19: Laplace Transformation \\ 20: Fourier Transforms \\ 21: Numerical Integration \\ 21.1: Classical Methods / 315 \\ 22: Solutions of Standard Ordinary Differential Equations \\ 22.2: Separation of Variables / 323 \\ 22.3: Linear First-Order Equations / 323 \\ 22.4: Bernoulli's Equation / 324 \\ 22.5: Exact Equations / 325 \\ 22.6: Homogeneous Equations / 325 \\ 22.7: Linear Differential Equations / 326 \\ 22.8: Constant Coefficient Linear Differential Equations \\ Homogeneous Case / 327 \\ 22.9: Linear Homogeneous Second-Order Equation 330 \\ 22.10: Constant Coefficient Linear Differential Equations \\ Inhomogeneous Case / 331 \\ 22.11: Linear Inhomogeneous Second-Order Equation 333 \\ 22.12: Determination of Particular Integrals by the Method of Undetermined Coefficients / 334 \\ 22.13: The Cauchy-Euler Equation / 336 \\ 22.14: Legendre's Equation / 337 \\ 22.15: Bessel's Equations / 337 \\ 22.16: Power Series and Frobenius Methods / 339 \\ 22.17: The Hypergeometric Equation / 344 \\ 22.18: Numerical Methods / 345 \\ 23: Vector Analysis \\ 23.1: Scalars and Vectors / 353 \\ 23.2: Scalar Products / 358 \\ 23.3: Vector Products / 359 \\ 23.4: Triple Products / 360 \\ 23.5: Products of Four Vectors / 361 \\ 23.6: Derivatives of Vector Functions of a Scalar t / 361 \\ 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 \\ 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 \\ 23.9: Line Integrals / 364 \\ 23.10: Vector Integral Theorems / 366 \\ 23.11: A Vector Rate of Change Theorem / 368 \\ 23.12: Useful Vector Identities and Results / 368 \\ 24: Systems of Orthogonal Coordinates \\ 24.1: Curvilinear Coordinates / 369 \\ 24.2: Vector Operators in Orthogonal Coordinates 371 \\ 24.3: Systems of Orthogonal Coordinates / 371 \\ 25: Partial Differential Equations and Special Functions \\ 25.1: Fundamental Ideas / 381 \\ 25.2: Method of Separation of Variables / 385 \\ 25.3: The Sturm--Liouville Problem and Special Functions / 387 \\ 25.4: A First-Order System and the Wave Equation 390 \\ 25.5: Conservation Equations (Laws) / 391 \\ 25.6: The Method of Characteristics / 392 \\ 25.7: Discontinuous Solutions (Shocks) / 396 \\ 25.8: Similarity Solutions / 398 \\ 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 \\ 26: The z-Transform \\ 26.1: The z-Transform and Transform Pairs / 403 \\ 27: Numerical Approximation \\ 27.2: Economization of Series / 411 \\ 27.3: Pade Approximation / 413 \\ 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

entry:
@Book{Jeffrey:1995:HMF,
  author =       "Alan Jeffrey",
  title =        "Handbook of Mathematical Formulas and Integrals",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xxiv + 410",
  year =         "1995",
  ISBN =         "0-08-052301-3, 0-12-382580-6 (e-book), 1-4832-9514-1
                 (e-book)",
  ISBN-13 =      "978-0-08-052301-9, 978-0-12-382580-3 (e-book),
                 978-1-4832-9514-5 (e-book)",
  LCCN =         "QA47 .J38 1995",
  bibdate =      "Wed Jun 12 14:33:38 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/book/9780123825803",
  abstract =     "If there is a formula to solve a given problem in
                 mathematics, you will find it in Alan Jeffrey's
                 \booktitle{Handbook of Mathematical Formulas and
                 Integrals}. Thanks to its unique thumb-tab indexing
                 feature, answers are easy to find based upon the type
                 of problem they solve. The Handbook covers important
                 formulas, functions, relations, and methods from
                 algebra, trigonometric and exponential functions,
                 combinatorics, probability, matrix theory, calculus and
                 vector calculus, both ordinary and partial differential
                 equations, Fourier series, orthogonal polynomials, and
                 Laplace transforms. Based on Gradshteyn and Ryzhik's
                 Table of Integrals, Series, and Products, Fifth Edition
                 (edited by Jeffrey), but far more accessible and
                 written with particular attention to the needs of
                 students and practicing scientists and engineers, this
                 book is an essential resource. Affordable and
                 authoritative, it is the first place to look for help
                 and a rewarding place to browse.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Tables; Formulae; Math{\'e}matiques;
                 Formules; formulas (algorithms); Mathematics.",
  tableofcontents = "0: Quick Reference List of Frequently Used Data \\
                 0.1: Useful Identities / 1 \\
                 0.2: Complex Relationships / 2 \\
                 0.3: Constants / 2 \\
                 0.4: Derivatives of Elementary Functions / 3 \\
                 0.5: Rules of Differentiation and Integration / 3 \\
                 0.6: Standard Integrals / 4 \\
                 0.7: Standard Series / 11 \\
                 0.8: Geometry / 13 \\
                 1: Numerical, Algebraic, and Analytical Results for
                 Series and Calculus \\
                 1.1: Algebraic Results Involving Real and Complex
                 Numbers / 25 \\
                 1.2: Finite Sums / 29 \\
                 1.3: Bernoulli and Euler Numbers and Polynomials 37 \\
                 1.4: Determinants / 47 \\
                 1.5: Matrices / 55 \\
                 1.6: Permutations and Combinations / 62 \\
                 1.7: Partial Fraction Decomposition / 63 \\
                 1.8: Convergence of Series / 66 \\
                 1.9: Infinite Products / 71 \\
                 1.10: Functional Series / 73 \\
                 1.11: Power Series / 74 \\
                 1.12: Taylor Series / 79 \\
                 1.13: Fourier Series / 81 \\
                 1.14: Asymptotic Expansions / 85 \\
                 1.15: Basic Results from the Calculus / 86 \\
                 2: Functions and Identities \\
                 2.1: Complex Numbers and Trigonometric and Hyperbolic
                 Functions / 101 \\
                 2.2: Logarithms and Exponentials / 112 \\
                 2.3: The Exponential Function / 114 \\
                 2.4: Trigonometric Identities / 115 \\
                 2.5: Hyperbolic Identities / 121 \\
                 2.6: The Logarithm / 126 \\
                 2.7: Inverse Trigonometric and Hyperbolic Functions /
                 128 \\
                 2.8: Series Representations of Trigonometric and
                 Hyperbolic Functions / 133 \\
                 2.9: Useful Limiting Values and Inequalities Involving
                 Elementary Functions / 136 \\
                 3: Derivatives of Elementary Functions \\
                 3.1: Derivatives of Algebraic, Logarithmic, and
                 Exponential Functions / 139 \\
                 3.2: Derivatives of Trigonometric Functions / 140 \\
                 3.3: Derivatives of Inverse Trigonometric Functions /
                 140 \\
                 3.4: Derivatives of Hyperbolic Functions / 141 \\
                 3.5: Derivatives of Inverse Hyperbolic Functions 142
                 \\
                 4: Indefinite Integrals of Algebraic Functions \\
                 4.1: Algebraic and Transcendental Functions / 145 \\
                 4.2: Indefinite Integrals of Rational Functions 146 \\
                 4.3: Nonrational Algebraic Functions / 158 \\
                 5: Indefinite Integrals of Exponential Functions \\
                 5.1: Basic Results / 167 \\
                 6: Indefinite Integrals of Logarithmic Functions \\
                 6.1: Combinations of Logarithms and Polynomials 173 \\
                 7: Indefinite Integrals of Hyperbolic Functions \\
                 7.1: Basic Results / 179 \\
                 7.2: Integrands Involving Powers of sinh(bx) or
                 cosh(bx) / 180 \\
                 7.3: Integrands Involving (a [plus or minus]
                 bx)[superscript m] sinh(cx) or (a + bx)[superscript m]
                 cosh(cx) / 181 \\
                 7.4: Integrands Involving x[superscript m]
                 sinh[superscript n] x or x[superscript m]
                 cosh[superscript n] x / 183 \\
                 7.5: Integrands Involving x[superscript m]
                 sinh[superscript -n] x or x[superscript m]
                 cosh[superscript -n] x / 183 \\
                 7.6: Integrands Involving (1 [plus or minus] cosh
                 x)[superscript -m] / 185 \\
                 7.7: Integrands Involving sinh(ax)cosh[superscript -n]
                 x or cosh(ax)sinh[superscript -n] x / 185 \\
                 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d)
                 / 186 \\
                 7.9: Integrands Involving tanh kx and coth kx 188 \\
                 7.10: Integrands Involving (a + bx)[superscript m] sinh
                 kx or (a + bx)[superscript m] cosh kx / 189 \\
                 8: Indefinite Integrals Involving Inverse Hyperbolic
                 Functions \\
                 8.1: Basic Results / 191 \\
                 8.2: Integrands Involving x[superscript -n]
                 arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 \\
                 8.3: Integrands Involving x[superscript n] arctanh(x/a)
                 or x[superscript n] arccoth(x/a) 194 \\
                 8.4: Integrands Involving x[superscript -n]
                 arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195
                 \\
                 9: Indefinite Integrals of Trigonometric Functions \\
                 9.1: Basic Results / 197 \\
                 9.2: Integrands Involving Powers of x and Powers of sin
                 x or cos x / 197 \\
                 9.3: Integrands Involving tan x and/or cot x 205 \\
                 9.4: Integrands Involving sin x and cos x / 207 \\
                 9.5: Integrands Involving Sines and Cosines with Linear
                 Arguments and Powers of x / 211 \\
                 10: Indefinite Integrals of Inverse Trigonometric
                 Functions \\
                 10.1: Integrands Involving Powers of x and Powers of
                 Inverse Trigonometric Functions / 215 \\
                 11: The Gamma, Beta, Pi, and Psi Functions \\
                 11.1: The Euler Integral and Limit and Infinite Product
                 Representations for [Gamma] (x) / 221 \\
                 12: Elliptic Integrals and Functions \\
                 12.1: Elliptic Integrals / 229 \\
                 12.2: Jacobian Elliptic Functions / 235 \\
                 12.3: Derivatives and Integrals / 237 \\
                 12.4: Inverse Jacobian Elliptic Functions / 237 \\
                 13: Probability Integrals and the Error Function \\
                 13.1: Normal Distribution / 239 \\
                 13.2: The Error Function / 242 \\
                 14: Fresnel Integrals, Sine and Cosine Integrals \\
                 14.1: Definitions, Series Representations, and Values
                 at Infinity / 245 \\
                 14.2: Definitions, Series Representations, and Values
                 at Infinity / 247 \\
                 15: Definite Integrals \\
                 15.1: Integrands Involving Powers of x / 249 \\
                 15.2: Integrands Involving Trigonometric Functions 251
                 \\
                 15.3: Integrands Involving the Exponential Function /
                 254 \\
                 15.4: Integrands Involving the Hyperbolic Function 256
                 \\
                 15.5: Integrands Involving the Logarithmic Function /
                 256 \\
                 16: Different Forms of Fourier Series \\
                 16.1: Fourier Series for f(x) on -[pi] [less than or
                 equal] x [less than or equal] [pi] / 257 \\
                 16.2: Fourier Series for f(x) on -L [less than or
                 equal] x [less than or equal] L / 258 \\
                 16.3: Fourier Series for f(x) on a [less than or equal]
                 x [less than or equal] b / 258 \\
                 16.4: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 259
                 \\
                 16.5: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L 259 \\
                 16.6: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 260
                 \\
                 16.7: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L 260 \\
                 16.8: Complex (Exponential) Fourier Series for f(x) on
                 -[pi] [less than or equal] x [less than or equal] [pi]
                 / 260 \\
                 16.9: Complex (Exponential) Fourier Series for f(x) on
                 -L [less than or equal] x [less than or equal] L 261
                 \\
                 16.10: Representative Examples of Fourier Series 261
                 \\
                 16.11: Fourier Series and Discontinuous Functions 265
                 \\
                 17: Bessel Functions \\
                 17.1: Bessel's Differential Equation / 269 \\
                 17.2: Series Expansions for J[subscript v](x) and
                 Y[subscript v](x) / 270 \\
                 17.3: Bessel Functions of Fractional Order / 272 \\
                 17.4: Asymptotic Representations for Bessel Functions /
                 273 \\
                 17.5: Zeros of Bessel Functions / 273 \\
                 17.6: Bessel's Modified Equation / 274 \\
                 17.7: Series Expansions for I[subscript v](x) and
                 K[subscript v](x) / 276 \\
                 17.8: Modified Bessel Functions of Fractional Order /
                 277 \\
                 17.9: Asymptotic Representations of Modified Bessel
                 Functions / 278 \\
                 17.10: Relationships between Bessel Functions 278 \\
                 17.11: Integral Representations of J[subscript n](x),
                 I[subscript n](x), and K[subscript n](x) / 281 \\
                 17.12: Indefinite Integrals of Bessel Functions 281 \\
                 17.13: Definite Integrals Involving Bessel Functions /
                 282 \\
                 17.14: Spherical Bessel Functions / 283 \\
                 18: Orthogonal Polynomials \\
                 18.2: Legendre Polynomials P[subscript n](x) 286 \\
                 18.3: Chebyshev Polynomials T[subscript n](x) and
                 U[subscript n](x) / 290 \\
                 18.4: Laguerre Polynomials L[subscript n](x) 294 \\
                 18.5: Hermite Polynomials H[subscript n](x) / 296 \\
                 19: Laplace Transformation \\
                 20: Fourier Transforms \\
                 21: Numerical Integration \\
                 21.1: Classical Methods / 315 \\
                 22: Solutions of Standard Ordinary Differential
                 Equations \\
                 22.2: Separation of Variables / 323 \\
                 22.3: Linear First-Order Equations / 323 \\
                 22.4: Bernoulli's Equation / 324 \\
                 22.5: Exact Equations / 325 \\
                 22.6: Homogeneous Equations / 325 \\
                 22.7: Linear Differential Equations / 326 \\
                 22.8: Constant Coefficient Linear Differential
                 Equations \\
                 Homogeneous Case / 327 \\
                 22.9: Linear Homogeneous Second-Order Equation 330 \\
                 22.10: Constant Coefficient Linear Differential
                 Equations \\
                 Inhomogeneous Case / 331 \\
                 22.11: Linear Inhomogeneous Second-Order Equation 333
                 \\
                 22.12: Determination of Particular Integrals by the
                 Method of Undetermined Coefficients / 334 \\
                 22.13: The Cauchy-Euler Equation / 336 \\
                 22.14: Legendre's Equation / 337 \\
                 22.15: Bessel's Equations / 337 \\
                 22.16: Power Series and Frobenius Methods / 339 \\
                 22.17: The Hypergeometric Equation / 344 \\
                 22.18: Numerical Methods / 345 \\
                 23: Vector Analysis \\
                 23.1: Scalars and Vectors / 353 \\
                 23.2: Scalar Products / 358 \\
                 23.3: Vector Products / 359 \\
                 23.4: Triple Products / 360 \\
                 23.5: Products of Four Vectors / 361 \\
                 23.6: Derivatives of Vector Functions of a Scalar t /
                 361 \\
                 23.7: Derivatives of Vector Functions of Several Scalar
                 Variables / 362 \\
                 23.8: Integrals of Vector Functions of a Scalar
                 Variable t / 363 \\
                 23.9: Line Integrals / 364 \\
                 23.10: Vector Integral Theorems / 366 \\
                 23.11: A Vector Rate of Change Theorem / 368 \\
                 23.12: Useful Vector Identities and Results / 368 \\
                 24: Systems of Orthogonal Coordinates \\
                 24.1: Curvilinear Coordinates / 369 \\
                 24.2: Vector Operators in Orthogonal Coordinates 371
                 \\
                 24.3: Systems of Orthogonal Coordinates / 371 \\
                 25: Partial Differential Equations and Special
                 Functions \\
                 25.1: Fundamental Ideas / 381 \\
                 25.2: Method of Separation of Variables / 385 \\
                 25.3: The Sturm--Liouville Problem and Special
                 Functions / 387 \\
                 25.4: A First-Order System and the Wave Equation 390
                 \\
                 25.5: Conservation Equations (Laws) / 391 \\
                 25.6: The Method of Characteristics / 392 \\
                 25.7: Discontinuous Solutions (Shocks) / 396 \\
                 25.8: Similarity Solutions / 398 \\
                 25.9: Burgers's Equation, the KdV Equation, and the
                 KdVB Equation / 400 \\
                 26: The z-Transform \\
                 26.1: The z-Transform and Transform Pairs / 403 \\
                 27: Numerical Approximation \\
                 27.2: Economization of Series / 411 \\
                 27.3: Pade Approximation / 413 \\
                 27.4: Finite Difference Approximations to Ordinary and
                 Partial Derivatives / 415",
}


bibtype: article
filename: elefunt.bib
label: Krattenthaler:1995:HHM
author: C. Krattenthaler
journal: j-J-SYMBOLIC-COMP
volume: 20
number: 5--6
pages: 737--744
month: nov
monthnumber: 11
year: 1995
CODEN: JSYCEH
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
MRclass: 05Axx (11Bxx 33-04 33Cxx 33Dxx)
MRnumber: 1 395 424
bibdate: Sat May 10 15:54:09 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.10 15:54:09 MDT
note: Symbolic computation in combinatorics $ Delta _1 $ (Ithaca, NY, 1993).
fjournal: Journal of Symbolic Computation
acknowledgement: ack-nhfb
classcodes: C7310 (Mathematics computing); C1100 (Mathematical techniques)
corpsource: Inst. fur Math., Wien Univ., Austria
journalURL: http://www.sciencedirect.com/science/journal/07477171
treatment: T Theoretical or Mathematical
rawauthor: C. Krattenthaler
rawnote: Symbolic computation in combinatorics $ \Delta_1 $ (Ithaca, NY, 1993).
title:
HYP and HYPQ: Mathematica packages for the manipulation of binomial sums and hypergeometric series, respectively $q$-binomial sums and basic hypergeometric series

keywords:
basic hypergeometric; binomial sums; HYP; hypergeometric series; HYPQ; Mathematica packages; mathematics computing; packages; q-binomial sums; series; series (mathematics); software; symbol manipulation

rawtitle:
{HYP} and {HYPQ}: {Mathematica} packages for the manipulation of binomial sums and hypergeometric series, respectively $q$-binomial sums and basic hypergeometric series

entry:
@Article{Krattenthaler:1995:HHM,
  author =       "C. Krattenthaler",
  title =        "{HYP} and {HYPQ}: {Mathematica} packages for the
                 manipulation of binomial sums and hypergeometric
                 series, respectively $q$-binomial sums and basic
                 hypergeometric series",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "20",
  number =       "5--6",
  pages =        "737--744",
  month =        nov # "--" # dec,
  year =         "1995",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "05Axx (11Bxx 33-04 33Cxx 33Dxx)",
  MRnumber =     "1 395 424",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Symbolic computation in combinatorics $ \Delta_1 $
                 (Ithaca, NY, 1993).",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics computing); C1100 (Mathematical
                 techniques)",
  corpsource =   "Inst. fur Math., Wien Univ., Austria",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "basic hypergeometric; binomial sums; HYP;
                 hypergeometric series; HYPQ; Mathematica packages;
                 mathematics computing; packages; q-binomial sums;
                 series; series (mathematics); software; symbol
                 manipulation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kwan:1995:CII
author: H. Kwan and R. L. Nelson, Jr. and E. E. Swartzlander, Jr.
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: Cascaded Implementation of an Iterative Inverse-Square-Root Algorithm, with Overflow Lookahead
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 115--122
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: H. Kwan and R. L. {Nelson, Jr.} and E. E. {Swartzlander, Jr.}
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: Cascaded Implementation of an Iterative Inverse-Square-Root Algorithm, with Overflow Lookahead
entry:
@InProceedings{Kwan:1995:CII,
  author =       "H. Kwan and R. L. {Nelson, Jr.} and E. E.
                 {Swartzlander, Jr.}",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Cascaded Implementation of an Iterative
                 Inverse-Square-Root Algorithm, with Overflow
                 Lookahead",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "115--122",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "We present an unconventional method of computing the
                 inverse of the square root. It implements the
                 equivalent of two iterations of a well-known
                 multiplicative method to obtain 24-bit mantissa
                 accuracy. We implement each ``iteration'' as a
                 \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lang:1995:VHR
author: T. Lang and P. Montuschi
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: Very-High Radix Combined Division and Square Root with Prescaling and Selection by Rounding
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 124--131
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: T. Lang and P. Montuschi
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: Very-High Radix Combined Division and Square Root with Prescaling and Selection by Rounding
entry:
@InProceedings{Lang:1995:VHR,
  author =       "T. Lang and P. Montuschi",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Very-High Radix Combined Division and Square Root with
                 Prescaling and Selection by Rounding",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "124--131",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "An algorithm for square root with prescaling is
                 developed and combined with a similar scheme for
                 division. An implementation is described, evaluated and
                 compared with other combined div/sqrt \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Lau:1995:NLC
author: H. T. (Hang Tong) Lau
title: A Numerical Library in C for Scientists and Engineers
publisher: pub-CRC
address: pub-CRC:adr
pages: xvii + 795
year: 1995
ISBN: 0-8493-7376-X OR 084937376X
ISBN13: 978-0-8493-7376-3 OR 9780849373763
LCCN: QA76.73.C15 L38 1995
bibdate: Fri Sep 26 14:29:10 MDT 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2008.09.26 14:29:10 MDT
URL: http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html
subject: C (Computer program language)
acknowledgement: ack-nhfb
rawauthor: H. T. (Hang Tong) Lau
rawtitle: A Numerical Library in {C} for Scientists and Engineers
TOC:
1. Elementary Procedures 1.1. Real vector and matrix Initialization 1.2. Real vector and matrix Duplication 1.3. Real vector and matrix Multiplication 1.4. Real vector vector products 1.5. Real matrix vector products 1.6. Real matrix matrix products 1.7. Real vector and matrix Elimination 1.8. Real vector and matrix Interchanging 1.9. Real vector and matrix Rotation 1.10. Real vector and matrix Norms 1.11. Real vector and matrix Scaling 1.12. Complex vector and matrix Multiplication 1.13. Complex vector and matrix Scalar products 1.14. Complex vector and matrix Elimination 1.15. Complex vector and matrix Rotation 1.16. Complex vector and matrix Norms 1.17. Complex vector and matrix Scaling 1.18. Complex monadic operations 1.19. Complex dyadic operations 1.20. Long integer arithmetic 2. Algebraic Evaluations 2.1. Evaluation of polynomials in Grunert form 2.2. Evaluation of general orthogonal polynomials 2.3. Evaluation of Chebyshev polynomials 2.4. Evaluation of Fourier series 2.5. Evaluation of continued fractions 2.6. Transformation of polynomial representation 2.7. Operations on orthogonal polynomials 3. Linear Algebra 3.1. Full real general matrices 3.2. Real Symmetric positive definite matrices 3.3. General real symmetric matrices 3.4. Real full rank overdetermined systems 3.5. Other real matrix problems 3.6. Real sparse non-symmetric band matrices 3.7. Real sparse non-symmetric tridiagonal matrices 3.8. Sparse symmetric positive definite band matrices 3.9. Symmetric positive definite tridiagonal matrices 3.10. Sparse real matrices Iterative methods 3.11. Similarity transformation 3.12. Other transformations 3.13. The (ordinary) eigenvalue problem 3.14. The generalized eigenvalue problem 3.15. Singular values 3.16. Zeros of polynomials 4. Analytic Evaluations 4.1. Evaluation of an infinite series 4.2. Quadrature 4.3. Numerical differentiation 5. Analytic Problems 5.1. Non-linear equations 5.2. Unconstrained optimization 5.3. Overdetermined nonlinear systems 5.4. Differential equations Initial value problems 5.5. Two point boundary value problems 5.6. Two-dimensional boundary value problems 5.7. Parameter estimation in differential equations 6. Special Functions 6.1. Elementary functions 6.2. Exponential integral 6.3. Gamma function 6.4. Error function 6.5. Bessel functions of integer order 6.6. Bessel functions of real order 7. Interpolation and Approximation 7.1. Real data in one dimension Appendix B: Prototype Declarations Appendix C: Procedure Descriptions Appendix D: Memory Management Utilities

shortTOC:
Introduction 1 Elementary Procedures 2 Algebraic Evaluations 3 Linear Algebra 4 Analytic Evaluations 5 Analytic Problems 6 Special Functions 7 Interpolation and Approximation

rawshortTOC:
Introduction \\ 1 Elementary Procedures \\ 2 Algebraic Evaluations \\ 3 Linear Algebra \\ 4 Analytic Evaluations \\ 5 Analytic Problems \\ 6 Special Functions \\ 7 Interpolation and Approximation

rawTOC:
1. Elementary Procedures \\ 1.1. Real vector and matrix Initialization \\ 1.2. Real vector and matrix Duplication \\ 1.3. Real vector and matrix Multiplication \\ 1.4. Real vector vector products \\ 1.5. Real matrix vector products \\ 1.6. Real matrix matrix products \\ 1.7. Real vector and matrix Elimination \\ 1.8. Real vector and matrix Interchanging \\ 1.9. Real vector and matrix Rotation \\ 1.10. Real vector and matrix Norms \\ 1.11. Real vector and matrix Scaling \\ 1.12. Complex vector and matrix Multiplication \\ 1.13. Complex vector and matrix Scalar products \\ 1.14. Complex vector and matrix Elimination \\ 1.15. Complex vector and matrix Rotation \\ 1.16. Complex vector and matrix Norms \\ 1.17. Complex vector and matrix Scaling \\ 1.18. Complex monadic operations \\ 1.19. Complex dyadic operations \\ 1.20. Long integer arithmetic \\ 2. Algebraic Evaluations \\ 2.1. Evaluation of polynomials in Grunert form \\ 2.2. Evaluation of general orthogonal polynomials \\ 2.3. Evaluation of Chebyshev polynomials \\ 2.4. Evaluation of Fourier series \\ 2.5. Evaluation of continued fractions \\ 2.6. Transformation of polynomial representation \\ 2.7. Operations on orthogonal polynomials \\ 3. Linear Algebra \\ 3.1. Full real general matrices \\ 3.2. Real Symmetric positive definite matrices \\ 3.3. General real symmetric matrices \\ 3.4. Real full rank overdetermined systems \\ 3.5. Other real matrix problems \\ 3.6. Real sparse non-symmetric band matrices \\ 3.7. Real sparse non-symmetric tridiagonal matrices \\ 3.8. Sparse symmetric positive definite band matrices \\ 3.9. Symmetric positive definite tridiagonal matrices \\ 3.10. Sparse real matrices \\ Iterative methods \\ 3.11. Similarity transformation \\ 3.12. Other transformations \\ 3.13. The (ordinary) eigenvalue problem \\ 3.14. The generalized eigenvalue problem \\ 3.15. Singular values \\ 3.16. Zeros of polynomials \\ 4. Analytic Evaluations \\ 4.1. Evaluation of an infinite series \\ 4.2. Quadrature \\ 4.3. Numerical differentiation \\ 5. Analytic Problems \\ 5.1. Non-linear equations \\ 5.2. Unconstrained optimization \\ 5.3. Overdetermined nonlinear systems \\ 5.4. Differential equations \\ Initial value problems \\ 5.5. Two point boundary value problems \\ 5.6. Two-dimensional boundary value problems \\ 5.7. Parameter estimation in differential equations \\ 6. Special Functions \\ 6.1. Elementary functions \\ 6.2. Exponential integral \\ 6.3. Gamma function \\ 6.4. Error function \\ 6.5. Bessel functions of integer order \\ 6.6. Bessel functions of real order \\ 7. Interpolation and Approximation \\ 7.1. Real data in one dimension \\ Appendix B: Prototype Declarations \\ Appendix C: Procedure Descriptions \\ Appendix D: Memory Management Utilities

entry:
@Book{Lau:1995:NLC,
  author =       "H. T. (Hang Tong) Lau",
  title =        "A Numerical Library in {C} for Scientists and
                 Engineers",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "xvii + 795",
  year =         "1995",
  ISBN =         "0-8493-7376-X",
  ISBN-13 =      "978-0-8493-7376-3",
  LCCN =         "QA76.73.C15 L38 1995",
  bibdate =      "Fri Sep 26 14:29:10 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Introduction \\
                 1 Elementary Procedures \\
                 2 Algebraic Evaluations \\
                 3 Linear Algebra \\
                 4 Analytic Evaluations \\
                 5 Analytic Problems \\
                 6 Special Functions \\
                 7 Interpolation and Approximation",
  subject =      "C (Computer program language)",
  tableofcontents = "1. Elementary Procedures \\
                 1.1. Real vector and matrix Initialization \\
                 1.2. Real vector and matrix Duplication \\
                 1.3. Real vector and matrix Multiplication \\
                 1.4. Real vector vector products \\
                 1.5. Real matrix vector products \\
                 1.6. Real matrix matrix products \\
                 1.7. Real vector and matrix Elimination \\
                 1.8. Real vector and matrix Interchanging \\
                 1.9. Real vector and matrix Rotation \\
                 1.10. Real vector and matrix Norms \\
                 1.11. Real vector and matrix Scaling \\
                 1.12. Complex vector and matrix Multiplication \\
                 1.13. Complex vector and matrix Scalar products \\
                 1.14. Complex vector and matrix Elimination \\
                 1.15. Complex vector and matrix Rotation \\
                 1.16. Complex vector and matrix Norms \\
                 1.17. Complex vector and matrix Scaling \\
                 1.18. Complex monadic operations \\
                 1.19. Complex dyadic operations \\
                 1.20. Long integer arithmetic \\
                 2. Algebraic Evaluations \\
                 2.1. Evaluation of polynomials in Grunert form \\
                 2.2. Evaluation of general orthogonal polynomials \\
                 2.3. Evaluation of Chebyshev polynomials \\
                 2.4. Evaluation of Fourier series \\
                 2.5. Evaluation of continued fractions \\
                 2.6. Transformation of polynomial representation \\
                 2.7. Operations on orthogonal polynomials \\
                 3. Linear Algebra \\
                 3.1. Full real general matrices \\
                 3.2. Real Symmetric positive definite matrices \\
                 3.3. General real symmetric matrices \\
                 3.4. Real full rank overdetermined systems \\
                 3.5. Other real matrix problems \\
                 3.6. Real sparse non-symmetric band matrices \\
                 3.7. Real sparse non-symmetric tridiagonal matrices \\
                 3.8. Sparse symmetric positive definite band matrices
                 \\
                 3.9. Symmetric positive definite tridiagonal matrices
                 \\
                 3.10. Sparse real matrices \\
                 Iterative methods \\
                 3.11. Similarity transformation \\
                 3.12. Other transformations \\
                 3.13. The (ordinary) eigenvalue problem \\
                 3.14. The generalized eigenvalue problem \\
                 3.15. Singular values \\
                 3.16. Zeros of polynomials \\
                 4. Analytic Evaluations \\
                 4.1. Evaluation of an infinite series \\
                 4.2. Quadrature \\
                 4.3. Numerical differentiation \\
                 5. Analytic Problems \\
                 5.1. Non-linear equations \\
                 5.2. Unconstrained optimization \\
                 5.3. Overdetermined nonlinear systems \\
                 5.4. Differential equations \\
                 Initial value problems \\
                 5.5. Two point boundary value problems \\
                 5.6. Two-dimensional boundary value problems \\
                 5.7. Parameter estimation in differential equations \\
                 6. Special Functions \\
                 6.1. Elementary functions \\
                 6.2. Exponential integral \\
                 6.3. Gamma function \\
                 6.4. Error function \\
                 6.5. Bessel functions of integer order \\
                 6.6. Bessel functions of real order \\
                 7. Interpolation and Approximation \\
                 7.1. Real data in one dimension \\
                 Appendix B: Prototype Declarations \\
                 Appendix C: Procedure Descriptions \\
                 Appendix D: Memory Management Utilities",
}


bibtype: inproceedings
filename: elefunt.bib
label: Leeser:1995:VSR
author: M. Leeser and J. O'Leary
title: Verification of a subtractive radix-$2$ square root algorithm and implementation
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 526--531
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. Leeser and J. O'Leary
rawtitle: Verification of a subtractive radix-$2$ square root algorithm and implementation
booktitle:
Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors, ICCD '95

rawbooktitle:
Proceedings of the {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors, {ICCD '95}

entry:
@InProceedings{Leeser:1995:VSR,
  author =       "M. Leeser and J. O'Leary",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors,
                 {ICCD '95}",
  title =        "Verification of a subtractive radix-$2$ square root
                 algorithm and implementation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "526--531",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Many modern microprocessors implement floating point
                 square root hardware using subtractive algorithms. Such
                 processors include the HP PA7200, the MIPS R4400, and
                 the Intel Pentium. The Intel Pentium division bug
                 highlights the importance of \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lether:1995:MAZ
author: F. G. Lether and P. R. Wenston
title: Minimax approximations to the zeros of $ P_n(x) $ and Gauss--Legendre quadrature
journal: j-J-COMPUT-APPL-MATH
volume: 59
number: 2
pages: 245--252
day: 19
month: may
monthnumber: 5
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:37 MST 2017
bibtimestamp: 2017.02.25 12:24:37 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042794000305
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: F. G. Lether and P. R. Wenston
rawtitle: Minimax approximations to the zeros of {$ P_n(x) $} and {Gauss--Legendre} quadrature
entry:
@Article{Lether:1995:MAZ,
  author =       "F. G. Lether and P. R. Wenston",
  title =        "Minimax approximations to the zeros of {$ P_n(x) $}
                 and {Gauss--Legendre} quadrature",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "59",
  number =       "2",
  pages =        "245--252",
  day =          "19",
  month =        may,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794000305",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lewanowicz:1995:AMC
author: Stanislaw Lewanowicz and Stefan Paszkowski
title: An analytic method for convergence acceleration of certain hypergeometric series
journal: j-MATH-COMPUT
volume: 64
number: 210
pages: 691--713
month: apr
monthnumber: 4
year: 1995
CODEN: MCMPAF
DOI: https://doi.org/10.2307/2153446
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33C45 (65B10 65D20)
MRnumber: 1277769 (95h:33006)
MRreviewer: Anton Hut'a
bibdate: Thu Dec 1 17:36:45 2011
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
affiliation: Inst. of Comput. Sci., Wroclaw Univ., Poland
classcodes: B0290 (Numerical analysis); C4100 (Numerical analysis)
corpsource: Inst. of Comput. Sci., Wroclaw Univ., Poland
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Stanis{\l}aw Lewanowicz and Stefan Paszkowski
rawtitle: An analytic method for convergence acceleration of certain hypergeometric series
keywords:
analytic method; convergence acceleration; convergence of numerical methods; fast converging expansions; hypergeometric; iterated transformation; mathematical constants; series; series (mathematics)

entry:
@Article{Lewanowicz:1995:AMC,
  author =       "Stanis{\l}aw Lewanowicz and Stefan Paszkowski",
  title =        "An analytic method for convergence acceleration of
                 certain hypergeometric series",
  journal =      j-MATH-COMPUT,
  volume =       "64",
  number =       "210",
  pages =        "691--713",
  month =        apr,
  year =         "1995",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2153446",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33C45 (65B10 65D20)",
  MRnumber =     "1277769 (95h:33006)",
  MRreviewer =   "Anton Hut'a",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Comput. Sci., Wroclaw Univ., Poland",
  classcodes =   "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "Inst. of Comput. Sci., Wroclaw Univ., Poland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "analytic method; convergence acceleration; convergence
                 of numerical methods; fast converging expansions;
                 hypergeometric; iterated transformation; mathematical
                 constants; series; series (mathematics)",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Liu:1995:SRV
author: S.-I. Liu
title: Square-rooting and vector summation circuits using current conveyors
volume: 142
number: 4
pages: 223--226
month: aug
monthnumber: 8
year: 1995
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: S.-I. Liu
rawtitle: Square-rooting and vector summation circuits using current conveyors
journal:
IEE Proceedings on Circuits, Devices and Systems [see also IEE Proceedings G - Circuits, Devices and Systems]

entry:
@Article{Liu:1995:SRV,
  author =       "S.-I. Liu",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G - Circuits, Devices and
                 Systems]",
  volume =       "142",
  number =       "4",
  pages =        "223--226",
  month =        aug,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "New analogue squaring, square-rooting and vector
                 summation circuits using current conveyors (CCIIs) are
                 presented. They consist of MOS transistors biased in
                 the triode region, a buffered unity-gain inverting
                 amplifier, resistors and CCIIs. A general \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Louie:1995:VPS
author: Marianne E. Louie and Milos D. Ercegovac
title: A Variable-Precision Square Root Implementation for Field Programmable Gate Arrays
journal: j-J-SUPERCOMPUTING
volume: 9
number: 3
pages: 315--336
month: sep
monthnumber: 9
year: 1995
CODEN: JOSUED
DOI: https://doi.org/10.1007/BF01212874
ISSN: 0920-8542 (print), 1573-0484 (electronic) OR 09208542 (print), 15730484 (electronic)
ISSNL: 0920-8542 OR 09208542
bibdate: Wed Jul 6 11:13:09 MDT 2005
bibtimestamp: 2005.07.06 11:13:09 MDT
fjournal: The Journal of Supercomputing
acknowledgement: ack-nhfb
affiliation: Dept. of Comput. Sci., California Univ., Los Angeles, CA, USA
corpsource: Dept. of Comput. Sci., California Univ., Los Angeles, CA, USA
journalURL: http://link.springer.com/journal/11227
treatment: P Practical
rawauthor: Marianne E. Louie and Milo{\v{s}} D. Ercegovac
rawtitle: A Variable-Precision Square Root Implementation for Field Programmable Gate Arrays
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3; http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995; 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/jsuper.bib

URL:
http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315; http://www.wkap.nl/oasis.htm/95692

keywords:
digital arithmetic; field programmable gate arrays; square root; square root implementation; variable-precision; Xilinx XC4010

entry:
@Article{Louie:1995:VPS,
  author =       "Marianne E. Louie and Milo{\v{s}} D. Ercegovac",
  title =        "A Variable-Precision Square Root Implementation for
                 Field Programmable Gate Arrays",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "9",
  number =       "3",
  pages =        "315--336",
  month =        sep,
  year =         "1995",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/BF01212874",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Jul 6 11:13:09 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3;
                 http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995;
                 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/jsuper.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315;
                 http://www.wkap.nl/oasis.htm/95692",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., California Univ., Los Angeles,
                 CA, USA",
  classification = "C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Dept. of Comput. Sci., California Univ., Los Angeles,
                 CA, USA",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
  keywords =     "digital arithmetic; field programmable gate arrays;
                 square root; square root implementation;
                 variable-precision; Xilinx XC4010",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Lucas:1995:EII
author: S. K. Lucas and H. A. Stone
title: Evaluating infinite integrals involving Bessel functions of arbitrary order
journal: j-J-COMPUT-APPL-MATH
volume: 64
number: 3
pages: 217--231
year: 1995
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(95)00142-5
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Thu Jul 8 13:22:49 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.07.08 13:22:49 ???
URL: http://www.sciencedirect.com/science/article/B6TYH-4002HHC-J/2/54f1e67d9bea3e951acc3c39556ab452
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: S. K. Lucas and H. A. Stone
rawtitle: Evaluating infinite integrals involving {Bessel} functions of arbitrary order
keywords:
$varepsilon $-algorithm; Bessel functions; Bessel zeros; infinite integration; mW transform; quadrature

remark:
This paper examines several methods for accurately integrating oscillatory functions, such as products of $ f(x) $ with a trigonometric function or a Bessel function. It also discusses finding zeros of Bessel functions, and sequence acceleration techniques.

entry:
@Article{Lucas:1995:EII,
  author =       "S. K. Lucas and H. A. Stone",
  title =        "Evaluating infinite integrals involving {Bessel}
                 functions of arbitrary order",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "64",
  number =       "3",
  pages =        "217--231",
  year =         "1995",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(95)00142-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Jul 8 13:22:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/B6TYH-4002HHC-J/2/54f1e67d9bea3e951acc3c39556ab452",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "$\varepsilon$-algorithm; Bessel functions; Bessel
                 zeros; infinite integration; mW transform; quadrature",
  remark =       "This paper examines several methods for accurately
                 integrating oscillatory functions, such as products of
                 $ f(x) $ with a trigonometric function or a Bessel
                 function. It also discusses finding zeros of Bessel
                 functions, and sequence acceleration techniques.",
}


bibtype: article
filename: elefunt.bib
label: Luther:1995:HAT
author: Wolfram Luther
title: Highly accurate tables for elementary functions
journal: j-BIT-NUM-MATH
volume: 35
number: 3
pages: 352--360
month: sep
monthnumber: 9
year: 1995
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01732609
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D20 (68U05)
MRnumber: 97h:65024
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
keywords: elementary functions
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Wolfram Luther
rawtitle: Highly accurate tables for elementary functions
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=3; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.mai.liu.se/BIT/contents/bit35.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=3&spage=352

entry:
@Article{Luther:1995:HAT,
  author =       "Wolfram Luther",
  title =        "Highly accurate tables for elementary functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "35",
  number =       "3",
  pages =        "352--360",
  month =        sep,
  year =         "1995",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01732609",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D20 (68U05)",
  MRnumber =     "97h:65024",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit35.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=3&spage=352",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lynch:1995:KTF
author: T. Lynch and A. Ahmed and M. Schulte and T. Callaway
title: The K5 Transcendental Functions
crossref: Knowles:1995:PSC
pages: 163--171
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf
acknowledgement: ack-nhfb
rawauthor: T. Lynch and A. Ahmed and M. Schulte and T. Callaway
rawtitle: The {K5} Transcendental Functions
entry:
@InProceedings{Lynch:1995:KTF,
  author =       "T. Lynch and A. Ahmed and M. Schulte and T. Callaway",
  title =        "The {K5} Transcendental Functions",
  crossref =     "Knowles:1995:PSC",
  pages =        "163--171",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Maroni:1995:IRB
author: P. Maroni
title: An integral representation for the Bessel form
journal: j-J-COMPUT-APPL-MATH
volume: 57
number: 1--2
pages: 251--260
day: 20
month: feb
monthnumber: 2
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:24:35 MST 2017
bibtimestamp: 2017.02.25 12:24:35 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042793E0249L
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: P. Maroni
rawtitle: An integral representation for the {Bessel} form
entry:
@Article{Maroni:1995:IRB,
  author =       "P. Maroni",
  title =        "An integral representation for the {Bessel} form",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "57",
  number =       "1--2",
  pages =        "251--260",
  day =          "20",
  month =        feb,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042793E0249L",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Matsubara:1995:NBS
author: G. Matsubara and N. Ide and H. Tago and S. Suzuki and N. Goto
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: 30-ns 55-b Shared Radix $2$ Division and Square Root Using a Self-Timed Circuit
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 98--105
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: G. Matsubara and N. Ide and H. Tago and S. Suzuki and N. Goto
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: 30-ns 55-b Shared Radix $2$ Division and Square Root Using a Self-Timed Circuit
entry:
@InProceedings{Matsubara:1995:NBS,
  author =       "G. Matsubara and N. Ide and H. Tago and S. Suzuki and
                 N. Goto",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "30-ns 55-b Shared Radix $2$ Division and Square Root
                 Using a Self-Timed Circuit",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "98--105",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "A shared radix 2 division and square root
                 implementation using a self-timed circuit is presented.
                 The same execution time for division and square root is
                 achieved by using an on-the-fly digit decoding and a
                 root multiple generation technique. Most \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Miller:1995:RCF
author: A. R. Miller and I. S. Moskowitz
title: Reduction of a class of Fox--Wright psi functions for certain rational parameters
journal: j-COMPUT-MATH-APPL
volume: 30
number: 11
pages: 73--82
month: dec
monthnumber: 12
year: 1995
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:19 MST 2017
bibtimestamp: 2017.03.01 21:48:19 MST
URL: http://www.sciencedirect.com/science/article/pii/089812219500165U
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: A. R. Miller and I. S. Moskowitz
rawtitle: Reduction of a class of {Fox--Wright} psi functions for certain rational parameters
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
From the abstract: ``The Fox--Wright Psi function is a special case of Fox's $H$-function and a generalization of the generalized hypergeometric function. In the present paper, we show that the Psi function reduces to a single generalized hypergeometric function when certain of its parameters are integers and to a finite sum of generalized hypergeometric functions when these parameters are rational numbers.''

entry:
@Article{Miller:1995:RCF,
  author =       "A. R. Miller and I. S. Moskowitz",
  title =        "Reduction of a class of {Fox--Wright} psi functions
                 for certain rational parameters",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "11",
  pages =        "73--82",
  month =        dec,
  year =         "1995",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500165U",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``The Fox--Wright Psi function is a
                 special case of Fox's $H$-function and a generalization
                 of the generalized hypergeometric function. In the
                 present paper, we show that the Psi function reduces to
                 a single generalized hypergeometric function when
                 certain of its parameters are integers and to a finite
                 sum of generalized hypergeometric functions when these
                 parameters are rational numbers.''",
}


bibtype: article
filename: elefunt.bib
label: Montuschi:1995:RRI
author: P. Montuschi and L. Ciminiera
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 1
pages: 144--146
month: jan
monthnumber: 1
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.368000
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
note: See cite Montuschi:1993:RIT.
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. Montuschi and L. Ciminiera
rawnote: See \cite{Montuschi:1993:RIT}.
title:
A remark on ``Reducing iteration time when result digit is zero for radix-$2$ SRT division and square root with redundant remainders''

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

entry:
@Article{Montuschi:1995:RRI,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "A remark on {``Reducing iteration time when result
                 digit is zero for radix-$2$ SRT division and square
                 root with redundant remainders''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "144--146",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.368000",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Montuschi:1993:RIT}.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "In a previous paper by P. Montuschi and L. Ciminiera
                 (ibid., vol. 42, no.2 p239-246, Feb 1993), an
                 architecture for shared radix 2 division and square
                 root has been presented whose main characteristic is
                 the ability to avoid any addition/subtraction,
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Muldoon:1995:EZB
author: Martin E. Muldoon
title: Electrostatics and zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 65
number: 1--3
pages: 299--308
day: 29
month: dec
monthnumber: 12
year: 1995
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 13:02:25 MST 2017
bibtimestamp: 2017.02.25 13:02:25 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795001182
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Martin E. Muldoon
rawtitle: Electrostatics and zeros of {Bessel} functions
entry:
@Article{Muldoon:1995:EZB,
  author =       "Martin E. Muldoon",
  title =        "Electrostatics and zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "65",
  number =       "1--3",
  pages =        "299--308",
  day =          "29",
  month =        dec,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001182",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: OLeary:1995:NRI
author: J. O'Leary and M. Leeser and J. Hickey and M. Aagaard
title: Non-Restoring Integer Square Root: a Case Study in Design by Principled Optimization
journal: j-LECT-NOTES-COMP-SCI
volume: 901
pages: 52--??
year: 1995
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat May 11 13:45:32 MDT 1996
bibtimestamp: 1996.05.11 13:45:32 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: J. O'Leary and M. Leeser and J. Hickey and M. Aagaard
rawtitle: Non-Restoring Integer Square Root: a Case Study in Design by Principled Optimization
entry:
@Article{OLeary:1995:NRI,
  author =       "J. O'Leary and M. Leeser and J. Hickey and M.
                 Aagaard",
  title =        "Non-Restoring Integer Square Root: a Case Study in
                 Design by Principled Optimization",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "901",
  pages =        "52--??",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat May 11 13:45:32 MDT 1996",
  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 =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: elefunt.bib
label: Paszkowski:1995:QHS
author: S. Paszkowski
title: Quasipower and hypergeometric series---construction and evaluation
journal: j-NUMER-ALGORITHMS
volume: 10
number: 3--4
pages: 337--361
month: oct
monthnumber: 10
year: 1995
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 41A58 (33-04 65B99)
MRnumber: 96k:41042
MRreviewer: Walter Schempp
bibdate: Fri Nov 6 18:06:29 MST 1998
bibtimestamp: 1998.11.06 18:06:29 MST
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
corpsource: Inst. for Low Temp. and Structure Res., Polish Acad. of Sci., Wroclaw, Poland
journalURL: http://link.springer.com/journal/11075
treatment: P Practical; T Theoretical or Mathematical
rawauthor: S. Paszkowski
rawtitle: Quasipower and hypergeometric series---construction and evaluation
bibsource:
http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

keywords:
approximation theory; Euler's dilogarithm; Hermite-Pade approximation; hypergeometric series; Levin's transforms; Pade approximants; power series; quasipower; recurrence relations; series (mathematics); transforms

entry:
@Article{Paszkowski:1995:QHS,
  author =       "S. Paszkowski",
  title =        "Quasipower and hypergeometric series---construction
                 and evaluation",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "3--4",
  pages =        "337--361",
  month =        oct,
  year =         "1995",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "41A58 (33-04 65B99)",
  MRnumber =     "96k:41042",
  MRreviewer =   "Walter Schempp",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290Z (Other numerical methods); C4130 (Interpolation
                 and function approximation); C4190 (Other numerical
                 methods)",
  corpsource =   "Inst. for Low Temp. and Structure Res., Polish Acad.
                 of Sci., Wroclaw, Poland",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "approximation theory; Euler's dilogarithm;
                 Hermite-Pade approximation; hypergeometric series;
                 Levin's transforms; Pade approximants; power series;
                 quasipower; recurrence relations; series (mathematics);
                 transforms",
  pubcountry =   "Switzerland",
  treatment =    "P Practical; T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Prabhu:1995:MRD
author: J. A. Prabhu and G. B. Zyner
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
title: 167 MHz Radix-$8$ Divide and Square Root Using Overlapped Radix-$2$ Stages
crossref: Knowles:1995:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 155--162
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: J. A. Prabhu and G. B. Zyner
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, 19--21 July 1995
rawtitle: {167 MHz} Radix-$8$ Divide and Square Root Using Overlapped Radix-$2$ Stages
entry:
@InProceedings{Prabhu:1995:MRD,
  author =       "J. A. Prabhu and G. B. Zyner",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "{167 MHz} Radix-$8$ Divide and Square Root Using
                 Overlapped Radix-$2$ Stages",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "155--162",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "UltraSPARC's IEEE-754 compliant floating point divide
                 and square root implementation is presented. Three
                 overlapping stages of SRT radix-$2$ quotient selection
                 logic enable an effective radix-$8$ calculation at 167
                 MHz while only a single radix-$2$ \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schwarz:1995:RQC
author: E. M. Schwarz
booktitle: Conference Record of the Twenty-Ninth Asilomar Conference on Signals, Systems and Computers, 1995
title: Rounding for quadratically converging algorithms for division and square root
crossref: Singh:1995:CRT
volume: 1
pages: 600--603
month: oct
monthnumber: 10
year: 1995
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-sfo
rawauthor: E. M. Schwarz
rawbooktitle: Conference Record of the Twenty-Ninth Asilomar Conference on Signals, Systems and Computers, 1995
rawtitle: Rounding for quadratically converging algorithms for division and square root
entry:
@InProceedings{Schwarz:1995:RQC,
  author =       "E. M. Schwarz",
  booktitle =    "Conference Record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems and Computers, 1995",
  title =        "Rounding for quadratically converging algorithms for
                 division and square root",
  crossref =     "Singh:1995:CRT",
  volume =       "1",
  pages =        "600--603",
  month =        oct,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Exactly rounded results are necessary for many
                 architectures such as IEEE 754 standard. For division
                 and square root, rounding is easy to perform if a
                 remainder is available. But for quadratically
                 converging algorithms, the remainder is not \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Sidhu:1995:EIF
author: Satinder S. Sidhu
title: Elliptic Integrals and Functions
journal: j-COMPUT-PHYS
volume: 9
number: 3
pages: 268--276
month: may
monthnumber: 5
year: 1995
CODEN: CPHYE2
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Thu Feb 02 18:05:53 2012
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2012.02.02 18:05:53 ???
fjournal: Computers in Physics
acknowledgement: ack-nhfb
rawauthor: Satinder S. Sidhu
rawtitle: Elliptic Integrals and Functions
entry:
@Article{Sidhu:1995:EIF,
  author =       "Satinder S. Sidhu",
  title =        "Elliptic Integrals and Functions",
  journal =      j-COMPUT-PHYS,
  volume =       "9",
  number =       "3",
  pages =        "268--276",
  month =        may # "\slash " # jun,
  year =         "1995",
  CODEN =        "CPHYE2",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Thu Feb 02 18:05:53 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers in Physics",
}


bibtype: article
filename: elefunt.bib
label: Smith:1995:CFA
author: Roger Alan Smith
title: A Continued-Fraction Analysis of Trigonometric Argument Reduction
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 11
pages: 1348--1351
month: nov
monthnumber: 11
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.475133
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Dec 08 10:21:28 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2006.12.08 10:21:28 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Roger Alan Smith
rawtitle: A Continued-Fraction Analysis of Trigonometric Argument Reduction
abstract:
The calculation of a trigonometric function of a large argument x is effectively carried out by finding the integer $N$ and $ 0 leq alpha < 1 $ such that $ x = (N + alpha ) pi / 4 $. This reduction modulo $ pi / 4 $ makes it possible to calculate a trigonometric function of a reduced argument, either $ alpha pi / 4 $ or $ (1 - alpha ) pi / 4 $, which lies in the interval $ (0, pi / 4) $. Payne and Hanek [1] described an efficient algorithm for computing $ alpha $ to a predetermined level of accuracy. They noted that if $x$ differs only slightly from an integral multiple $ pi / 2 $, the reduction must be carried out quite accurately to avoid loss of significance in the reduced argument. We present a simple method using continued fractions for determining, for all numbers $x$ for which the greatest number of insignificant leading bits occur. Applications are made IEEE single-precision and double-precision formats and two extended-precision formats.

keywords:
argument reduction; computer arithmetic; continued fractions; nonlinear optimization; Payne/Hanek radian reduction; range reduction; trigonometric functions

rawabstract:
The calculation of a trigonometric function of a large argument x is effectively carried out by finding the integer $N$ and $ 0 \leq \alpha < 1 $ such that $ x = (N + \alpha) \pi / 4 $. This reduction modulo $ \pi / 4 $ makes it possible to calculate a trigonometric function of a reduced argument, either $ \alpha \pi / 4 $ or $ (1 - \alpha) \pi / 4 $, which lies in the interval $ (0, \pi / 4) $. Payne and Hanek [1] described an efficient algorithm for computing $ \alpha $ to a predetermined level of accuracy. They noted that if $x$ differs only slightly from an integral multiple $ \pi / 2 $, the reduction must be carried out quite accurately to avoid loss of significance in the reduced argument. We present a simple method using continued fractions for determining, for all numbers $x$ for which the greatest number of insignificant leading bits occur. Applications are made IEEE single-precision and double-precision formats and two extended-precision formats.

entry:
@Article{Smith:1995:CFA,
  author =       "Roger Alan Smith",
  title =        "A Continued-Fraction Analysis of Trigonometric
                 Argument Reduction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "11",
  pages =        "1348--1351",
  month =        nov,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.475133",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Dec 08 10:21:28 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The calculation of a trigonometric function of a large
                 argument x is effectively carried out by finding the
                 integer $N$ and $ 0 \leq \alpha < 1 $ such that $ x =
                 (N + \alpha) \pi / 4 $. This reduction modulo $ \pi / 4
                 $ makes it possible to calculate a trigonometric
                 function of a reduced argument, either $ \alpha \pi / 4
                 $ or $ (1 - \alpha) \pi / 4 $, which lies in the
                 interval $ (0, \pi / 4) $. Payne and Hanek [1]
                 described an efficient algorithm for computing $ \alpha
                 $ to a predetermined level of accuracy. They noted that
                 if $x$ differs only slightly from an integral multiple
                 $ \pi / 2 $, the reduction must be carried out quite
                 accurately to avoid loss of significance in the reduced
                 argument. We present a simple method using continued
                 fractions for determining, for all numbers $x$ for
                 which the greatest number of insignificant leading bits
                 occur. Applications are made IEEE single-precision and
                 double-precision formats and two extended-precision
                 formats.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "argument reduction; computer arithmetic; continued
                 fractions; nonlinear optimization; Payne/Hanek radian
                 reduction; range reduction; trigonometric functions",
}


bibtype: inproceedings
filename: elefunt.bib
label: Soderquist:1995:APC
author: Peter Soderquist and Miriam Leeser
crossref: Knowles:1995:PSC
pages: 132--139
month: jul
monthnumber: 7
year: 1995
bibdate: Mon May 20 06:05:24 MDT 2002
bibtimestamp: 2002.05.20 06:05:24 MDT
URL: http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf
keywords: ARITH-12
acknowledgement: ack-sfo
rawauthor: Peter Soderquist and Miriam Leeser
title:
An Area / Performance Comparison of Subtractive and Multiplicative Divide / Square Root Implementations

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Proceedings database

rawtitle:
An Area\slash Performance Comparison of Subtractive and Multiplicative Divide\slash Square Root Implementations

entry:
@InProceedings{Soderquist:1995:APC,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "An Area\slash Performance Comparison of Subtractive
                 and Multiplicative Divide\slash Square Root
                 Implementations",
  crossref =     "Knowles:1995:PSC",
  pages =        "132--139",
  month =        jul,
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12",
}


bibtype: book
filename: elefunt.bib
label: Varchenko:1995:MHF
author: A. N. (Aleksandr Nikolaevich) Varchenko
volume: 21
publisher: pub-WORLD-SCI
address: pub-WORLD-SCI:adr
pages: ix + 371
year: 1995
ISBN: 981-02-1880-X OR 981021880X
ISBN13: 978-981-02-1880-5 OR 9789810218805
LCCN: QA353.H9 V37 1995
bibdate: Sat Oct 30 21:12:24 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:12:24 MDT
series: Advanced series in mathematical physics
acknowledgement: ack-nhfb
rawauthor: A. N. (Aleksandr Nikolaevich) Varchenko
title:
Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups

subject:
Hypergeometric functions; Kac-Moody algebras; Representations of Lie algebras; Representations of quantum groups

TOC:
1. Introduction 2. Construction of complexes calculating homology of the complement of a configuration 3. Construction of homology complexes for discriminantal configuration 4. Algebraic interpretation of chain complexes of a discriminantal configuration 5. Quasiisomorphism of two-sided Hochschild complexes to suitable one-sided Hochschild complexes 6. Bundle properties of a discriminantal configuration 7. R-matrix for the two-sided Hochschild complexes 8. Monodromy 9. R-matrix operator as the canonical element, quantum doubles 10. Hypergeometric integrals 11. Kac--Moody Lie algebras without Serre's relations and their doubles 12. Hypergeometric integrals of a discriminantal configuration 13. Resonances at infinity 14. Degenerations of discriminantal configurations 15. Remarks on homology groups of a configuration with coefficients in local systems more general than complex one-dimensional

rawtitle:
Multidimensional Hypergeometric Functions and Representation Theory of {Lie} Algebras and Quantum Groups

rawTOC:
1. Introduction \\ 2. Construction of complexes calculating homology of the complement of a configuration \\ 3. Construction of homology complexes for discriminantal configuration \\ 4. Algebraic interpretation of chain complexes of a discriminantal configuration \\ 5. Quasiisomorphism of two-sided Hochschild complexes to suitable one-sided Hochschild complexes \\ 6. Bundle properties of a discriminantal configuration \\ 7. R-matrix for the two-sided Hochschild complexes \\ 8. Monodromy \\ 9. R-matrix operator as the canonical element, quantum doubles \\ 10. Hypergeometric integrals \\ 11. Kac--Moody Lie algebras without Serre's relations and their doubles \\ 12. Hypergeometric integrals of a discriminantal configuration \\ 13. Resonances at infinity \\ 14. Degenerations of discriminantal configurations \\ 15. Remarks on homology groups of a configuration with coefficients in local systems more general than complex one-dimensional

entry:
@Book{Varchenko:1995:MHF,
  author =       "A. N. (Aleksandr Nikolaevich) Varchenko",
  title =        "Multidimensional Hypergeometric Functions and
                 Representation Theory of {Lie} Algebras and Quantum
                 Groups",
  volume =       "21",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "ix + 371",
  year =         "1995",
  ISBN =         "981-02-1880-X",
  ISBN-13 =      "978-981-02-1880-5",
  LCCN =         "QA353.H9 V37 1995",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Advanced series in mathematical physics",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Kac-Moody algebras;
                 Representations of Lie algebras; Representations of
                 quantum groups",
  tableofcontents = "1. Introduction \\
                 2. Construction of complexes calculating homology of
                 the complement of a configuration \\
                 3. Construction of homology complexes for
                 discriminantal configuration \\
                 4. Algebraic interpretation of chain complexes of a
                 discriminantal configuration \\
                 5. Quasiisomorphism of two-sided Hochschild complexes
                 to suitable one-sided Hochschild complexes \\
                 6. Bundle properties of a discriminantal configuration
                 \\
                 7. R-matrix for the two-sided Hochschild complexes \\
                 8. Monodromy \\
                 9. R-matrix operator as the canonical element, quantum
                 doubles \\
                 10. Hypergeometric integrals \\
                 11. Kac--Moody Lie algebras without Serre's relations
                 and their doubles \\
                 12. Hypergeometric integrals of a discriminantal
                 configuration \\
                 13. Resonances at infinity \\
                 14. Degenerations of discriminantal configurations \\
                 15. Remarks on homology groups of a configuration with
                 coefficients in local systems more general than complex
                 one-dimensional",
}


bibtype: book
filename: elefunt.bib
label: Vilenkin:1995:RLG
author: N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii Ulsianovich) Klimyk
title: Representation of Lie Groups and Special Functions: Recent Advances
volume: 316
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: xvi + 497
year: 1995
ISBN: 0-7923-3210-5 OR 0792332105
ISBN13: 978-0-7923-3210-7 OR 9780792332107
LCCN: QA176 .V55 1995
bibdate: Sat Oct 30 16:43:03 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 16:43:03 MDT
series: Mathematics and its applications
remark: Translated to English from Russian by V. A. Groza and A. A. Groza.
subject: Representations of Lie groups; Functions, Special; Integral transforms
acknowledgement: ack-nhfb
rawauthor: N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii Ulsianovich) Klimyk
rawtitle: Representation of {Lie} Groups and Special Functions: Recent Advances
URL:
http://www.loc.gov/catdir/enhancements/fy0823/95108075-d.html; http://www.loc.gov/catdir/enhancements/fy0823/95108075-t.html

TOC:
Preface / xiii 1. $h$-Harmonic Polynomials, $h$-Hankel Transform, and Coxeter Groups / 1 2. Symmetric Polynomials and Symmetric Functions / 67 3. Hypergeometric Functions Related to Jack Polynomials / 185 4. Clebsch--Gordan Coefficients and Racah Coefficients of Finite Dimensional Representations / 265 5. Clebsch--Gordan Coefficients of the Group $U(n)$ and Related Generalizations of Hypergeometric Functions / 317 6. Gel'fand Hypergeometric Functions / 393 Bibliography / 463 Supplementary Bibliography / 484 Bibliography Notes / 488 Subject Index / 494

rawTOC:
Preface / xiii \\ 1. $h$-Harmonic Polynomials, $h$-Hankel Transform, and Coxeter Groups / 1 \\ 2. Symmetric Polynomials and Symmetric Functions / 67 \\ 3. Hypergeometric Functions Related to Jack Polynomials / 185 \\ 4. Clebsch--Gordan Coefficients and Racah Coefficients of Finite Dimensional Representations / 265 \\ 5. Clebsch--Gordan Coefficients of the Group $U(n)$ and Related Generalizations of Hypergeometric Functions / 317 \\ 6. Gel'fand Hypergeometric Functions / 393 \\ Bibliography / 463 \\ Supplementary Bibliography / 484 \\ Bibliography Notes / 488 \\ Subject Index / 494

entry:
@Book{Vilenkin:1995:RLG,
  author =       "N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii
                 Ulsianovich) Klimyk",
  title =        "Representation of {Lie} Groups and Special Functions:
                 Recent Advances",
  volume =       "316",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xvi + 497",
  year =         "1995",
  ISBN =         "0-7923-3210-5",
  ISBN-13 =      "978-0-7923-3210-7",
  LCCN =         "QA176 .V55 1995",
  bibdate =      "Sat Oct 30 16:43:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematics and its applications",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0823/95108075-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0823/95108075-t.html",
  acknowledgement = ack-nhfb,
  remark =       "Translated to English from Russian by V. A. Groza and
                 A. A. Groza.",
  subject =      "Representations of Lie groups; Functions, Special;
                 Integral transforms",
  tableofcontents = "Preface / xiii \\
                 1. $h$-Harmonic Polynomials, $h$-Hankel Transform, and
                 Coxeter Groups / 1 \\
                 2. Symmetric Polynomials and Symmetric Functions / 67
                 \\
                 3. Hypergeometric Functions Related to Jack Polynomials
                 / 185 \\
                 4. Clebsch--Gordan Coefficients and Racah Coefficients
                 of Finite Dimensional Representations / 265 \\
                 5. Clebsch--Gordan Coefficients of the Group $U(n)$ and
                 Related Generalizations of Hypergeometric Functions /
                 317 \\
                 6. Gel'fand Hypergeometric Functions / 393 \\
                 Bibliography / 463 \\
                 Supplementary Bibliography / 484 \\
                 Bibliography Notes / 488 \\
                 Subject Index / 494",
}


bibtype: article
filename: elefunt.bib
label: Vrahatis:1995:RPP
author: M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A. Zafiropoulos and T. N. Grapsa
journal: j-COMP-PHYS-COMM
volume: 92
number: 2--3
pages: 252--266
month: dec
monthnumber: 12
year: 1995
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(95)00115-9
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:01 MST 2012
bibtimestamp: 2012.02.13 21:30:01 MST
note: See erratum cite Vrahatis:1999:ESP.
URL: http://www.sciencedirect.com/science/article/pii/0010465595001159
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A. Zafiropoulos and T. N. Grapsa
rawnote: See erratum \cite{Vrahatis:1999:ESP}.
title:
RFSFNS: a portable package for the numerical determination of the number and the calculation of roots of Bessel functions

rawtitle:
{RFSFNS}: a portable package for the numerical determination of the number and the calculation of roots of {Bessel} functions

entry:
@Article{Vrahatis:1995:RPP,
  author =       "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
                 Zafiropoulos and T. N. Grapsa",
  title =        "{RFSFNS}: a portable package for the numerical
                 determination of the number and the calculation of
                 roots of {Bessel} functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "92",
  number =       "2--3",
  pages =        "252--266",
  month =        dec,
  year =         "1995",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(95)00115-9",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:01 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Vrahatis:1999:ESP}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465595001159",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Watson:1995:TTB
author: G. N. (George Neville) Watson
title: A Treatise on the Theory of Bessel Functions
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
edition: Second
pages: vi + 804
year: 1995
LCCN: QA408 .W2 1995
bibdate: Sat Apr 19 09:15:26 MDT 2008
bibtimestamp: 2008.04.19 09:15:26 MDT
series: Cambridge mathematical library
remark: First published 1922. Second edition 1944. Reprinted 1966.
subject: Bessel functions
acknowledgement: ack-nhfb
rawauthor: G. N. (George Neville) Watson
rawtitle: A Treatise on the Theory of {Bessel} Functions
ISBN:
0-521-48391-3 (paperback), 0-521-06743-X (hardcover) OR 0521483913 (paperback), 052106743X (hardcover)

ISBN13:
978-0-521-48391-9 (paperback), 978-0-521-06743-0 (hardcover) OR 9780521483919 (paperback), 9780521067430 (hardcover)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; z3950.loc.gov:7090/Voyager

URL:
http://www.loc.gov/catdir/description/cam028/96139881.html; http://www.loc.gov/catdir/toc/cam029/96139881.html

TOC:
1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices

rawTOC:
1. Bessel functions before 1826 \\ 2. The Bessel coefficients \\ 3. Bessel functions \\ 4. Differential equations \\ 5. Miscellaneous properties of Bessel functions \\ 6. Integral representations of Bessel functions \\ 7. Asymptotic expansions of Bessel functions \\ 8. Bessel functions of large order \\ 9. Polynomials associated with Bessel functions \\ 10. Functions associated with Bessel functions \\ 11. Addition theorems \\ 12. Definite integrals \\ 13. Infinitive integrals \\ 14. Multiple integrals \\ 15. The zeros of Bessel functions \\ 16. Neumann series and Lommel's functions of two variables \\ 17. Kapteyn series \\ 18. Series of Fourier-Bessel and Dini \\ 19. Schl{\"o}mlich series \\ 20. The tabulation of Bessel functions \\ Tables of Bessel functions \\ Bibliography \\ Indices

entry:
@Book{Watson:1995:TTB,
  author =       "G. N. (George Neville) Watson",
  title =        "A Treatise on the Theory of {Bessel} Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "vi + 804",
  year =         "1995",
  ISBN =         "0-521-48391-3 (paperback), 0-521-06743-X (hardcover)",
  ISBN-13 =      "978-0-521-48391-9 (paperback), 978-0-521-06743-0
                 (hardcover)",
  LCCN =         "QA408 .W2 1995",
  bibdate =      "Sat Apr 19 09:15:26 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Cambridge mathematical library",
  URL =          "http://www.loc.gov/catdir/description/cam028/96139881.html;
                 http://www.loc.gov/catdir/toc/cam029/96139881.html",
  acknowledgement = ack-nhfb,
  remark =       "First published 1922. Second edition 1944. Reprinted
                 1966.",
  subject =      "Bessel functions",
  tableofcontents = "1. Bessel functions before 1826 \\
                 2. The Bessel coefficients \\
                 3. Bessel functions \\
                 4. Differential equations \\
                 5. Miscellaneous properties of Bessel functions \\
                 6. Integral representations of Bessel functions \\
                 7. Asymptotic expansions of Bessel functions \\
                 8. Bessel functions of large order \\
                 9. Polynomials associated with Bessel functions \\
                 10. Functions associated with Bessel functions \\
                 11. Addition theorems \\
                 12. Definite integrals \\
                 13. Infinitive integrals \\
                 14. Multiple integrals \\
                 15. The zeros of Bessel functions \\
                 16. Neumann series and Lommel's functions of two
                 variables \\
                 17. Kapteyn series \\
                 18. Series of Fourier-Bessel and Dini \\
                 19. Schl{\"o}mlich series \\
                 20. The tabulation of Bessel functions \\
                 Tables of Bessel functions \\
                 Bibliography \\
                 Indices",
  xxauthor =     "G. N. Watson",
}


bibtype: article
filename: elefunt.bib
label: Wong:1995:EHS
author: W. F. Wong and Yoshio Oyanagi and Eiichi Goto
title: Evaluation of the Hitachi S-3800 Supercomputer Using Six Benchmarks
journal: j-IJSAHPC
volume: 9
number: 1
pages: 58--70
month: Spring
year: 1995
CODEN: IJSAE9
ISSN: 0890-2720 OR 08902720
bibdate: Tue Feb 18 09:07:32 MST 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.02.18 09:07:32 MST
fjournal: International Journal of Supercomputer Applications and High Performance Computing
acknowledgement: ack-nhfb
affiliation: Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore
affiliationaddress: Singapore
journalURL: http://hpc.sagepub.com/content/by/year
journalabr: Int J Supercomput Appl High Perform Comput
rawauthor: W. F. Wong and Yoshio Oyanagi and Eiichi Goto
rawtitle: Evaluation of the {Hitachi S-3800} Supercomputer Using Six Benchmarks
abstract:
The S-3000 series is the third generation of Hitachi's supercomputers. It is claimed to be currently the fastest single processor supercomputer. In this paper, we introduce the S-3000 and, using six benchmarks we designed, evaluate a member of this series of supercomputer, the top of the range S-3800, against its predecessor, the Hitachi HITAC S-820. Our purpose is to determine in what areas the S-3800 is an improvement over its predecessor. The suite of benchmarks include kernels for random number generation, elementary function computation, FFT, dense matrix operations, SOR, and list vector (scatter / gather) operations. The use of small-to medium-sized kernels, as opposed to large application benchmarks, help to better understand the behavior of the machine. Our findings support the claim that the S-3000 series is at least twice as fast as the previous generation of Hitachi supercomputers.

keywords:
Benchmarks; Computer selection and evaluation; Computer testing; Fast Fourier transforms; Fastest single processor; Hitachi supercomputer; Matrix algebra; Medium sized kernels; Performance; Random number generation; Supercomputers; Vectors

rawabstract:
The S-3000 series is the third generation of Hitachi's supercomputers. It is claimed to be currently the fastest single processor supercomputer. In this paper, we introduce the S-3000 and, using six benchmarks we designed, evaluate a member of this series of supercomputer, the top of the range S-3800, against its predecessor, the Hitachi HITAC S-820. Our purpose is to determine in what areas the S-3800 is an improvement over its predecessor. The suite of benchmarks include kernels for random number generation, elementary function computation, FFT, dense matrix operations, SOR, and list vector (scatter\slash gather) operations. The use of small-to medium-sized kernels, as opposed to large application benchmarks, help to better understand the behavior of the machine. Our findings support the claim that the S-3000 series is at least twice as fast as the previous generation of Hitachi supercomputers.

entry:
@Article{Wong:1995:EHS,
  author =       "W. F. Wong and Yoshio Oyanagi and Eiichi Goto",
  title =        "Evaluation of the {Hitachi S-3800} Supercomputer Using
                 Six Benchmarks",
  journal =      j-IJSAHPC,
  volume =       "9",
  number =       "1",
  pages =        "58--70",
  month =        "Spring",
  year =         "1995",
  CODEN =        "IJSAE9",
  ISSN =         "0890-2720",
  bibdate =      "Tue Feb 18 09:07:32 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The S-3000 series is the third generation of Hitachi's
                 supercomputers. It is claimed to be currently the
                 fastest single processor supercomputer. In this paper,
                 we introduce the S-3000 and, using six benchmarks we
                 designed, evaluate a member of this series of
                 supercomputer, the top of the range S-3800, against its
                 predecessor, the Hitachi HITAC S-820. Our purpose is to
                 determine in what areas the S-3800 is an improvement
                 over its predecessor. The suite of benchmarks include
                 kernels for random number generation, elementary
                 function computation, FFT, dense matrix operations,
                 SOR, and list vector (scatter\slash gather) operations.
                 The use of small-to medium-sized kernels, as opposed to
                 large application benchmarks, help to better understand
                 the behavior of the machine. Our findings support the
                 claim that the S-3000 series is at least twice as fast
                 as the previous generation of Hitachi supercomputers.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore",
  affiliationaddress = "Singapore",
  classification = "722.4; 921.3; 921.6; 922.2",
  fjournal =     "International Journal of Supercomputer Applications
                 and High Performance Computing",
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
  journalabr =   "Int J Supercomput Appl High Perform Comput",
  keywords =     "Benchmarks; Computer selection and evaluation;
                 Computer testing; Fast Fourier transforms; Fastest
                 single processor; Hitachi supercomputer; Matrix
                 algebra; Medium sized kernels; Performance; Random
                 number generation; Supercomputers; Vectors",
}


bibtype: article
filename: elefunt.bib
label: Wong:1995:FEE
author: W. F. Wong and E. Goto
title: Fast evaluation of the elementary functions in single precision
journal: j-IEEE-TRANS-COMPUT
volume: 44
number: 3
pages: 453--457
month: mar
monthnumber: 3
year: 1995
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.372037
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Dec 14 11:25:18 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.14 11:25:18 MST
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of Singapore, Singapore
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Error analysis; Floating point arithmetic
rawauthor: W. F. Wong and E. Goto
rawtitle: Fast evaluation of the elementary functions in single precision
abstract:
In this paper we introduce a new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method. We assume the availability of large and fast (at least for read purposes) memory. We call this method the ATA (Add-Table lookup-Add) method. As the name implies, the hardware required for the method are adders (both two/ and multi/operand adders) and fast tables. For IEEE single precision numbers our initial estimates indicate that we can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trigonometric and inverse trigonometric functions, within the latency of two to four floating point multiplies.

keywords:
Adders; Difference method; Elementary functions; Fast evaluation; Floating point multiplies; Inverse trigonometric functions; Logarithm functions; Reciprocal; Single precision; Square root; Truncated Taylor series

rawabstract:
In this paper we introduce a new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method. We assume the availability of large and fast (at least for read purposes) memory. We call this method the ATA (Add-Table lookup-Add) method. As the name implies, the hardware required for the method are adders (both two/ and multi/operand adders) and fast tables. For IEEE single precision numbers our initial estimates indicate that we can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trigonometric and inverse trigonometric functions, within the latency of two to four floating point multiplies.

entry:
@Article{Wong:1995:FEE,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast evaluation of the elementary functions in single
                 precision",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "3",
  pages =        "453--457",
  month =        mar,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.372037",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In this paper we introduce a new method for the fast
                 evaluation of the elementary functions in single
                 precision based on the evaluation of truncated Taylor
                 series using a difference method. We assume the
                 availability of large and fast (at least for read
                 purposes) memory. We call this method the ATA
                 (Add-Table lookup-Add) method. As the name implies, the
                 hardware required for the method are adders (both two/
                 and multi/operand adders) and fast tables. For IEEE
                 single precision numbers our initial estimates indicate
                 that we can calculate the basic elementary functions,
                 namely reciprocal, square root, logarithm, exponential,
                 trigonometric and inverse trigonometric functions,
                 within the latency of two to four floating point
                 multiplies.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Difference method; Elementary functions; Fast
                 evaluation; Floating point multiplies; Inverse
                 trigonometric functions; Logarithm functions;
                 Reciprocal; Single precision; Square root; Truncated
                 Taylor series",
  pubcountry =   "USA",
  thesaurus =    "Error analysis; Floating point arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Ypma:1995:HDN
author: Tjalling J. Ypma
title: Historical Development of the Newton--Raphson Method
journal: j-SIAM-REVIEW
volume: 37
number: 4
pages: 531--551
month: dec
monthnumber: 12
year: 1995
CODEN: SIREAD
DOI: https://doi.org/10.1137/1037125
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 01A05 (65-03)
MRnumber: 97b:01003
MRreviewer: M. Z. Nashed
bibdate: Sat Mar 29 09:55:35 MDT 2014
bibtimestamp: 2014.03.29 09:55:35 MDT
URL: http://epubs.siam.org/23425.htm; http://link.aip.org/link/?SIR/37/531/1
fjournal: SIAM Review
acknowledgement: ack-nhfb
affiliation: Western Washington Univ
affiliationaddress: Bellingham, WA, USA
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: December 1995
rawauthor: Tjalling J. Ypma
rawtitle: Historical Development of the {Newton--Raphson} Method
bibsource:
Compendex database; http://epubs.siam.org/toc/siread/37/4; http://www.siam.org/journals/sirev/sirev374.htm; 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/siamreview.bib

abstract:
This expository paper traces the development of the Newton--Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.

keywords:
Algebra; Algorithms; Approximation theory; Differentiation (calculus); Finite difference method; Fluxional calculus; Isaac Newton; Iterative methods; Joseph Raphson; Linearization; Newton--Raphson method; Nonlinear algebraic equations; Nonlinear equations; Nonpolynomial equation; Polynomials; Secant method; Thomas Simpson

rawabstract:
This expository paper traces the development of the Newton--Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.

entry:
@Article{Ypma:1995:HDN,
  author =       "Tjalling J. Ypma",
  title =        "Historical Development of the {Newton--Raphson}
                 Method",
  journal =      j-SIAM-REVIEW,
  volume =       "37",
  number =       "4",
  pages =        "531--551",
  month =        dec,
  year =         "1995",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1037125",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "01A05 (65-03)",
  MRnumber =     "97b:01003",
  MRreviewer =   "M. Z. Nashed",
  bibdate =      "Sat Mar 29 09:55:35 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/37/4;
                 http://www.siam.org/journals/sirev/sirev374.htm;
                 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/siamreview.bib",
  URL =          "http://epubs.siam.org/23425.htm;
                 http://link.aip.org/link/?SIR/37/531/1",
  abstract =     "This expository paper traces the development of the
                 Newton--Raphson method for solving nonlinear algebraic
                 equations through the extant notes, letters, and
                 publications of Isaac Newton, Joseph Raphson, and
                 Thomas Simpson. It is shown how Newton's formulation
                 differed from the iterative process of Raphson, and
                 that Simpson was the first to give a general
                 formulation, in terms of fluxional calculus, applicable
                 to nonpolynomial equations. Simpson's extension of the
                 method to systems of equations is exhibited.",
  acknowledgement = ack-nhfb,
  affiliation =  "Western Washington Univ",
  affiliationaddress = "Bellingham, WA, USA",
  classification = "921.1; 921.2; 921.6",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Algebra; Algorithms; Approximation theory;
                 Differentiation (calculus); Finite difference method;
                 Fluxional calculus; Isaac Newton; Iterative methods;
                 Joseph Raphson; Linearization; Newton--Raphson method;
                 Nonlinear algebraic equations; Nonlinear equations;
                 Nonpolynomial equation; Polynomials; Secant method;
                 Thomas Simpson",
  onlinedate =   "December 1995",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1995:TMAa
author: J. Zhang and J. A. Belward
title: Tau-method approximations for the Bessel function $ Y_0 (z) $
journal: j-COMPUT-MATH-APPL
volume: 30
number: 7
pages: 5--14
month: oct
monthnumber: 10
year: 1995
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(95)00120-N
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sun Jun 12 08:33:42 2011
bibtimestamp: 2011.06.12 08:33:42 ???
URL: http://www.sciencedirect.com/science/article/pii/089812219500120N
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. Zhang and J. A. Belward
rawtitle: Tau-method approximations for the {Bessel} function {$ Y_0 (z) $}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Zhang:1995:TMAa,
  author =       "J. Zhang and J. A. Belward",
  title =        "Tau-method approximations for the {Bessel} function {$
                 Y_0 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "7",
  pages =        "5--14",
  month =        oct,
  year =         "1995",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(95)00120-N",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 08:33:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500120N",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1995:TMAb
author: J. Zhang
title: Tau-method approximations for the Bessel function $ Y_1 (z) $
journal: j-COMPUT-MATH-APPL
volume: 30
number: 7
pages: 15--19
month: oct
monthnumber: 10
year: 1995
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(95)00121-E
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sun Jun 12 09:26:01 2011
bibtimestamp: 2011.06.12 09:26:01 ???
URL: http://www.sciencedirect.com/science/article/pii/089812219500121E
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. Zhang
rawtitle: Tau-method approximations for the {Bessel} function {$ Y_1 (z) $}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
From p. 18 (conclusions section), ``We may use this method to approximate the Bessel functions of other integer orders. ldots It is therefore advisable to use the recurrence relations of the Bessel functions to compute function values for $ n > 1 $ ldots ''. [This is a similar limitation as with Chebyshev and minimax polynomial approximations: they are valid only for a single order the Bessel function.]

entry:
@Article{Zhang:1995:TMAb,
  author =       "J. Zhang",
  title =        "Tau-method approximations for the {Bessel} function {$
                 Y_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "7",
  pages =        "15--19",
  month =        oct,
  year =         "1995",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(95)00121-E",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 09:26:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500121E",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From p. 18 (conclusions section), ``We may use this
                 method to approximate the Bessel functions of other
                 integer orders. \ldots{} It is therefore advisable to
                 use the recurrence relations of the Bessel functions to
                 compute function values for $ n > 1 $ \ldots''. [This
                 is a similar limitation as with Chebyshev and minimax
                 polynomial approximations: they are valid only for a
                 single order the Bessel function.]",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ahrendt:1996:FHC
author: Timm Ahrendt
title: Fast High-Precision Computations of Complex Square Roots
crossref: LakshmanYN:1996:IPI
pages: 142--149
year: 1996
bibdate: Thu Mar 12 08:43:16 MST 1998
bibtimestamp: 1998.03.12 08:43:16 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/
keywords: algebraic computation; algorithms; ISSAC; measurement; SIGNUM; SIGSAM; symbolic computation
acknowledgement: ack-nhfb
rawauthor: Timm Ahrendt
rawtitle: Fast High-Precision Computations of Complex Square Roots
bibsource:
http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

subject:
bf I.1.2 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf F.1.1 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Models of Computation, Bounded-action devices. bf G.1.5 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. bf G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.

entry:
@InProceedings{Ahrendt:1996:FHC,
  author =       "Timm Ahrendt",
  title =        "Fast High-Precision Computations of Complex Square
                 Roots",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "142--149",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; measurement;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Bounded-action devices.
                 {\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
  xxtitle =      "Fast high-precision computation of complex square
                 roots",
}


bibtype: book
filename: elefunt.bib
label: Baker:1996:PA
author: George A. (George Allen) Baker, Jr. and P. R. Graves-Morris
title: Pade approximants
volume: 59
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
edition: Second
pages: xiv + 746
year: 1996
DOI: https://doi.org/10.1017/CBO9780511530074
LCCN: QA221 .B35 1996
bibdate: Sat May 3 06:18:56 MDT 2025
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.05.03 06:18:56 MDT
series: Encyclopedia of mathematics and its applications
acknowledgement: ack-nhfb
authordates: 1932--
rawauthor: George A. (George Allen) {Baker, Jr.} and P. R. Graves-Morris
rawtitle: {Pad{\'e}} approximants
ISBN:
1-107-08857-7 (e-book), 0-511-53007-2 (e-book), 0-511-95902-8 (e-book), 0-521-13509-5 (paperback), 0-521-45007-1 (hardcover) OR 1107088577 (ebook), 0511530072 (ebook), 0511959028 (ebook), 0521135095 (paperback), 0521450071 (hardcover)

ISBN13:
978-1-107-08857-3 (e-book), 978-0-511-53007-4 (e-book), 978-0-511-95902-8 (e-book), 978-0-521-13509-2 (paperback), 978-0-521-45007-2 (hardcover) OR 9781107088573 (ebook), 9780511530074 (ebook), 9780511959028 (ebook), 9780521135092 (paperback), 9780521450072 (hardcover)

abstract:
The Pade approximant of a given power series is a rational function of numerator degree $L$ and denominator degree $M$ whose power series agrees with the given one up to degree $ L + M$ inclusively. A collection of Pade approximants formed by using a suitable set of values of $L$ and $M$ often provides a means of obtaining information about the function outside its circle of convergence, and of more rapidly evaluating the function within its circle of convergence. Applications of these ideas in physics, chemistry, electrical engineering, and other areas have led to a large number of generalizations of Pade approximants that are tailor-made for specific applications. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pade approximation, computational methods, and integral and algebraic approximants. The book is written with a smooth progression from elementary ideas to some of the frontiers of research in approximation theory. Its main purpose is to make the various techniques described accessible to scientists, engineers, and other researchers who may wish to use them, while also presenting the rigorous mathematical theory.

remark:
The first edition of this book was reviewed in 1982 as 'the most extensive treatment of Pade approximants actually available'. This second edition has been thoroughly updated, with a substantial chapter on multiseries approximants. Applications to statistical mechanics and critical phenomena are extensively covered, and there are extended sections devoted to circuit design, matrix Pade approximation, and computational methods. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.

subject:
Pade approximant; Approximation theory; Functions; Approximants de Pade; Theorie de l'approximation; Fonctions (Mathematiques); functions (mathematics); Approximation theory; Functions; Pade approximant

TOC:
1. Introduction and definitions 2. Elementary developments 3. Pade approximants and numerical methods 4. Connection with continued fractions 5. Stieltjes series and Polya series 6. Convergence theory 7. Extensions of Pade approximations 8. Multiseries approximants 9. Connection with integral equations and quantum mechanics 10. Connection with numerical analysis 11. Connection with quantum field theory Appendix: A FORTRAN function

rawabstract:
The Pad{\'e} approximant of a given power series is a rational function of numerator degree $L$ and denominator degree $M$ whose power series agrees with the given one up to degree $ L + M$ inclusively. A collection of Pad{\'e} approximants formed by using a suitable set of values of $L$ and $M$ often provides a means of obtaining information about the function outside its circle of convergence, and of more rapidly evaluating the function within its circle of convergence. Applications of these ideas in physics, chemistry, electrical engineering, and other areas have led to a large number of generalizations of Pad{\'e} approximants that are tailor-made for specific applications. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pad{\'e} approximation, computational methods, and integral and algebraic approximants. The book is written with a smooth progression from elementary ideas to some of the frontiers of research in approximation theory. Its main purpose is to make the various techniques described accessible to scientists, engineers, and other researchers who may wish to use them, while also presenting the rigorous mathematical theory.

rawTOC:
1. Introduction and definitions \\ 2. Elementary developments \\ 3. Pad{\`e} approximants and numerical methods \\ 4. Connection with continued fractions \\ 5. Stieltjes series and Polya series \\ 6. Convergence theory \\ 7. Extensions of Pad{\`e} approximations \\ 8. Multiseries approximants \\ 9. Connection with integral equations and quantum mechanics \\ 10. Connection with numerical analysis \\ 11. Connection with quantum field theory \\ Appendix: A FORTRAN function

entry:
@Book{Baker:1996:PA,
  author =       "George A. (George Allen) {Baker, Jr.} and P. R.
                 Graves-Morris",
  title =        "{Pad{\'e}} approximants",
  volume =       "59",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "xiv + 746",
  year =         "1996",
  DOI =          "https://doi.org/10.1017/CBO9780511530074",
  ISBN =         "1-107-08857-7 (e-book), 0-511-53007-2 (e-book),
                 0-511-95902-8 (e-book), 0-521-13509-5 (paperback),
                 0-521-45007-1 (hardcover)",
  ISBN-13 =      "978-1-107-08857-3 (e-book), 978-0-511-53007-4
                 (e-book), 978-0-511-95902-8 (e-book), 978-0-521-13509-2
                 (paperback), 978-0-521-45007-2 (hardcover)",
  LCCN =         "QA221 .B35 1996",
  bibdate =      "Sat May 3 06:18:56 MDT 2025",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Encyclopedia of mathematics and its applications",
  abstract =     "The Pad{\'e} approximant of a given power series is a
                 rational function of numerator degree $L$ and
                 denominator degree $M$ whose power series agrees with
                 the given one up to degree $ L + M$ inclusively. A
                 collection of Pad{\'e} approximants formed by using a
                 suitable set of values of $L$ and $M$ often provides a
                 means of obtaining information about the function
                 outside its circle of convergence, and of more rapidly
                 evaluating the function within its circle of
                 convergence. Applications of these ideas in physics,
                 chemistry, electrical engineering, and other areas have
                 led to a large number of generalizations of Pad{\'e}
                 approximants that are tailor-made for specific
                 applications. Applications to statistical mechanics and
                 critical phenomena are extensively covered, and there
                 are newly extended sections devoted to circuit design,
                 matrix Pad{\'e} approximation, computational methods,
                 and integral and algebraic approximants. The book is
                 written with a smooth progression from elementary ideas
                 to some of the frontiers of research in approximation
                 theory. Its main purpose is to make the various
                 techniques described accessible to scientists,
                 engineers, and other researchers who may wish to use
                 them, while also presenting the rigorous mathematical
                 theory.",
  acknowledgement = ack-nhfb,
  author-dates = "1932--",
  remark =       "The first edition of this book was reviewed in 1982 as
                 'the most extensive treatment of Pad{\'e} approximants
                 actually available'. This second edition has been
                 thoroughly updated, with a substantial chapter on
                 multiseries approximants. Applications to statistical
                 mechanics and critical phenomena are extensively
                 covered, and there are extended sections devoted to
                 circuit design, matrix Pad{\`e} approximation, and
                 computational methods. This succinct and
                 straightforward treatment will appeal to scientists,
                 engineers, and mathematicians alike.",
  subject =      "Pad{\'e} approximant; Approximation theory; Functions;
                 Approximants de Pad{\'e}; Th{\'e}orie de
                 l'approximation; Fonctions (Math{\'e}matiques);
                 functions (mathematics); Approximation theory;
                 Functions; Pad{\'e} approximant",
  tableofcontents = "1. Introduction and definitions \\
                 2. Elementary developments \\
                 3. Pad{\`e} approximants and numerical methods \\
                 4. Connection with continued fractions \\
                 5. Stieltjes series and Polya series \\
                 6. Convergence theory \\
                 7. Extensions of Pad{\`e} approximations \\
                 8. Multiseries approximants \\
                 9. Connection with integral equations and quantum
                 mechanics \\
                 10. Connection with numerical analysis \\
                 11. Connection with quantum field theory \\
                 Appendix: A FORTRAN function",
}


bibtype: article
filename: elefunt.bib
label: Balla:1996:SCB
author: K. Balla and V. H. Linh
title: The simultaneous computation of Bessel functions of first and second kind
journal: j-COMPUT-MATH-APPL
volume: 31
number: 4--5
pages: 87--97
month: feb
monthnumber: 2
year: 1996
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:26 MST 2017
bibtimestamp: 2017.03.01 21:48:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122195002200
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: K. Balla and V. H. Linh
rawtitle: The simultaneous computation of {Bessel} functions of first and second kind
entry:
@Article{Balla:1996:SCB,
  author =       "K. Balla and V. H. Linh",
  title =        "The simultaneous computation of {Bessel} functions of
                 first and second kind",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "31",
  number =       "4--5",
  pages =        "87--97",
  month =        feb # "\slash " # mar,
  year =         "1996",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:26 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122195002200",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: incollection
filename: elefunt.bib
label: Barnett:1996:CSB
author: A. R. Barnett
title: The Calculation of Spherical Bessel and Coulomb Functions
crossref: Bartschat:1996:CAP
chapter: 9
pages: 181--202
year: 1996
DOI: https://doi.org/10.1007/978-3-642-61010-3_9
bibdate: Fri Apr 25 14:36:10 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.04.25 14:36:10 ???
keywords: COUL90; Lentz continued fraction algorithm; RICBES; SPBESJY; Steen continued fraction algorithm
acknowledgement: ack-nhfb
rawauthor: A. R. Barnett
rawtitle: The Calculation of Spherical {Bessel} and {Coulomb} Functions
entry:
@InCollection{Barnett:1996:CSB,
  author =       "A. R. Barnett",
  title =        "The Calculation of Spherical {Bessel} and {Coulomb}
                 Functions",
  crossref =     "Bartschat:1996:CAP",
  chapter =      "9",
  pages =        "181--202",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-3-642-61010-3_9",
  bibdate =      "Fri Apr 25 14:36:10 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "COUL90; Lentz continued fraction algorithm; RICBES;
                 SPBESJY; Steen continued fraction algorithm",
}


bibtype: article
filename: elefunt.bib
label: Cappuccino:1996:DDH
author: G. Cappuccino and P. Corsonello and G. Cocorullo
title: Design and demonstration of high throughput square rooting circuit
journal: j-ELECT-LETTERS
volume: 32
number: 5
pages: 434--436
month: feb
monthnumber: 2
year: 1996
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19960316
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
rawauthor: G. Cappuccino and P. Corsonello and G. Cocorullo
rawtitle: Design and demonstration of high throughput square rooting circuit
entry:
@Article{Cappuccino:1996:DDH,
  author =       "G. Cappuccino and P. Corsonello and G. Cocorullo",
  title =        "Design and demonstration of high throughput square
                 rooting circuit",
  journal =      j-ELECT-LETTERS,
  volume =       "32",
  number =       "5",
  pages =        "434--436",
  month =        feb,
  year =         "1996",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19960316",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220;
                 https://digital-library.theiet.org/journal/el",
}


bibtype: article
filename: elefunt.bib
label: Chaudhry:1996:ACF
author: M. A. Chaudhry and N. M. Temme and E. J. M. Veling
title: Asymptotics and closed form of a generalized incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 67
number: 2
pages: 371--379
day: 29
month: mar
monthnumber: 3
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:48 MST 2017
bibtimestamp: 2017.02.25 12:27:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795000186
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. A. Chaudhry and N. M. Temme and E. J. M. Veling
rawtitle: Asymptotics and closed form of a generalized incomplete gamma function
entry:
@Article{Chaudhry:1996:ACF,
  author =       "M. A. Chaudhry and N. M. Temme and E. J. M. Veling",
  title =        "Asymptotics and closed form of a generalized
                 incomplete gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "67",
  number =       "2",
  pages =        "371--379",
  day =          "29",
  month =        mar,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795000186",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Dawid:1996:DCA
author: Herbert Dawid and Heinrich Meyr
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 307--318
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.485569
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:09 MDT 2011
bibtimestamp: 2011.07.06 19:47:09 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485569
fjournal: IEEE Transactions on Computers
ZMnumber: 1057.68740
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Herbert Dawid and Heinrich Meyr
title:
The Differential CORDIC Algorithm: Constant Scale Factor Redundant Implementation Without Correcting Iterations

bibsource:
https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

keywords:
68W05,68W35,68M07; Computational complexity; Computer architecture; Delay; Digital arithmetic; Iterative algorithms; Iterative methods; Logic; Parallel architectures; Signal processing algorithms; Student members

rawtitle:
The Differential {CORDIC} Algorithm: Constant Scale Factor Redundant Implementation Without Correcting Iterations

entry:
@Article{Dawid:1996:DCA,
  author =       "Herbert Dawid and Heinrich Meyr",
  title =        "The Differential {CORDIC} Algorithm: Constant Scale
                 Factor Redundant Implementation Without Correcting
                 Iterations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "307--318",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485569",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485569",
  ZMnumber =     "1057.68740",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "68W05,68W35,68M07; Computational complexity; Computer
                 architecture; Delay; Digital arithmetic; Iterative
                 algorithms; Iterative methods; Logic; Parallel
                 architectures; Signal processing algorithms; Student
                 members",
  ZBmath =       "1966848",
}


bibtype: inproceedings
filename: elefunt.bib
label: Guyot:1996:STD
author: A. Guyot and M. Renaudin and B. El Hassan and V. Levering
booktitle: Proceedings of the Ninth International Conference on VLSI Design, 1996
title: Self timed division and square-root extraction
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 376--381
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: A. Guyot and M. Renaudin and B. {El Hassan} and V. Levering
rawbooktitle: Proceedings of the Ninth International Conference on {VLSI} Design, 1996
rawtitle: Self timed division and square-root extraction
entry:
@InProceedings{Guyot:1996:STD,
  author =       "A. Guyot and M. Renaudin and B. {El Hassan} and V.
                 Levering",
  booktitle =    "Proceedings of the Ninth International Conference on
                 {VLSI} Design, 1996",
  title =        "Self timed division and square-root extraction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "376--381",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper describes a self-timed integrated circuit
                 for division and square-root extraction. First it
                 concentrates on the development and the proof of a new
                 mathematical algorithm. Then the design methodology and
                 the architecture of a self-timed \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Heinrich:1996:AAF
author: Peter Heinrich
title: Algorithm Alley: a Fast Integer Square Root
journal: j-DDJ
volume: 21
number: 4
pages: 113--114, 130
month: apr
monthnumber: 4
year: 1996
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Peter Heinrich
rawtitle: Algorithm Alley: a Fast Integer Square Root
bibsource:
http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Heinrich:1996:AAF,
  author =       "Peter Heinrich",
  title =        "Algorithm Alley: a Fast Integer Square Root",
  journal =      j-DDJ,
  volume =       "21",
  number =       "4",
  pages =        "113--114, 130",
  month =        apr,
  year =         "1996",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: techreport
filename: elefunt.bib
label: Hickey:1996:FSP
author: Timothy J. Hickey and Qun Ju
title: Fast, Sound, and Precise Narrowing of the Exponential Function
type: Technical report
institution: Computer Science Department, Brandeis University
address: Waltham, MA, USA 02254
pages: 113--114, 130
month: mar
monthnumber: 3
year: 1996
bibdate: Sat Nov 05 15:42:23 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.11.05 15:42:23 ???
URL: http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz
acknowledgement: ack-nhfb
rawauthor: Timothy J. Hickey and Qun Ju
rawtitle: Fast, Sound, and Precise Narrowing of the Exponential Function
entry:
@TechReport{Hickey:1996:FSP,
  author =       "Timothy J. Hickey and Qun Ju",
  title =        "Fast, Sound, and Precise Narrowing of the Exponential
                 Function",
  type =         "Technical report",
  institution =  "Computer Science Department, Brandeis University",
  address =      "Waltham, MA, USA 02254",
  month =        mar,
  year =         "1996",
  bibdate =      "Sat Nov 05 15:42:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Homeier:1996:CAI
author: H. H. H. Homeier
title: On Convergence Acceleration for the Iterative Solution of the Inverse Dyson Equation
journal: j-J-MOL-STRUCT-THEOCHEM
volume: 368
pages: 81--91
year: 1996
CODEN: THEODJ
ISSN: 0166-1280 (print), 1872-7999 (electronic) OR 01661280 (print), 18727999 (electronic)
ISSNL: 0166-1280 OR 01661280
note: Proceedings of the 2nd Electronic Computational Chemistry Conference.
URL: http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954
fjournal: Journal of molecular structure. Theochem
keywords: convergence acceleration
journalURL: http://www.sciencedirect.com/science/journal/01661280
rawauthor: H. H. H. Homeier
rawnote: Proceedings of the 2nd {Electronic Computational Chemistry Conference}.
rawtitle: On Convergence Acceleration for the Iterative Solution of the Inverse {Dyson} Equation
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Homeier:1996:CAI,
  author =       "H. H. H. Homeier",
  title =        "On Convergence Acceleration for the Iterative Solution
                 of the Inverse {Dyson} Equation",
  journal =      j-J-MOL-STRUCT-THEOCHEM,
  volume =       "368",
  pages =        "81--91",
  year =         "1996",
  CODEN =        "THEODJ",
  ISSN =         "0166-1280 (print), 1872-7999 (electronic)",
  ISSN-L =       "0166-1280",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 2nd {Electronic Computational
                 Chemistry Conference}.",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954",
  fjournal =     "Journal of molecular structure. Theochem",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01661280",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-QM-95-4, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1995",
}


bibtype: techreport
filename: elefunt.bib
label: Homeier:1996:KMP
author: H. H. H. Homeier
number: Homeier:1996:KMP
institution: inst-IPTC
address: inst-IPTC:adr
pages: 81--91
year: 1996
URL: http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962
keywords: convergence acceleration
rawauthor: H. H. H. Homeier
title:
Zur Konvergenzverbesserung der Moller--Plesset Storungsreihe (English: On Convergence Acceleration of the Moller--Plesset Perturbation Series)

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

note:
Poster CP 14.77, Fruhjahrstagung des Arbeitskreises Festkorperphysik bei der DPG, Regensburg 1996. Abstract: Verhandl. DPG (VI) 31, 2165-2166 (1996).

rawnote:
Poster CP 14.77, {Fr{\"u}hjahrstagung des Arbeitskreises Festk{\"o}rperphysik bei der DPG, Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31, 2165-2166 (1996).

rawtitle:
{Zur Konvergenzverbesserung der M{\o}ller--Plesset St{\"o}rungsreihe} ({English}: {On} Convergence Acceleration of the {M{\o}ller--Plesset} Perturbation Series)

entry:
@TechReport{Homeier:1996:KMP,
  author =       "H. H. H. Homeier",
  title =        "{Zur Konvergenzverbesserung der M{\o}ller--Plesset
                 St{\"o}rungsreihe} ({English}: {On} Convergence
                 Acceleration of the {M{\o}ller--Plesset} Perturbation
                 Series)",
  number =       "Homeier:1996:KMP",
  institution =  inst-IPTC,
  address =      inst-IPTC:adr,
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Poster CP 14.77, {Fr{\"u}hjahrstagung des
                 Arbeitskreises Festk{\"o}rperphysik bei der DPG,
                 Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31,
                 2165-2166 (1996).",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Ito:1996:SRI
author: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
title: Square rooting by iterative multiply-additions
journal: j-INFO-PROC-LETT
volume: 60
number: 5
pages: 267--269
day: 8
month: dec
monthnumber: 12
year: 1996
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68M07
MRnumber: 97i:68014
bibdate: Wed Nov 11 12:16:26 MST 1998
bibtimestamp: 1998.11.11 12:16:26 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
corpsource: Dept. of Inf. Sci., Kyoto Univ., Japan
journalURL: http://www.sciencedirect.com/science/journal/00200190
treatment: T Theoretical or Mathematical
rawauthor: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
rawtitle: Square rooting by iterative multiply-additions
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
computer arithmetic; convergence of numerical methods; digital arithmetic; iterative methods; iterative multiply-additions; linear converging ratio; multiplicative methods; Newton--Raphson method; read-only storage; ROM sizes; square root algorithm

entry:
@Article{Ito:1996:SRI,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Square rooting by iterative multiply-additions",
  journal =      j-INFO-PROC-LETT,
  volume =       "60",
  number =       "5",
  pages =        "267--269",
  day =          "8",
  month =        dec,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07",
  MRnumber =     "97i:68014",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Dept. of Inf. Sci., Kyoto Univ., Japan",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "computer arithmetic; convergence of numerical methods;
                 digital arithmetic; iterative methods; iterative
                 multiply-additions; linear converging ratio;
                 multiplicative methods; Newton--Raphson method;
                 read-only storage; ROM sizes; square root algorithm",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Jeffrey:1996:UBL
author: D. J. Jeffrey and D. E. G. Hare and Robert M. Corless
title: Unwinding the branches of the Lambert $W$ function
journal: j-MATH-SCI
volume: 21
number: 1
pages: 1--7
month: jun
monthnumber: 6
year: 1996
ISSN: 0312-3685 (print), 1475-6080 (electronic) OR 03123685 (print), 14756080 (electronic)
ISSNL: 0312-3685 OR 03123685
bibdate: Sat Oct 06 09:02:19 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.10.06 09:02:19 ???
URL: http://www.appliedprobability.org/data/files/TMS%20articles/21_1_1.pdf
fjournal: The Mathematical Scientist
acknowledgement: ack-nhfb
journalURL: http://www.appliedprobability.org/content.aspx?Group=tms&Page=allissues
rawauthor: D. J. Jeffrey and D. E. G. Hare and Robert M. Corless
rawtitle: Unwinding the branches of the {Lambert $W$} function
entry:
@Article{Jeffrey:1996:UBL,
  author =       "D. J. Jeffrey and D. E. G. Hare and Robert M.
                 Corless",
  title =        "Unwinding the branches of the {Lambert $W$} function",
  journal =      j-MATH-SCI,
  volume =       "21",
  number =       "1",
  pages =        "1--7",
  month =        jun,
  year =         "1996",
  ISSN =         "0312-3685 (print), 1475-6080 (electronic)",
  ISSN-L =       "0312-3685",
  bibdate =      "Sat Oct 06 09:02:19 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.appliedprobability.org/data/files/TMS%20articles/21_1_1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Scientist",
  journal-URL =  "http://www.appliedprobability.org/content.aspx?Group=tms&Page=allissues",
}


bibtype: unpublished
filename: elefunt.bib
label: Kahan:1996:TCR
author: W. Kahan
title: A Test for Correctly Rounded SQRT
pages: 4
year: 1996
bibdate: Mon Apr 25 05:47:38 2005
bibtimestamp: 2005.04.25 05:47:38 ???
note: Lecture notes.
URL: http://www.cs.berkeley.edu/~wkahan/SQRTest.ps
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Lecture notes.
rawtitle: A Test for Correctly Rounded {SQRT}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Unpublished{Kahan:1996:TCR,
  author =       "W. Kahan",
  title =        "A Test for Correctly Rounded {SQRT}",
  pages =        "4",
  year =         "1996",
  bibdate =      "Mon Apr 25 05:47:38 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Lecture notes.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SQRTest.ps",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: elefunt.bib
label: Kalantari:1996:HOI
author: B. Kalantari and I. Kalantari
title: High order iterative methods for approximating square roots
journal: j-BIT-NUM-MATH
volume: 36
number: 2
pages: 395--399
month: jun
monthnumber: 6
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01731991
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D15 (65H99)
MRnumber: 97k:65039
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: B. Kalantari and I. Kalantari
rawtitle: High order iterative methods for approximating square roots
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395

entry:
@Article{Kalantari:1996:HOI,
  author =       "B. Kalantari and I. Kalantari",
  title =        "High order iterative methods for approximating square
                 roots",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "395--399",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731991",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D15 (65H99)",
  MRnumber =     "97k:65039",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Kantabutra:1996:HCE
author: Vitit Kantabutra
title: On hardware for computing exponential and trigonometric functions
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 328--339
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.485571
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:09 MDT 2011
bibtimestamp: 2011.07.06 19:47:09 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Vitit Kantabutra
rawtitle: On hardware for computing exponential and trigonometric functions
abstract:
This paper presents new, fast hardware for computing the exponential function, sine, and cosine. The main new idea is to use low-precision arithmetic components to approximate high precision computations, and then to correct very quickly the approximation error periodically so that the effect is to get high precision computation at near low-precision speed. The algorithm used in the paper is a nontrivial modification of the well-known CORDIC algorithm, and might be applicable to the computation of other functions than the ones presented.

rawabstract:
This paper presents new, fast hardware for computing the exponential function, sine, and cosine. The main new idea is to use low-precision arithmetic components to approximate high precision computations, and then to correct very quickly the approximation error periodically so that the effect is to get high precision computation at near low-precision speed. The algorithm used in the paper is a nontrivial modification of the well-known CORDIC algorithm, and might be applicable to the computation of other functions than the ones presented.

entry:
@Article{Kantabutra:1996:HCE,
  author =       "Vitit Kantabutra",
  title =        "On hardware for computing exponential and
                 trigonometric functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "328--339",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485571",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571",
  abstract =     "This paper presents new, fast hardware for computing
                 the exponential function, sine, and cosine. The main
                 new idea is to use low-precision arithmetic components
                 to approximate high precision computations, and then to
                 correct very quickly the approximation error
                 periodically so that the effect is to get high
                 precision computation at near low-precision speed. The
                 algorithm used in the paper is a nontrivial
                 modification of the well-known CORDIC algorithm, and
                 might be applicable to the computation of other
                 functions than the ones presented.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1996:PF
author: K. S. Kolbig
title: The polygamma function $ psi ^(k)(x) $ for $ x = 1 / 4 $ and $ x = 3 / 4 $
journal: j-J-COMPUT-APPL-MATH
volume: 75
number: 1
pages: 43--46
day: 12
month: nov
monthnumber: 11
year: 1996
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(96)00055-6
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796000556
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: K. S. K{\"o}lbig
rawtitle: The polygamma function $ \psi^{(k)}(x) $ for $ x = 1 / 4 $ and $ x = 3 / 4 $
entry:
@Article{Kolbig:1996:PF,
  author =       "K. S. K{\"o}lbig",
  title =        "The polygamma function $ \psi^{(k)}(x) $ for $ x = 1 /
                 4 $ and $ x = 3 / 4 $",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "1",
  pages =        "43--46",
  day =          "12",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(96)00055-6",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000556",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lang:1996:BPU
author: T. Lang and R. Wong
journal: j-J-COMPUT-APPL-MATH
volume: 71
number: 2
pages: 311--329
day: 27
month: jul
monthnumber: 7
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:56 MST 2017
bibtimestamp: 2017.02.25 12:35:56 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795002200
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: T. Lang and R. Wong
title:
``Best possible'' upper bounds for the first two positive zeros of the Bessel function $ J_v(x) $: the infinite case

rawtitle:
``{Best} possible'' upper bounds for the first two positive zeros of the {Bessel} function {$ J_v(x) $}: the infinite case

entry:
@Article{Lang:1996:BPU,
  author =       "T. Lang and R. Wong",
  title =        "``{Best} possible'' upper bounds for the first two
                 positive zeros of the {Bessel} function {$ J_v(x) $}:
                 the infinite case",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "71",
  number =       "2",
  pages =        "311--329",
  day =          "27",
  month =        jul,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795002200",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lehoucq:1996:CEU
author: R. B. Lehoucq
title: The Computation of Elementary Unitary Matrices
journal: j-TOMS
volume: 22
number: 4
pages: 393--400
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Oct 24 11:37:20 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: R. B. Lehoucq
rawtitle: The Computation of Elementary Unitary Matrices
abstract:
The construction of elementary unitary matrices that transform a complex vector to a multiple of $ e_1 $, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the LAPACK subroutine CLARFG. Comparisons are also given.

subject:
bf F.2: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. bf G.1.3: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
The construction of elementary unitary matrices that transform a complex vector to a multiple of $ e_1 $, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the {LAPACK} subroutine {CLARFG}. Comparisons are also given.

entry:
@Article{Lehoucq:1996:CEU,
  author =       "R. B. Lehoucq",
  title =        "The Computation of Elementary Unitary Matrices",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "393--400",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The construction of elementary unitary matrices that
                 transform a complex vector to a multiple of $ e_1 $,
                 the first column of the identity matrix, is studied. We
                 present four variants and their software
                 implementation, including a discussion on the {LAPACK}
                 subroutine {CLARFG}. Comparisons are also given.",
  accepted =     "June 1996",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}


bibtype: article
filename: elefunt.bib
label: Lether:1996:RAF
author: Frank G. Lether
title: Rational approximation formulas for computing the positive zeros of $ J_0 (x) $
journal: j-J-COMPUT-APPL-MATH
volume: 67
number: 1
pages: 167--172
day: 20
month: feb
monthnumber: 2
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:48 MST 2017
bibtimestamp: 2017.02.25 12:27:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795002197
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Frank G. Lether
rawtitle: Rational approximation formulas for computing the positive zeros of {$ J_0 (x) $}
entry:
@Article{Lether:1996:RAF,
  author =       "Frank G. Lether",
  title =        "Rational approximation formulas for computing the
                 positive zeros of {$ J_0 (x) $}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "67",
  number =       "1",
  pages =        "167--172",
  day =          "20",
  month =        feb,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795002197",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Li:1996:NNR
author: Yamin Li and Wanming Chu
title: A new non-restoring square root algorithm and its VLSI implementations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 538--544
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Yamin Li and Wanming Chu
rawtitle: A new non-restoring square root algorithm and its {VLSI} implementations
booktitle:
Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '96

rawbooktitle:
Proceedings of the {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors: {ICCD '96}

entry:
@InProceedings{Li:1996:NNR,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD '96}",
  title =        "A new non-restoring square root algorithm and its
                 {VLSI} implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "538--544",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a new non-restoring square root algorithm
                 that is very efficient to implement. The new algorithm
                 presented here has the following features unlike other
                 square root algorithms. First, the focus of the
                 ``non-restoring'' is on the {\&} \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lorch:1996:BPU
author: Lee Lorch and Riccardo Uberti
title: ``Best possible'' upper bounds for the first positive zeros of Bessel functions --- the finite part
journal: j-J-COMPUT-APPL-MATH
volume: 75
number: 2
pages: 249--258
day: 28
month: nov
monthnumber: 11
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796000659
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Lee Lorch and Riccardo Uberti
rawtitle:
``{Best} possible'' upper bounds for the first positive zeros of {Bessel} functions --- the finite part

entry:
@Article{Lorch:1996:BPU,
  author =       "Lee Lorch and Riccardo Uberti",
  title =        "``{Best} possible'' upper bounds for the first
                 positive zeros of {Bessel} functions --- the finite
                 part",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "2",
  pages =        "249--258",
  day =          "28",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000659",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: techreport
filename: elefunt.bib
label: Lozier:1996:PST
author: Daniel W. Lozier
title: A Proposed Software Test Service for Special Functions
type: Technical Report
number: NISTIR 5916
institution: pub-NIST
address: pub-NIST:adr
pages: 11
month: oct
monthnumber: 10
year: 1996
bibdate: Fri Jul 09 06:02:16 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:02:16 ???
note: Published in cite Lozier:1997:PST.
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawnote: Published in \cite{Lozier:1997:PST}.
rawtitle: A Proposed Software Test Service for Special Functions
entry:
@TechReport{Lozier:1996:PST,
  author =       "Daniel W. Lozier",
  title =        "A Proposed Software Test Service for Special
                 Functions",
  type =         "Technical Report",
  number =       "NISTIR 5916",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "11",
  month =        oct,
  year =         "1996",
  bibdate =      "Fri Jul 09 06:02:16 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Lozier:1997:PST}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Lozier:1996:SNS
author: Daniel W. Lozier
title: Software Needs in Special Functions
journal: j-J-COMPUT-APPL-MATH
volume: 66
pages: 345--358
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Fri Jul 09 05:51:55 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 05:51:55 ???
fjournal: Journal of Computational and Applied Mathematics
remark: See preprint cite Lozier:1994:SNS.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Daniel W. Lozier
rawtitle: Software Needs in Special Functions
entry:
@Article{Lozier:1996:SNS,
  author =       "Daniel W. Lozier",
  title =        "Software Needs in Special Functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "66",
  number =       "??",
  pages =        "345--358",
  month =        "????",
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Jul 09 05:51:55 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  remark =       "See preprint \cite{Lozier:1994:SNS}.",
}


bibtype: article
filename: elefunt.bib
label: Macleod:1996:AMS
author: Allan J. Macleod
title: Algorithm 757: MISCFUN, a software package to compute uncommon special functions
journal: j-TOMS
volume: 22
number: 3
pages: 288--301
month: sep
monthnumber: 9
year: 1996
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 31 16:07:02 MDT 1996
bibtimestamp: 1996.08.31 16:07:02 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Allan J. Macleod
rawtitle: {Algorithm 757}: {MISCFUN}, a software package to compute uncommon special functions
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

URL:
http://doi.acm.org/10.1145/232826.232846; http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/

abstract:
MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.

subject:
bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.

rawabstract:
MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.

entry:
@Article{Macleod:1996:AMS,
  author =       "Allan J. Macleod",
  title =        "{Algorithm 757}: {MISCFUN}, a software package to
                 compute uncommon special functions",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "288--301",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/232826.232846;
                 http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/",
  abstract =     "MISCFUN (MISCellaneous FUNctions) is a Fortran package
                 for the evaluation of several special functions, which
                 are not used often enough to have been included in the
                 standard libraries or packages. The package uses
                 Chebyshev expansions as the underlying method of
                 approximation, with the Chebyshev coefficients given to
                 20D. A wide variety of functions are included, and the
                 package is designed so that other functions can be
                 added in a standard manner.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Certification and
                 testing.",
}


bibtype: article
filename: elefunt.bib
label: Oleksy:1996:CAM
author: Cz. Oleksy
title: A convergence acceleration method of Fourier series
journal: j-COMP-PHYS-COMM
volume: 96
number: 1
pages: 17--26
year: 1996
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(96)00044-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
MRclass: 65B05
MRnumber: 1396682 (97c:65012)
bibdate: Thu Dec 1 17:36:45 2011
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Computer Physics Communications
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Cz. Oleksy
rawtitle: A convergence acceleration method of {Fourier} series
entry:
@Article{Oleksy:1996:CAM,
  author =       "Cz. Oleksy",
  title =        "A convergence acceleration method of {Fourier}
                 series",
  journal =      j-COMP-PHYS-COMM,
  volume =       "96",
  number =       "1",
  pages =        "17--26",
  year =         "1996",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(96)00044-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65B05",
  MRnumber =     "1396682 (97c:65012)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Panteliou:1996:DII
author: S. D. Panteliou and A. D. Dimarogonas and I. N. Katz
journal: j-COMPUT-MATH-APPL
volume: 32
number: 8
pages: 51--57
month: oct
monthnumber: 10
year: 1996
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:33 MST 2017
bibtimestamp: 2017.03.01 21:48:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122196001666
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: S. D. Panteliou and A. D. Dimarogonas and I. N. Katz
title:
Direct and inverse interpolation for Jacobian elliptic functions, zeta function of Jacobi and complete elliptic integrals of the second kind

rawtitle:
Direct and inverse interpolation for {Jacobian} elliptic functions, zeta function of {Jacobi} and complete elliptic integrals of the second kind

entry:
@Article{Panteliou:1996:DII,
  author =       "S. D. Panteliou and A. D. Dimarogonas and I. N. Katz",
  title =        "Direct and inverse interpolation for {Jacobian}
                 elliptic functions, zeta function of {Jacobi} and
                 complete elliptic integrals of the second kind",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "32",
  number =       "8",
  pages =        "51--57",
  month =        oct,
  year =         "1996",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122196001666",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: book
filename: elefunt.bib
label: Patel:1996:HND
author: Jagdish K. Patel and Campbell B. Read
title: Handbook of the Normal Distribution
volume: 150
publisher: pub-DEKKER
address: pub-DEKKER:adr
edition: Second revised and expanded
pages: ix + 431
year: 1996
ISBN: 0-8247-9342-0 (hardcover) OR 0824793420 (hardcover)
ISBN13: 978-0-8247-9342-5 (hardcover) OR 9780824793425 (hardcover)
LCCN: QA273.6 .P373 1996
bibdate: Sat Dec 16 17:22:16 MST 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.12.16 17:22:16 MST
series: Statistics, textbooks and monographs
URL: http://www.loc.gov/catdir/enhancements/fy0647/95049404-d.html
subject: Gaussian distribution
acknowledgement: ack-nhfb
rawauthor: Jagdish K. Patel and Campbell B. Read
rawtitle: Handbook of the Normal Distribution
TOC:
Genesis: an historical background Basic properties Expansions and algorithms Characterizations Sampling distributions Limit theorems and expansions Normal approximations to distributions Order statistics from normal samples The bivariate normal distribution Bivariate normal sampling distributions Point estimation Statistical intervals

rawTOC:
Genesis: an historical background \\ Basic properties \\ Expansions and algorithms \\ Characterizations \\ Sampling distributions \\ Limit theorems and expansions \\ Normal approximations to distributions \\ Order statistics from normal samples \\ The bivariate normal distribution \\ Bivariate normal sampling distributions \\ Point estimation \\ Statistical intervals

entry:
@Book{Patel:1996:HND,
  author =       "Jagdish K. Patel and Campbell B. Read",
  title =        "Handbook of the Normal Distribution",
  volume =       "150",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  edition =      "Second revised and expanded",
  pages =        "ix + 431",
  year =         "1996",
  ISBN =         "0-8247-9342-0 (hardcover)",
  ISBN-13 =      "978-0-8247-9342-5 (hardcover)",
  LCCN =         "QA273.6 .P373 1996",
  bibdate =      "Sat Dec 16 17:22:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Statistics, textbooks and monographs",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0647/95049404-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Gaussian distribution",
  tableofcontents = "Genesis: an historical background \\
                 Basic properties \\
                 Expansions and algorithms \\
                 Characterizations \\
                 Sampling distributions \\
                 Limit theorems and expansions \\
                 Normal approximations to distributions \\
                 Order statistics from normal samples \\
                 The bivariate normal distribution \\
                 Bivariate normal sampling distributions \\
                 Point estimation \\
                 Statistical intervals",
}


bibtype: article
filename: elefunt.bib
label: Plofker:1996:ESM
author: Kim Plofker
title: An Example of the Secant Method of Iterative Approximation in a Fifteenth-Century Sanskrit Text
journal: j-HIST-MATH
volume: 23
number: 3
pages: 246--256
month: aug
monthnumber: 8
year: 1996
CODEN: HIMADS
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:19:07 MDT 2013
bibtimestamp: 2013.06.26 06:19:07 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086096900269
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: Kim Plofker
rawtitle: An Example of the Secant Method of Iterative Approximation in a {Fifteenth-Century Sanskrit} Text
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib

entry:
@Article{Plofker:1996:ESM,
  author =       "Kim Plofker",
  title =        "An Example of the Secant Method of Iterative
                 Approximation in a {Fifteenth-Century Sanskrit} Text",
  journal =      j-HIST-MATH,
  volume =       "23",
  number =       "3",
  pages =        "246--256",
  month =        aug,
  year =         "1996",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:19:07 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086096900269",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}


bibtype: article
filename: elefunt.bib
label: Qiu:1996:SEC
author: S.-L. Qiu and M. K. Vamanamurthy
title: Sharp Estimates for Complete Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 27
number: 3
pages: 823--834
month: may
monthnumber: 5
year: 1996
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33E05
MRnumber: 97f:33033
MRreviewer: G. D. Anderson
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: S.-L. Qiu and M. K. Vamanamurthy
rawtitle: Sharp Estimates for Complete Elliptic Integrals
entry:
@Article{Qiu:1996:SEC,
  author =       "S.-L. Qiu and M. K. Vamanamurthy",
  title =        "Sharp Estimates for Complete Elliptic Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "27",
  number =       "3",
  pages =        "823--834",
  month =        may,
  year =         "1996",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05",
  MRnumber =     "97f:33033",
  MRreviewer =   "G. D. Anderson",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: inproceedings
filename: elefunt.bib
label: Rao:1996:RTS
author: V. M. Rao and B. Nowrouzian
booktitle: Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996
title: Rounding techniques for signed binary arithmetic
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 294--297
year: 1996
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: V. M. Rao and B. Nowrouzian
rawbooktitle: Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996
rawtitle: Rounding techniques for signed binary arithmetic
abstract:
This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.

rawabstract:
This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.

entry:
@InProceedings{Rao:1996:RTS,
  author =       "V. M. Rao and B. Nowrouzian",
  booktitle =    "Canadian Conference on Electrical and Computer
                 Engineering. 26--29 May 1996",
  title =        "Rounding techniques for signed binary arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "294--297",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This paper is concerned with the derivation of the
                 relationship that exists between the number truncation
                 in two's complement (TC) arithmetic and the
                 corresponding truncation in signed-binary (SB)
                 arithmetic. The resulting relationship is subsequently
                 exploited and applied to the development of a pair of
                 novel techniques for SB rounding. These techniques are
                 then translated into algorithm suitable for two-level
                 logic implementation. Finally, the resulting algorithms
                 are applied to the design and implementation of a
                 high-speed SB-kernel based TC multiply-accumulate
                 arithmetic architecture.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Schatzman:1996:ADF
author: James C. Schatzman
title: Accuracy of the discrete Fourier transform and the fast Fourier transform
journal: j-SIAM-J-SCI-COMP
volume: 17
number: 5
pages: 1150--1166
month: sep
monthnumber: 9
year: 1996
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827593247023
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
MRclass: 65T20 (42A65 42C10 68Q25)
MRnumber: 97e:65155
bibdate: Fri Dec 4 14:47:53 MST 1998
bibtimestamp: 1998.12.04 14:47:53 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/24702
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
ajournal: SIAM J. Sci. Comput.
journalURL: http://epubs.siam.org/sisc
rawauthor: James C. Schatzman
rawtitle: Accuracy of the discrete {Fourier} transform and the fast {Fourier} transform
bibsource:
http://epubs.siam.org/toc/sjoce3/17/5; 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/siamjscicomput.bib

remark:
This article analyzes errors in computing one-dimensional Fourier transforms, the fast way (FFT) and the slow way. The author identifies two main causes of accuracy loss in the computed transforms: (1) inaccurate sine and cosine functions, and (2) failure to use accurate summation methods, such as Kahan's compensated summation.

entry:
@Article{Schatzman:1996:ADF,
  author =       "James C. Schatzman",
  title =        "Accuracy of the discrete {Fourier} transform and the
                 fast {Fourier} transform",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "17",
  number =       "5",
  pages =        "1150--1166",
  month =        sep,
  year =         "1996",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827593247023",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65T20 (42A65 42C10 68Q25)",
  MRnumber =     "97e:65155",
  bibdate =      "Fri Dec 4 14:47:53 MST 1998",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/17/5;
                 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/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/24702",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM J. Sci. Comput.",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  remark =       "This article analyzes errors in computing
                 one-dimensional Fourier transforms, the fast way (FFT)
                 and the slow way. The author identifies two main causes
                 of accuracy loss in the computed transforms: (1)
                 inaccurate sine and cosine functions, and (2) failure
                 to use accurate summation methods, such as Kahan's
                 compensated summation.",
}


bibtype: article
filename: elefunt.bib
label: Schwarz:1996:HSA
author: Eric M. Schwarz and Michael J. Flynn
title: Hardware Starting Approximation Method and Its Application to the Square Root Operation
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 12
pages: 1356--1369
month: dec
monthnumber: 12
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.545966
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Eric M. Schwarz and Michael J. Flynn
rawtitle: Hardware Starting Approximation Method and Its Application to the Square Root Operation
entry:
@Article{Schwarz:1996:HSA,
  author =       "Eric M. Schwarz and Michael J. Flynn",
  title =        "Hardware Starting Approximation Method and Its
                 Application to the Square Root Operation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "12",
  pages =        "1356--1369",
  month =        dec,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.545966",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Quadratically converging algorithms for high-order
                 arithmetic operations typically are accelerated by a
                 starting approximation. The higher the precision of the
                 starting approximation, the less number of iterations
                 required for convergence. \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Sinclair:1996:ORS
author: R. Sinclair
title: Optimization of reciprocals and square roots on the i860 microprocessor
journal: j-INT-J-HIGH-SPEED-COMPUTING
volume: 8
number: 1
pages: 57--64
year: 1996
CODEN: IHSCEZ
ISSN: 0129-0533 OR 01290533
bibdate: Mon Feb 25 11:19:22 MST 2002
bibtimestamp: 2002.02.25 11:19:22 MST
fjournal: International Journal of High Speed Computing (IJHSC)
acknowledgement: ack-nhfb
journalURL: http://www.worldscientific.com/worldscinet/ijhsc
rawauthor: R. Sinclair
rawtitle: Optimization of reciprocals and square roots on the {i860} microprocessor
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Article1st database

entry:
@Article{Sinclair:1996:ORS,
  author =       "R. Sinclair",
  title =        "Optimization of reciprocals and square roots on the
                 {i860} microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "8",
  number =       "1",
  pages =        "57--64",
  year =         "1996",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Mon Feb 25 11:19:22 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Article1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing
                 (IJHSC)",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}


bibtype: article
filename: elefunt.bib
label: Snyder:1996:RAF
author: W. Van Snyder
title: Remark on Algorithm 723: Fresnel Integrals
journal: j-TOMS
volume: 22
number: 4
pages: 498--500
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
DOI: https://doi.org/10.1145/235815.235825
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
note: See cite Snyder:1993:AFI.
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms, performance
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. Van Snyder
rawnote: See \cite{Snyder:1993:AFI}.
rawtitle: Remark on {Algorithm 723}: {Fresnel} Integrals
abstract:
it Algorithm 723: Fresnel Integrals has been improved to provide more precise results for $ x gg 0 $.

subject:
bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.

rawabstract:
{\it Algorithm 723: Fresnel Integrals} has been improved to provide more precise results for $ x \gg 0 $.

entry:
@Article{Snyder:1996:RAF,
  author =       "W. Van Snyder",
  title =        "Remark on {Algorithm 723}: {Fresnel} Integrals",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "498--500",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235825",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Snyder:1993:AFI}.",
  abstract =     "{\it Algorithm 723: Fresnel Integrals} has been
                 improved to provide more precise results for $ x \gg 0
                 $.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Rational
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}


bibtype: book
filename: elefunt.bib
label: Temme:1996:SFI
author: N. M. Temme
title: Special Functions: an Introduction to the Classical Functions of Mathematical Physics
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xii + 374
year: 1996
DOI: https://doi.org/10.1002/9781118032572
ISBN: 0-471-11313-1 OR 0471113131
ISBN13: 978-0-471-11313-3 OR 9780471113133
LCCN: QC20.7.F87 T46 1996
bibdate: Mon Nov 24 21:41:54 MST 2008
bibtimestamp: 2008.11.24 21:41:54 MST
subject: functions, special; mathematical physics; boundary value problems
acknowledgement: ack-nhfb
rawauthor: N. M. Temme
rawtitle: Special Functions: an Introduction to the Classical Functions of Mathematical Physics
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.bibsys.no:2100/BIBSYS; z3950.loc.gov:7090/Voyager

TOC:
1 Bernoulli, Euler and Stirling Numbers / 1 1.1. Bernoulli Numbers and Polynomials / 2 1.1.1. Definitions and Properties / 3 1.1.2. A Simple Difference Equation / 6 1.1.3. Euler's Summation Formula / 9 1.2. Euler Numbers and Polynomials / 14 1.2.1. Definitions and Properties / 15 1.2.2. Boole's Summation Formula / 17 1.3. Stirling Numbers / 18 1.4. Remarks and Comments for Further Reading / 21 1.5. Exercises and Further Examples / 22 2 Useful Methods and Techniques / 29 2.1. Some Theorems from Analysis / 29 2.2. Asymptotic Expansions of Integrals / 31 2.2.1. Watson's Lemma / 32 2.2.2. The Saddle Point Method / 34 2.2.3. Other Asymptotic Methods / 38 2.3. Exercises and Further Examples / 39 3 The Gamma Function / 41 3.1. Introduction / 41 3.1.1. The Fundamental Recursion Property / 42 3.1.2. Another Look at the Gamma Function / 42 3.2. Important Properties / 43 3.2.1. Prym's Decomposition / 43 3.2.2. The Cauchy--Saalschutz Representation / 44 3.2.3. The Beta Integral / 45 3.2.4. The Multiplication Formula / 46 3.2.5. The Reflection Formula / 46 3.2.6. The Reciprocal Gamma Function / 48 3.2.7. A Complex Contour for the Beta Integral / 49 3.3. Infinite Products / 50 3.3.1. Gauss' Multiplication Formula / 52 3.4. Logarithmic Derivative of the Gamma Function / 53 3.5. Riemann's Zeta Function / 57 3.6. Asymptotic Expansions / 61 3.6.1. Estimations of the Remainder / 64 3.6.2. Ratio of Two Gamma Functions / 66 3.6.3. Application of the Saddle Point Method / 69 3.7. Remarks and Comments for Further Reading / 71 3.8. Exercises and Further Examples / 72 4 Differential Equations / 79 4.1. Separating the Wave Equation / 79 4.1.1. Separating the Variables / 81 4.2. Differential Equations in the Complex Plane / 83 4.2.1. Singular Points / 83 4.2.2. Transformation of the Point at Infinity / 84 4.2.3. The Solution Near a Regular Point / 85 4.2.4. Power Series Expansions Around a Regular Point / 90 4.2.5. Power Series Expansions Around a Regular Singular Point / 92 4.3. Sturm's Comparison Theorem / 97 4.4. Integrals as Solutions of Differential Equations / 98 4.5. The Liouville Transformation / 103 4.6. Remarks and Comments for Further Reading / 104 4.7. Exercises and Further Examples / 104 5 Hypergeometric Functions / 107 5.1. Definitions and Simple Relations / 107 5.2. Analytic Continuation / 109 5.2.1. Three Functional Relations / 110 5.2.2. A Contour Integral Representation / 111 5.3. The Hypergeometric Differential Equation / 112 5.4. The Singular Points of the Differential Equation / 114 5.5. The Riemann--Papperitz Equation / 116 5.6. Barnes' Contour Integral for $F(a, b; c; z)$ / 119 5.7. Recurrence Relations / 121 5.8. Quadratic Transformations / 122 5.9. Generalized Hypergeometric Functions / 124 5.9.1. A First Introduction to g-functions / 125 5.10. Remarks and Comments for Further Reading / 127 5.11. Exercises and Further Examples / 128 6 Orthogonal Polynomials / 133 6.1. General Orthogonal Polynomials / 133 6.1.1. Zeros of Orthogonal Polynomials / 137 6.1.2. Gauss Quadrature / 138 6.2. Classical Orthogonal Polynomials / 141 6.3. Definitions by the Rodrigues Formula / 142 6.4. Recurrence Relations / 146 6.5. Differential Equations / 149 6.6. Explicit Representations / 151 6.7. Generating Functions / 154 6.8. Legendre Polynomials / 156 6.8.1. The Norm of the Legendre Polynomials / 156 6.8.2. Integral Expressions for the Legendre Polynomials / 156 6.8.3. Some Bounds on Legendre Polynomials / 157 6.8.4. An Asymptotic Expansion as n is Large / 158 6.9. Expansions in Terms of Orthogonal Polynomials / 160 6.9.1. An Optimal Result in Connection with Legendre Polynomials / 160 6.9.2. Numerical Aspects of Chebyshev Polynomials / 162 6.10. Remarks and Comments for Further Reading / 164 6.11. Exercises and Further Examples / 164 7 Confluent Hypergeometric Functions / 171 7.1. The $M$-function / 172 7.2. The $U$-function / 175 7.3. Special Cases and Further Relations / 177 7.3.1. Whittaker Functions / 178 7.3.2. Coulomb Wave Functions / 178 7 3.3. Parabolic Cylinder Functions / 179 7 3.4. Error Functions / 180 7.3.5. Exponential Integrals / 180 7.3.6. Fresnel Integrals / 182 7.3.7. Incomplete Gamma Functions / 185 7.3.8. Bessel Functions / 186 7.3.9. Orthogonal Polynomials / 186 7.4. Remarks and Comments for Further Reading / 186 7.5. Exercises and Further Examples / 187 8 Legendre Functions / 193 8.1. The Legendre Differential Equation / 194 8.2. Ordinary Legendre Functions / 194 8.3. Other Solutions of the Differential Equation / 196 8.4. A Few More Series Expansions / 198 8.5. The function $Q_n(z)$ / 200 8.6. Integral Representations / 202 8.7. Associated Legendre Functions / 209 8.8. Remarks and Comments for Further Reading / 213 8.9. Exercises and Further Examples / 214 9 Bessel Functions / 219 9.1. Introduction / 219 9.2. Integral Representations / 220 9.3. Cylinder Functions / 223 9.4. Further Properties / 227 9.5. Modified Bessel Functions / 232 9.6. Integral Representations for the $I$- and $K$-Functions / 234 9.7. Asymptotic Expansions / 238 9.8. Zeros of Bessel Functions / 241 9.9. Orthogonality Relations, Fourier--Bessel Series / 244 9.10. Remarks and Comments for Further Reading / 247 9.11. Exercises and Further Examples / 247 10 Separating the Wave Equation / 257 10.1. General Transformations / 258 10.2. Special Coordinate Systems / 259 10.2.1. Cylindrical Coordinates / 259 10.2.2. Spherical Coordinates / 261 10.2.3. Elliptic Cylinder Coordinates / 263 10.2.4. Parabolic Cylinder Coordinates / 264 10.2.5. Oblate Spheroidal Coordinates / 266 10.3. Boundary Value Problems / 268 10.3.1. Heat Conduction in a Cylinder / 268 10.3.2. Diffraction of a Plane Wave Due to a Sphere / 270 10.4. Remarks and Comments for Further Reading / 271 10.5. Exercises and Further Examples / 272 11 Special Statistical Distribution Functions / 275 11.1. Error Functions / 275 11.1.1. The Error Function and Asymptotic Expansions / 276 11.2. Incomplete Gamma Functions / 277 11.2.1. Series Expansions / 279 11.2.2. Continued Fraction for $Gamma (a, z)$ / 280 11.2.3. Contour Integral for the Incomplete Gamma Functions / 282 11.2.4. Uniform Asymptotic Expansions / 283 11.2.5. Numerical Aspects / 286 11.3. Incomplete Beta Functions / 288 11.3.1. Recurrence Relations / 289 11.3.2. Contour Integral for the Incomplete Beta Function / 290 11.3.3. Asymptotic Expansions / 291 11.3.4. Numerical Aspects / 297 11.4. Non-Central Chi-Squared Distribution / 298 11.4.1. A Few More Integral Representations / 300 11.4.2. Asymptotic Expansion; $m$ Fixed, $j$ Large / 302 11.4.3. Asymptotic Expansion; $j$ Large, $m$ Arbitrary / 303 11.4.4. Numerical Aspects / 305 11.5. An Incomplete Bessel Function / 308 11.6. Remarks and Comments for Further Reading / 309 11.7. Exercises and Further Examples / 310 12 Elliptic Integrals and Elliptic Functions / 319 12.1. Complete Integrals of the First and Second Kind / 315 12.1.1. The Simple Pendulum / 316 12.1.2. Arithmetic Geometric Mean / 318 12.2. Incomplete Elliptic Integrals / 321 12.3. Elliptic Functions and Theta Functions / 322 12.3.1. Elliptic Functions / 323 12.3.2. Theta Functions / 324 12.4. Numerical Aspects / 328 12.5. Remarks and Comments for Further Reading / 329 12.6. Exercises and Further Examples / 330 13 Numerical Aspects of Special Functions / 333 13.1. A Simple Recurrence Relation / 334 13.2. Introduction to the General Theory / 335 13.3. Examples / 338 13.4. Miller's Algorithm / 343 13.5. How to Compute a Continued Fraction / 347 Bibliography / 349 Notations and Symbols / 361 Index / 365

shortTOC:
Bernoulli, Euler and Stirling numbers Useful methods and techniques The gamma function Differential equations Hypergeometric functions Orthogonal polynomials Confluent hypergeometric functions Legendre functions Bessel functions Separating the wave equation Special statistical distribution functions Elliptic integrals and elliptic functions Numerical aspects of special functions

rawshortTOC:
Bernoulli, Euler and Stirling numbers \\ Useful methods and techniques \\ The gamma function \\ Differential equations \\ Hypergeometric functions \\ Orthogonal polynomials \\ Confluent hypergeometric functions \\ Legendre functions \\ Bessel functions \\ Separating the wave equation \\ Special statistical distribution functions \\ Elliptic integrals and elliptic functions \\ Numerical aspects of special functions

rawTOC:
1 Bernoulli, Euler and Stirling Numbers / 1 \\ 1.1. Bernoulli Numbers and Polynomials / 2 \\ 1.1.1. Definitions and Properties / 3 \\ 1.1.2. A Simple Difference Equation / 6 \\ 1.1.3. Euler's Summation Formula / 9 \\ 1.2. Euler Numbers and Polynomials / 14 \\ 1.2.1. Definitions and Properties / 15 \\ 1.2.2. Boole's Summation Formula / 17 \\ 1.3. Stirling Numbers / 18 \\ 1.4. Remarks and Comments for Further Reading / 21 \\ 1.5. Exercises and Further Examples / 22 \\ 2 Useful Methods and Techniques / 29 \\ 2.1. Some Theorems from Analysis / 29 \\ 2.2. Asymptotic Expansions of Integrals / 31 \\ 2.2.1. Watson's Lemma / 32 \\ 2.2.2. The Saddle Point Method / 34 \\ 2.2.3. Other Asymptotic Methods / 38 \\ 2.3. Exercises and Further Examples / 39 \\ 3 The Gamma Function / 41 \\ 3.1. Introduction / 41 \\ 3.1.1. The Fundamental Recursion Property / 42 \\ 3.1.2. Another Look at the Gamma Function / 42 \\ 3.2. Important Properties / 43 \\ 3.2.1. Prym's Decomposition / 43 \\ 3.2.2. The Cauchy--Saalsch{\"u}tz Representation / 44 \\ 3.2.3. The Beta Integral / 45 \\ 3.2.4. The Multiplication Formula / 46 \\ 3.2.5. The Reflection Formula / 46 \\ 3.2.6. The Reciprocal Gamma Function / 48 \\ 3.2.7. A Complex Contour for the Beta Integral / 49 \\ 3.3. Infinite Products / 50 \\ 3.3.1. Gauss' Multiplication Formula / 52 \\ 3.4. Logarithmic Derivative of the Gamma Function / 53 \\ 3.5. Riemann's Zeta Function / 57 \\ 3.6. Asymptotic Expansions / 61 \\ 3.6.1. Estimations of the Remainder / 64 \\ 3.6.2. Ratio of Two Gamma Functions / 66 \\ 3.6.3. Application of the Saddle Point Method / 69 \\ 3.7. Remarks and Comments for Further Reading / 71 \\ 3.8. Exercises and Further Examples / 72 \\ 4 Differential Equations / 79 \\ 4.1. Separating the Wave Equation / 79 \\ 4.1.1. Separating the Variables / 81 \\ 4.2. Differential Equations in the Complex Plane / 83 \\ 4.2.1. Singular Points / 83 \\ 4.2.2. Transformation of the Point at Infinity / 84 \\ 4.2.3. The Solution Near a Regular Point / 85 \\ 4.2.4. Power Series Expansions Around a Regular Point / 90 \\ 4.2.5. Power Series Expansions Around a Regular Singular Point / 92 \\ 4.3. Sturm's Comparison Theorem / 97 \\ 4.4. Integrals as Solutions of Differential Equations / 98 \\ 4.5. The Liouville Transformation / 103 \\ 4.6. Remarks and Comments for Further Reading / 104 \\ 4.7. Exercises and Further Examples / 104 \\ 5 Hypergeometric Functions / 107 \\ 5.1. Definitions and Simple Relations / 107 \\ 5.2. Analytic Continuation / 109 \\ 5.2.1. Three Functional Relations / 110 \\ 5.2.2. A Contour Integral Representation / 111 \\ 5.3. The Hypergeometric Differential Equation / 112 \\ 5.4. The Singular Points of the Differential Equation / 114 \\ 5.5. The Riemann--Papperitz Equation / 116 \\ 5.6. Barnes' Contour Integral for $F(a, b; c; z)$ / 119 \\ 5.7. Recurrence Relations / 121 \\ 5.8. Quadratic Transformations / 122 \\ 5.9. Generalized Hypergeometric Functions / 124 \\ 5.9.1. A First Introduction to g-functions / 125 \\ 5.10. Remarks and Comments for Further Reading / 127 \\ 5.11. Exercises and Further Examples / 128 \\ 6 Orthogonal Polynomials / 133 \\ 6.1. General Orthogonal Polynomials / 133 \\ 6.1.1. Zeros of Orthogonal Polynomials / 137 \\ 6.1.2. Gauss Quadrature / 138 \\ 6.2. Classical Orthogonal Polynomials / 141 \\ 6.3. Definitions by the Rodrigues Formula / 142 \\ 6.4. Recurrence Relations / 146 \\ 6.5. Differential Equations / 149 \\ 6.6. Explicit Representations / 151 \\ 6.7. Generating Functions / 154 \\ 6.8. Legendre Polynomials / 156 \\ 6.8.1. The Norm of the Legendre Polynomials / 156 \\ 6.8.2. Integral Expressions for the Legendre Polynomials / 156 \\ 6.8.3. Some Bounds on Legendre Polynomials / 157 \\ 6.8.4. An Asymptotic Expansion as n is Large / 158 \\ 6.9. Expansions in Terms of Orthogonal Polynomials / 160 \\ 6.9.1. An Optimal Result in Connection with Legendre Polynomials / 160 \\ 6.9.2. Numerical Aspects of Chebyshev Polynomials / 162 \\ 6.10. Remarks and Comments for Further Reading / 164 \\ 6.11. Exercises and Further Examples / 164 \\ 7 Confluent Hypergeometric Functions / 171 \\ 7.1. The $M$-function / 172 \\ 7.2. The $U$-function / 175 \\ 7.3. Special Cases and Further Relations / 177 \\ 7.3.1. Whittaker Functions / 178 \\ 7.3.2. Coulomb Wave Functions / 178 \\ 7 3.3. Parabolic Cylinder Functions / 179 \\ 7 3.4. Error Functions / 180 \\ 7.3.5. Exponential Integrals / 180 \\ 7.3.6. Fresnel Integrals / 182 \\ 7.3.7. Incomplete Gamma Functions / 185 \\ 7.3.8. Bessel Functions / 186 \\ 7.3.9. Orthogonal Polynomials / 186 \\ 7.4. Remarks and Comments for Further Reading / 186 \\ 7.5. Exercises and Further Examples / 187 \\ 8 Legendre Functions / 193 \\ 8.1. The Legendre Differential Equation / 194 \\ 8.2. Ordinary Legendre Functions / 194 \\ 8.3. Other Solutions of the Differential Equation / 196 \\ 8.4. A Few More Series Expansions / 198 \\ 8.5. The function $Q_n(z)$ / 200 \\ 8.6. Integral Representations / 202 \\ 8.7. Associated Legendre Functions / 209 \\ 8.8. Remarks and Comments for Further Reading / 213 \\ 8.9. Exercises and Further Examples / 214 \\ 9 Bessel Functions / 219 \\ 9.1. Introduction / 219 \\ 9.2. Integral Representations / 220 \\ 9.3. Cylinder Functions / 223 \\ 9.4. Further Properties / 227 \\ 9.5. Modified Bessel Functions / 232 \\ 9.6. Integral Representations for the $I$- and $K$-Functions / 234 \\ 9.7. Asymptotic Expansions / 238 \\ 9.8. Zeros of Bessel Functions / 241 \\ 9.9. Orthogonality Relations, Fourier--Bessel Series / 244 \\ 9.10. Remarks and Comments for Further Reading / 247 \\ 9.11. Exercises and Further Examples / 247 \\ 10 Separating the Wave Equation / 257 \\ 10.1. General Transformations / 258 \\ 10.2. Special Coordinate Systems / 259 \\ 10.2.1. Cylindrical Coordinates / 259 \\ 10.2.2. Spherical Coordinates / 261 \\ 10.2.3. Elliptic Cylinder Coordinates / 263 \\ 10.2.4. Parabolic Cylinder Coordinates / 264 \\ 10.2.5. Oblate Spheroidal Coordinates / 266 \\ 10.3. Boundary Value Problems / 268 \\ 10.3.1. Heat Conduction in a Cylinder / 268 \\ 10.3.2. Diffraction of a Plane Wave Due to a Sphere / 270 \\ 10.4. Remarks and Comments for Further Reading / 271 \\ 10.5. Exercises and Further Examples / 272 \\ 11 Special Statistical Distribution Functions / 275 \\ 11.1. Error Functions / 275 \\ 11.1.1. The Error Function and Asymptotic Expansions / 276 \\ 11.2. Incomplete Gamma Functions / 277 \\ 11.2.1. Series Expansions / 279 \\ 11.2.2. Continued Fraction for $\Gamma(a, z)$ / 280 \\ 11.2.3. Contour Integral for the Incomplete Gamma Functions / 282 \\ 11.2.4. Uniform Asymptotic Expansions / 283 \\ 11.2.5. Numerical Aspects / 286 \\ 11.3. Incomplete Beta Functions / 288 \\ 11.3.1. Recurrence Relations / 289 \\ 11.3.2. Contour Integral for the Incomplete Beta Function / 290 \\ 11.3.3. Asymptotic Expansions / 291 \\ 11.3.4. Numerical Aspects / 297 \\ 11.4. Non-Central Chi-Squared Distribution / 298 \\ 11.4.1. A Few More Integral Representations / 300 \\ 11.4.2. Asymptotic Expansion; $m$ Fixed, $j$ Large / 302 \\ 11.4.3. Asymptotic Expansion; $j$ Large, $m$ Arbitrary / 303 \\ 11.4.4. Numerical Aspects / 305 \\ 11.5. An Incomplete Bessel Function / 308 \\ 11.6. Remarks and Comments for Further Reading / 309 \\ 11.7. Exercises and Further Examples / 310 \\ 12 Elliptic Integrals and Elliptic Functions / 319 \\ 12.1. Complete Integrals of the First and Second Kind / 315 \\ 12.1.1. The Simple Pendulum / 316 \\ 12.1.2. Arithmetic Geometric Mean / 318 \\ 12.2. Incomplete Elliptic Integrals / 321 \\ 12.3. Elliptic Functions and Theta Functions / 322 \\ 12.3.1. Elliptic Functions / 323 \\ 12.3.2. Theta Functions / 324 \\ 12.4. Numerical Aspects / 328 \\ 12.5. Remarks and Comments for Further Reading / 329 \\ 12.6. Exercises and Further Examples / 330 \\ 13 Numerical Aspects of Special Functions / 333 \\ 13.1. A Simple Recurrence Relation / 334 \\ 13.2. Introduction to the General Theory / 335 \\ 13.3. Examples / 338 \\ 13.4. Miller's Algorithm / 343 \\ 13.5. How to Compute a Continued Fraction / 347 \\ Bibliography / 349 \\ Notations and Symbols / 361 \\ Index / 365

entry:
@Book{Temme:1996:SFI,
  author =       "N. M. Temme",
  title =        "Special Functions: an Introduction to the Classical
                 Functions of Mathematical Physics",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 374",
  year =         "1996",
  DOI =          "https://doi.org/10.1002/9781118032572",
  ISBN =         "0-471-11313-1",
  ISBN-13 =      "978-0-471-11313-3",
  LCCN =         "QC20.7.F87 T46 1996",
  bibdate =      "Mon Nov 24 21:41:54 MST 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Bernoulli, Euler and Stirling numbers \\
                 Useful methods and techniques \\
                 The gamma function \\
                 Differential equations \\
                 Hypergeometric functions \\
                 Orthogonal polynomials \\
                 Confluent hypergeometric functions \\
                 Legendre functions \\
                 Bessel functions \\
                 Separating the wave equation \\
                 Special statistical distribution functions \\
                 Elliptic integrals and elliptic functions \\
                 Numerical aspects of special functions",
  subject =      "functions, special; mathematical physics; boundary
                 value problems",
  tableofcontents = "1 Bernoulli, Euler and Stirling Numbers / 1 \\
                 1.1. Bernoulli Numbers and Polynomials / 2 \\
                 1.1.1. Definitions and Properties / 3 \\
                 1.1.2. A Simple Difference Equation / 6 \\
                 1.1.3. Euler's Summation Formula / 9 \\
                 1.2. Euler Numbers and Polynomials / 14 \\
                 1.2.1. Definitions and Properties / 15 \\
                 1.2.2. Boole's Summation Formula / 17 \\
                 1.3. Stirling Numbers / 18 \\
                 1.4. Remarks and Comments for Further Reading / 21 \\
                 1.5. Exercises and Further Examples / 22 \\
                 2 Useful Methods and Techniques / 29 \\
                 2.1. Some Theorems from Analysis / 29 \\
                 2.2. Asymptotic Expansions of Integrals / 31 \\
                 2.2.1. Watson's Lemma / 32 \\
                 2.2.2. The Saddle Point Method / 34 \\
                 2.2.3. Other Asymptotic Methods / 38 \\
                 2.3. Exercises and Further Examples / 39 \\
                 3 The Gamma Function / 41 \\
                 3.1. Introduction / 41 \\
                 3.1.1. The Fundamental Recursion Property / 42 \\
                 3.1.2. Another Look at the Gamma Function / 42 \\
                 3.2. Important Properties / 43 \\
                 3.2.1. Prym's Decomposition / 43 \\
                 3.2.2. The Cauchy--Saalsch{\"u}tz Representation / 44
                 \\
                 3.2.3. The Beta Integral / 45 \\
                 3.2.4. The Multiplication Formula / 46 \\
                 3.2.5. The Reflection Formula / 46 \\
                 3.2.6. The Reciprocal Gamma Function / 48 \\
                 3.2.7. A Complex Contour for the Beta Integral / 49 \\
                 3.3. Infinite Products / 50 \\
                 3.3.1. Gauss' Multiplication Formula / 52 \\
                 3.4. Logarithmic Derivative of the Gamma Function / 53
                 \\
                 3.5. Riemann's Zeta Function / 57 \\
                 3.6. Asymptotic Expansions / 61 \\
                 3.6.1. Estimations of the Remainder / 64 \\
                 3.6.2. Ratio of Two Gamma Functions / 66 \\
                 3.6.3. Application of the Saddle Point Method / 69 \\
                 3.7. Remarks and Comments for Further Reading / 71 \\
                 3.8. Exercises and Further Examples / 72 \\
                 4 Differential Equations / 79 \\
                 4.1. Separating the Wave Equation / 79 \\
                 4.1.1. Separating the Variables / 81 \\
                 4.2. Differential Equations in the Complex Plane / 83
                 \\
                 4.2.1. Singular Points / 83 \\
                 4.2.2. Transformation of the Point at Infinity / 84 \\
                 4.2.3. The Solution Near a Regular Point / 85 \\
                 4.2.4. Power Series Expansions Around a Regular Point /
                 90 \\
                 4.2.5. Power Series Expansions Around a Regular
                 Singular Point / 92 \\
                 4.3. Sturm's Comparison Theorem / 97 \\
                 4.4. Integrals as Solutions of Differential Equations /
                 98 \\
                 4.5. The Liouville Transformation / 103 \\
                 4.6. Remarks and Comments for Further Reading / 104 \\
                 4.7. Exercises and Further Examples / 104 \\
                 5 Hypergeometric Functions / 107 \\
                 5.1. Definitions and Simple Relations / 107 \\
                 5.2. Analytic Continuation / 109 \\
                 5.2.1. Three Functional Relations / 110 \\
                 5.2.2. A Contour Integral Representation / 111 \\
                 5.3. The Hypergeometric Differential Equation / 112 \\
                 5.4. The Singular Points of the Differential Equation /
                 114 \\
                 5.5. The Riemann--Papperitz Equation / 116 \\
                 5.6. Barnes' Contour Integral for $F(a, b; c; z)$ / 119
                 \\
                 5.7. Recurrence Relations / 121 \\
                 5.8. Quadratic Transformations / 122 \\
                 5.9. Generalized Hypergeometric Functions / 124 \\
                 5.9.1. A First Introduction to g-functions / 125 \\
                 5.10. Remarks and Comments for Further Reading / 127
                 \\
                 5.11. Exercises and Further Examples / 128 \\
                 6 Orthogonal Polynomials / 133 \\
                 6.1. General Orthogonal Polynomials / 133 \\
                 6.1.1. Zeros of Orthogonal Polynomials / 137 \\
                 6.1.2. Gauss Quadrature / 138 \\
                 6.2. Classical Orthogonal Polynomials / 141 \\
                 6.3. Definitions by the Rodrigues Formula / 142 \\
                 6.4. Recurrence Relations / 146 \\
                 6.5. Differential Equations / 149 \\
                 6.6. Explicit Representations / 151 \\
                 6.7. Generating Functions / 154 \\
                 6.8. Legendre Polynomials / 156 \\
                 6.8.1. The Norm of the Legendre Polynomials / 156 \\
                 6.8.2. Integral Expressions for the Legendre
                 Polynomials / 156 \\
                 6.8.3. Some Bounds on Legendre Polynomials / 157 \\
                 6.8.4. An Asymptotic Expansion as n is Large / 158 \\
                 6.9. Expansions in Terms of Orthogonal Polynomials /
                 160 \\
                 6.9.1. An Optimal Result in Connection with Legendre
                 Polynomials / 160 \\
                 6.9.2. Numerical Aspects of Chebyshev Polynomials / 162
                 \\
                 6.10. Remarks and Comments for Further Reading / 164
                 \\
                 6.11. Exercises and Further Examples / 164 \\
                 7 Confluent Hypergeometric Functions / 171 \\
                 7.1. The $M$-function / 172 \\
                 7.2. The $U$-function / 175 \\
                 7.3. Special Cases and Further Relations / 177 \\
                 7.3.1. Whittaker Functions / 178 \\
                 7.3.2. Coulomb Wave Functions / 178 \\
                 7 3.3. Parabolic Cylinder Functions / 179 \\
                 7 3.4. Error Functions / 180 \\
                 7.3.5. Exponential Integrals / 180 \\
                 7.3.6. Fresnel Integrals / 182 \\
                 7.3.7. Incomplete Gamma Functions / 185 \\
                 7.3.8. Bessel Functions / 186 \\
                 7.3.9. Orthogonal Polynomials / 186 \\
                 7.4. Remarks and Comments for Further Reading / 186 \\
                 7.5. Exercises and Further Examples / 187 \\
                 8 Legendre Functions / 193 \\
                 8.1. The Legendre Differential Equation / 194 \\
                 8.2. Ordinary Legendre Functions / 194 \\
                 8.3. Other Solutions of the Differential Equation / 196
                 \\
                 8.4. A Few More Series Expansions / 198 \\
                 8.5. The function $Q_n(z)$ / 200 \\
                 8.6. Integral Representations / 202 \\
                 8.7. Associated Legendre Functions / 209 \\
                 8.8. Remarks and Comments for Further Reading / 213 \\
                 8.9. Exercises and Further Examples / 214 \\
                 9 Bessel Functions / 219 \\
                 9.1. Introduction / 219 \\
                 9.2. Integral Representations / 220 \\
                 9.3. Cylinder Functions / 223 \\
                 9.4. Further Properties / 227 \\
                 9.5. Modified Bessel Functions / 232 \\
                 9.6. Integral Representations for the $I$- and
                 $K$-Functions / 234 \\
                 9.7. Asymptotic Expansions / 238 \\
                 9.8. Zeros of Bessel Functions / 241 \\
                 9.9. Orthogonality Relations, Fourier--Bessel Series /
                 244 \\
                 9.10. Remarks and Comments for Further Reading / 247
                 \\
                 9.11. Exercises and Further Examples / 247 \\
                 10 Separating the Wave Equation / 257 \\
                 10.1. General Transformations / 258 \\
                 10.2. Special Coordinate Systems / 259 \\
                 10.2.1. Cylindrical Coordinates / 259 \\
                 10.2.2. Spherical Coordinates / 261 \\
                 10.2.3. Elliptic Cylinder Coordinates / 263 \\
                 10.2.4. Parabolic Cylinder Coordinates / 264 \\
                 10.2.5. Oblate Spheroidal Coordinates / 266 \\
                 10.3. Boundary Value Problems / 268 \\
                 10.3.1. Heat Conduction in a Cylinder / 268 \\
                 10.3.2. Diffraction of a Plane Wave Due to a Sphere /
                 270 \\
                 10.4. Remarks and Comments for Further Reading / 271
                 \\
                 10.5. Exercises and Further Examples / 272 \\
                 11 Special Statistical Distribution Functions / 275 \\
                 11.1. Error Functions / 275 \\
                 11.1.1. The Error Function and Asymptotic Expansions /
                 276 \\
                 11.2. Incomplete Gamma Functions / 277 \\
                 11.2.1. Series Expansions / 279 \\
                 11.2.2. Continued Fraction for $\Gamma(a, z)$ / 280 \\
                 11.2.3. Contour Integral for the Incomplete Gamma
                 Functions / 282 \\
                 11.2.4. Uniform Asymptotic Expansions / 283 \\
                 11.2.5. Numerical Aspects / 286 \\
                 11.3. Incomplete Beta Functions / 288 \\
                 11.3.1. Recurrence Relations / 289 \\
                 11.3.2. Contour Integral for the Incomplete Beta
                 Function / 290 \\
                 11.3.3. Asymptotic Expansions / 291 \\
                 11.3.4. Numerical Aspects / 297 \\
                 11.4. Non-Central Chi-Squared Distribution / 298 \\
                 11.4.1. A Few More Integral Representations / 300 \\
                 11.4.2. Asymptotic Expansion; $m$ Fixed, $j$ Large /
                 302 \\
                 11.4.3. Asymptotic Expansion; $j$ Large, $m$ Arbitrary
                 / 303 \\
                 11.4.4. Numerical Aspects / 305 \\
                 11.5. An Incomplete Bessel Function / 308 \\
                 11.6. Remarks and Comments for Further Reading / 309
                 \\
                 11.7. Exercises and Further Examples / 310 \\
                 12 Elliptic Integrals and Elliptic Functions / 319 \\
                 12.1. Complete Integrals of the First and Second Kind /
                 315 \\
                 12.1.1. The Simple Pendulum / 316 \\
                 12.1.2. Arithmetic Geometric Mean / 318 \\
                 12.2. Incomplete Elliptic Integrals / 321 \\
                 12.3. Elliptic Functions and Theta Functions / 322 \\
                 12.3.1. Elliptic Functions / 323 \\
                 12.3.2. Theta Functions / 324 \\
                 12.4. Numerical Aspects / 328 \\
                 12.5. Remarks and Comments for Further Reading / 329
                 \\
                 12.6. Exercises and Further Examples / 330 \\
                 13 Numerical Aspects of Special Functions / 333 \\
                 13.1. A Simple Recurrence Relation / 334 \\
                 13.2. Introduction to the General Theory / 335 \\
                 13.3. Examples / 338 \\
                 13.4. Miller's Algorithm / 343 \\
                 13.5. How to Compute a Continued Fraction / 347 \\
                 Bibliography / 349 \\
                 Notations and Symbols / 361 \\
                 Index / 365",
}


bibtype: article
filename: elefunt.bib
label: Temme:1996:UAI
author: N. M. Temme
journal: j-METHODS-APPL-ANAL
volume: 3
number: 3
pages: 335--344
year: 1996
DOI: https://doi.org/10.4310/MAA.1996.v3.n3.a3
ISSN: 1073-2772 (print), 1945-0001 (electronic) OR 10732772 (print), 19450001 (electronic)
ISSNL: 1073-2772 OR 10732772
MRclass: 33B20 (41A60)
MRnumber: 1421474
MRreviewer: Richard B. Paris
bibdate: Sat Feb 18 15:19:00 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 15:19:00 ???
fjournal: Methods and Applications of Analysis
acknowledgement: ack-nhfb
journalURL: http://www.intlpress.com/MAA/
rawauthor: N. M. Temme
title:
Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

rawtitle:
Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

entry:
@Article{Temme:1996:UAI,
  author =       "N. M. Temme",
  title =        "Uniform asymptotics for the incomplete gamma functions
                 starting from negative values of the parameters",
  journal =      j-METHODS-APPL-ANAL,
  volume =       "3",
  number =       "3",
  pages =        "335--344",
  year =         "1996",
  DOI =          "https://doi.org/10.4310/MAA.1996.v3.n3.a3",
  ISSN =         "1073-2772 (print), 1945-0001 (electronic)",
  ISSN-L =       "1073-2772",
  MRclass =      "33B20 (41A60)",
  MRnumber =     "1421474",
  MRreviewer =   "Richard B. Paris",
  bibdate =      "Sat Feb 18 15:19:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Methods and Applications of Analysis",
  journal-URL =  "http://www.intlpress.com/MAA/",
}


bibtype: article
filename: elefunt.bib
label: Waissi:1996:SAS
author: Gary R. Waissi and Donald F. Rossin
title: A sigmoid approximation of the standard normal integral
journal: j-APPL-MATH-COMP
volume: 77
number: 1
pages: 91--95
month: jun
monthnumber: 6
year: 1996
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/0096-3003(95)00190-5
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:02:39 MST 2012
bibtimestamp: 2012.11.20 21:02:39 MST
URL: http://www.sciencedirect.com/science/article/pii/0096300395001905
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: Gary R. Waissi and Donald F. Rossin
rawtitle: A sigmoid approximation of the standard normal integral
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Waissi:1996:SAS,
  author =       "Gary R. Waissi and Donald F. Rossin",
  title =        "A sigmoid approximation of the standard normal
                 integral",
  journal =      j-APPL-MATH-COMP,
  volume =       "77",
  number =       "1",
  pages =        "91--95",
  month =        jun,
  year =         "1996",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(95)00190-5",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0096300395001905",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}


bibtype: book
filename: elefunt.bib
label: Walz:1996:AE
author: Guido Walz
title: Asymptotics and Extrapolation
volume: 88
publisher: pub-AKADEMIE-VERLAG
address: pub-AKADEMIE-VERLAG:adr
pages: 330
year: 1996
ISBN: 3-05-501732-3 OR 3055017323
ISBN13: 978-3-05-501732-2 OR 9783055017322
LCCN: QA281 .W349 1996
bibdate: Thu Dec 1 10:25:13 MST 2011
bibsource: catalog.princeton.edu:7090/voyager; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:25:13 MST
series: Mathematical research
subject: Extrapolation; Asymptotic expansions
acknowledgement: ack-nhfb
rawauthor: Guido Walz
rawtitle: Asymptotics and Extrapolation
TOC:
Part I: Asymptotic Expansions 1. Asymptotic Systems and Expansions / 15 2. Geometric Asymptotic Expansions / 21 3. Logarithmic Asymptotic Expansions / 39 Part II: Linear Extrapolation Methods 4. Fundamental Concepts and General Philosophy / 193 5. Error Bounds, Stopping Rules and Monotonicity / 244 6. Generalizations and Final Remarks / 289 Historical Notes / 303 References / 308 Index / 329

rawTOC:
Part I: Asymptotic Expansions \\ 1. Asymptotic Systems and Expansions / 15 \\ 2. Geometric Asymptotic Expansions / 21 \\ 3. Logarithmic Asymptotic Expansions / 39 \\ Part II: Linear Extrapolation Methods \\ 4. Fundamental Concepts and General Philosophy / 193 \\ 5. Error Bounds, Stopping Rules and Monotonicity / 244 \\ 6. Generalizations and Final Remarks / 289 \\ Historical Notes / 303 \\ References / 308\\ Index / 329

entry:
@Book{Walz:1996:AE,
  author =       "Guido Walz",
  title =        "Asymptotics and Extrapolation",
  volume =       "88",
  publisher =    pub-AKADEMIE-VERLAG,
  address =      pub-AKADEMIE-VERLAG:adr,
  pages =        "330",
  year =         "1996",
  ISBN =         "3-05-501732-3",
  ISBN-13 =      "978-3-05-501732-2",
  LCCN =         "QA281 .W349 1996",
  bibdate =      "Thu Dec 1 10:25:13 MST 2011",
  bibsource =    "catalog.princeton.edu:7090/voyager;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematical research",
  acknowledgement = ack-nhfb,
  subject =      "Extrapolation; Asymptotic expansions",
  tableofcontents = "Part I: Asymptotic Expansions \\
                 1. Asymptotic Systems and Expansions / 15 \\
                 2. Geometric Asymptotic Expansions / 21 \\
                 3. Logarithmic Asymptotic Expansions / 39 \\
                 Part II: Linear Extrapolation Methods \\
                 4. Fundamental Concepts and General Philosophy / 193
                 \\
                 5. Error Bounds, Stopping Rules and Monotonicity / 244
                 \\
                 6. Generalizations and Final Remarks / 289 \\
                 Historical Notes / 303 \\
                 References / 308\\
                 Index / 329",
}


bibtype: article
filename: elefunt.bib
label: Weniger:1996:CWF
author: Ernst Joachim Weniger
journal: j-COMPUT-PHYS
volume: 10
number: 5
pages: 496--??
month: sep
monthnumber: 9
year: 1996
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168579
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:46:03 MDT 2019
bibtimestamp: 2019.04.10 08:46:03 MDT
URL: https://aip.scitation.org/doi/10.1063/1.168579
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: Ernst Joachim Weniger
title:
Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations

rawtitle:
Computation of the {Whittaker} function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations

entry:
@Article{Weniger:1996:CWF,
  author =       "Ernst Joachim Weniger",
  title =        "Computation of the {Whittaker} function of the second
                 kind by summing its divergent asymptotic series with
                 the help of nonlinear sequence transformations",
  journal =      j-COMPUT-PHYS,
  volume =       "10",
  number =       "5",
  pages =        "496--??",
  month =        sep,
  year =         "1996",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168579",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:03 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168579",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Williams:1996:TMF
author: K. B. Williams
journal: j-CCCUJ
volume: 14
number: 12
pages: 49--54, 58--65
month: dec
monthnumber: 12
year: 1996
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Thu Nov 14 06:34:33 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.11.14 06:34:33 ???
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawauthor: K. B. Williams
title:
Testing Math Functions: When requirements are tight, we must carefully examine all potential sources of error. Make sure your math library isn't the weak link in the chain

note:
Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.

rawnote:
Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.

rawtitle:
Testing Math Functions: When requirements are tight, we must carefully examine all potential sources of error. {Make} sure your math library isn't the weak link in the chain

entry:
@Article{Williams:1996:TMF,
  author =       "K. B. Williams",
  title =        "Testing Math Functions: When requirements are tight,
                 we must carefully examine all potential sources of
                 error. {Make} sure your math library isn't the weak
                 link in the chain",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "12",
  pages =        "49--54, 58--65",
  month =        dec,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Thu Nov 14 06:34:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Describes a package that extends the
                 Cody-Waite-Plauger work on the ELEFUNT package for the
                 testing of the elementary functions, including the
                 inverse hyperbolic functions, cube root, and Bessel
                 functions of the first and second kinds. The C++
                 package implements 192-bit extended precision versions
                 of all of the functions, so that accurate results are
                 available for comparison with the normal
                 double-precision results.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: article
filename: elefunt.bib
label: Zahle:1996:FDW
author: M. Zahle and H. Ziezold
title: Fractional derivatives of Weierstrass-type functions
journal: j-J-COMPUT-APPL-MATH
volume: 76
number: 1--2
pages: 265--275
day: 17
month: dec
monthnumber: 12
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796001100
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Z{\"a}hle and H. Ziezold
rawtitle: Fractional derivatives of {Weierstrass}-type functions
entry:
@Article{Zahle:1996:FDW,
  author =       "M. Z{\"a}hle and H. Ziezold",
  title =        "Fractional derivatives of {Weierstrass}-type
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "76",
  number =       "1--2",
  pages =        "265--275",
  day =          "17",
  month =        dec,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001100",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Zhang:1996:CSF
author: Shanjie Zhang and Jianming Jin
title: Computation of Special Functions
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xxvi + 717
year: 1996
ISBN: 0-471-11963-6 OR 0471119636
ISBN13: 978-0-471-11963-0 OR 9780471119630
LCCN: QA351.C45 1996
bibdate: Wed Mar 22 14:39:04 2000
bibtimestamp: 2000.03.22 14:39:04 ???
acknowledgement: ack-nhfb
rawauthor: Shanjie Zhang and Jianming Jin
rawtitle: Computation of Special Functions
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

TOC:
Preface / xi Acknowledgments / xvii List of Computer Programs / xix 1: Bernoulli and Euler Numbers / 1 1.1 Bernoulli Numbers / 1 1.2 Euler Numbers / 6 1.3 Mathematical Table / 10 References / 11 2: Orthogonal Polynomials / 12 2.1 Introduction / 12 2.2 Chebyshev Polynomials / 13 2.3 Laguerre Polynomials / 18 2.4 Hermite Polynomials / 20 2.5 Numerical Computation / 23 2.6 Application in Numerical Integration / 27 References / 43 3: Gamma, Beta, and Psi Functions / 44 3.1 Gamma Function / 44 3.2 Beta Function / 53 3.3 Psi Function / 55 3.4 Incomplete Gamma Function / 61 3.5 Incomplete Beta Function / 64 3.6 Mathematical Tables / 66 References and Further Reading / 76 4: Legendre Functions / 77 4.1 Introduction / 77 4.2 Legendre Functions of the First Kind / 78 4.3 Legendre Functions of the Second Kind / 83 4.4 Associated Legendre Functions of the First Kind / 89 4.5 Associated Legendre Functions of the Second Kind / 96 4.6 Legendre Functions with an Arbitrary Degree / 104 4.7 Mathematical Tables / 113 References and Further Reading / 125 5: Bessel Functions / 126 5.1 Introduction / 126 5.2 Computation of $J_0(x)$, $J_1(x)$, $Y_0(x)$, and $Y_1(x)$ / 131 5.3 Computation of $J_n(x)$ and $Y_n(x)$ with Real Arguments / 140 5.4 Computation of $Y_n(z)$ and$ Y_n(z)$ with Complex Arguments / 149 5.5 Computation of $J_nu (z)$ and $J_nu (z)$ with an Arbitrary Order / 161 5.6 Assessment of Validity and Accuracy of Computation / 175 5.7 Zeros of Bessel Functions / 180 5.8 Lambda Functions / 182 5.9 Mathematical Tables / 184 References and Further Reading / 201 6: Modified Bessel Functions / 202 6.1 Introduction / 202 6.2 Computation of $I_0(x)$, $I_1(x)$, $K_0(x)$, and $K_1(x)$ / 207 6.3 Computation of $I_n(x)$ and $K_n(x)$ with Real Arguments / 213 6.4 Computation of $I_n(z)$ and $K_n(z)$ with Complex Arguments / 217 6.5 Computation of $I_nu (z)$ and $K_nu (z)$ with an Arbitrary Order / 225 6.6 Computation of $H_nu ^(1)(z)$ and $H_nu ^(2)(z)$ for Complex Arguments / 235 6.7 Mathematical Tables / 239 References and Further Reading / 251 7: Integrals of Bessel Functions / 252 7.1 Simple Integrals of Bessel Functions / 252 7.2 Simple Integrals of Modified Bessel Functions / 261 7.3 Curves and Tables / 268 References / 272 8: Spherical Bessel Functions / 273 8.1 Spherical Bessel Functions / 273 8.2 Riccati--Bessel Functions / 283 8.3 Modified Spherical Bessel Functions / 286 8.4 Mathematical Tables / 295 References and Further Reading / 306 9: Kelvin Functions / 307 9.1 Introduction / 307 9.2 Mathematical Properties / 311 9.3 Asymptotic Expansions / 312 9.4 Numerical Computation / 315 9.5 Zeros of Kelvin Functions / 321 9.6 Mathematical Tables / 321 Reference / 324 10: Airy Functions / 325 10.1 Introduction / 325 10.2 Numerical Computation / 329 10.3 Mathematical Tables / 336 References / 340 11: Struve Functions / 341 11.1 Struve Functions / 341 11.2 Modified Struve Functions / 353 11.3 Mathematical Tables / 362 References / 365 12: Hypergeometric and Confluent Hypergeometric Functions / 366 12.1 Definition of Hypergeometric Functions / 366 12.2 Properties of Hypergeometric Functions / 368 12.3 Linear Transformation Formulas / 369 12.4 Recurrence Relations for Hypergeometric Functions / 372 12.5 Special Functions Expressed as Hypergeometric Functions / 373 12.6 Numerical Computation of Hypergeometric Functions / 374 12.7 Definition of Confluent Hypergeometric Functions / 385 12.8 Properties of Confluent Hypergeometric Functions / 387 12.9 Recurrence Relations for Confluent Hypergeometric Functions / 389 12.10 Special Functions Expressed as Confluent Hypergeometric Functions / 394 12.11 Definition of Whittaker Functions / 395 12.12 Numerical Computation of Confluent Hypergeometric Functions / 398 12.13 Mathematical Tables / 411 References and Further Reading / 424 13: Parabolic Cylinder Functions / 425 13.1 Introduction / 425 13.2 Definitions of Parabolic Cylinder Functions / 428 13.3 Basic Properties / 432 13.4 Series and Asymptotic Expansions / 437 13.5 Numerical Computation / 438 13.6 Mathematical Tables / 455 References and Further Reading / 474 14: Mathieu Functions / 475 14.1 Definition of Mathieu Functions / 475 14.2 Determination of Expansion Coefficients and Characteristic Values / 477 14.3 Approximate Calculation of Characteristic Values / 482 14.4 Expansion of Mathieu Functions When $|q| < 1$ / 485 14.5 Properties of Mathieu Functions / 487 14.6 Definition of Modified Mathieu Functions / 489 14.7 Properties of Modified Mathieu Functions / 496 14.8 Numerical Computation: Algorithms and Computer Programs / 501 14.9 Mathematical Tables / 520 References and Further Reading / 535 15: Spheroidal Wave Functions / 536 15.1 Spheroidal Coordinate Systems / 536 15.2 Wave Equation and Its Solution in Spheroidal Coordinates / 540 15.3 Definitions of Angular and Radial Prolate Spheroidal Wave Functions / 542 15.4 Determination of Characteristic Values and Expansion Coefficients / 550 15.5 Evaluation of Prolate Radial Wave Functions of the Second Kind for Small $c xi $ / 556 15.6 Definitions of Angular and Radial Oblate Spheroidal Wave Functions / 559 15.7 Evaluation of Oblate Radial Wave Functions of the Second Kind for Small $c xi $ / 561 15.8 Numerical Computation: Algorithms and Computer Programs / 569 15.9 Mathematical Tables / 594 References / 619 16: Error Function and Fresnel Integrals / 620 16.1 Introduction to Error Function / 620 16.2 Numerical Computation of Error Function / 621 16.3 Gaussian Probability Integral / 624 16.4 Introduction to Fresnel Integrals / 625 16.5 Series and Asymptotic Expansions of Fresnel Integrals / 629 16.6 Numerical Computation of Fresnel Integrals / 630 16.7 Zeros of Error Function and Fresnel Integrals / 635 16.8 Mathematical Tables / 636 References and Further Reading / 643 17: Cosine and Sine Integrals / 644 17.1 Introduction / 644 17.2 Series and Asymptotic Expansions / 646 17.3 Numerical Computation / 647 17.4 Mathematical Table / 651 References and Further Readings / 653 18: Elliptic Integrals and Jacobian Elliptic Functions / 654 18.1 Introduction to Elliptic Integrals / 654 18.2 Series Expansion of Elliptic Integrals / 659 18.3 Numerical Computation of Elliptic Integrals / 661 18.4 Introduction to Jacobian Elliptic Functions / 666 18.5 Numerical Computation of Jacobian Elliptic Functions / 670 18.6 Mathematical Tables / 672 References and Further Reading / 679 19: Exponential Integrals / 680 19.1 Introduction / 680 19.2 Series, Asymptotic, and Continued Fraction Expressions / 682 19.3 Rational Approximations / 683 19.4 Numerical Computation / 684 19.5 Mathematical Tables / 688 References / 693 20: Summary of Methods for Computing Special Functions / 694 Appendix A: Derivation of Some Special Differential Equations / 697 A.1 Helmholtz Equation and Separation of Variables / 697 A.2 Circular Cylindrical Coordinates / 698 A.3 Elliptic Cylindrical Coordinates / 700 A.4 Parabolic Cylindrical Coordinates / 700 A.5 Spherical Coordinates / 701 A.6 Prolate Spheroidal Coordinates / 701 A.7 Oblate Spheroidal Coordinates / 702 A.8 Parabolic Coordinates / 703 References / 703 Appendix B: Root-Finding Methods / 704 B.1 Newton's Method / 704 B.2 Modified Newton's Method / 706 B.3 Secant Method / 706 Reference / 706 Appendix C: About the Software / 707 Index / 709 Index of Computer Programs / 715

shortTOC:
Preface / xi Acknowledgments / xvii List of Computer Programs / xix 1: Bernoulli and Euler Numbers / 1 2: Orthogonal Polynomials / 12 3: Gamma, Beta, and Psi Functions / 44 4: Legendre Functions / 77 5: Bessel Functions / 126 6: Modified Bessel Functions / 202 7: Integrals of Bessel Functions / 252 8: Spherical Bessel Functions / 273 9: Kelvin Functions / 307 10: Airy Functions / 325 11: Struve Functions / 341 12: Hypergeometric and Confluent Hypergeometric / 366 13: Parabolic Cylinder Functions / 425 14: Mathieu Functions / 475 15: Spheroidal Wave Functions / 536 16: Error Function and Fresnel Integrals / 620 17: Cosine and Sine Integrals / 644 18: Elliptic Integrals and Jacobian Elliptic Functions 19: Exponential Integrals / 680 20: Summary of Methods for Computing Special Functions Appendix A: Derivation of Some Special Differential Appendix B: Root-Finding Methods / 704 Reference / 706 Appendix C: About the Software / 707 Index / 709 Index of Computer Programs / 715

rawshortTOC:
Preface / xi \\ Acknowledgments / xvii \\ List of Computer Programs / xix \\ 1: Bernoulli and Euler Numbers / 1 \\ 2: Orthogonal Polynomials / 12 \\ 3: Gamma, Beta, and Psi Functions / 44 \\ 4: Legendre Functions / 77 \\ 5: Bessel Functions / 126 \\ 6: Modified Bessel Functions / 202 \\ 7: Integrals of Bessel Functions / 252 \\ 8: Spherical Bessel Functions / 273 \\ 9: Kelvin Functions / 307 \\ 10: Airy Functions / 325 \\ 11: Struve Functions / 341 \\ 12: Hypergeometric and Confluent Hypergeometric / 366 \\ 13: Parabolic Cylinder Functions / 425 \\ 14: Mathieu Functions / 475 \\ 15: Spheroidal Wave Functions / 536 \\ 16: Error Function and Fresnel Integrals / 620 \\ 17: Cosine and Sine Integrals / 644 \\ 18: Elliptic Integrals and Jacobian Elliptic Functions 19: Exponential Integrals / 680 \\ 20: Summary of Methods for Computing Special Functions Appendix A: Derivation of Some Special Differential Appendix B: Root-Finding Methods / 704 \\ Reference / 706 \\ Appendix C: About the Software / 707 \\ Index / 709 \\ Index of Computer Programs / 715

rawTOC:
Preface / xi \\ Acknowledgments / xvii \\ List of Computer Programs / xix \\ 1: Bernoulli and Euler Numbers / 1 \\ 1.1 Bernoulli Numbers / 1 \\ 1.2 Euler Numbers / 6 \\ 1.3 Mathematical Table / 10 \\ References / 11 \\ 2: Orthogonal Polynomials / 12 \\ 2.1 Introduction / 12 \\ 2.2 Chebyshev Polynomials / 13 \\ 2.3 Laguerre Polynomials / 18 \\ 2.4 Hermite Polynomials / 20 \\ 2.5 Numerical Computation / 23 \\ 2.6 Application in Numerical Integration / 27 \\ References / 43 \\ 3: Gamma, Beta, and Psi Functions / 44 \\ 3.1 Gamma Function / 44 \\ 3.2 Beta Function / 53 \\ 3.3 Psi Function / 55 \\ 3.4 Incomplete Gamma Function / 61 \\ 3.5 Incomplete Beta Function / 64 \\ 3.6 Mathematical Tables / 66 \\ References and Further Reading / 76 \\ 4: Legendre Functions / 77 \\ 4.1 Introduction / 77 \\ 4.2 Legendre Functions of the First Kind / 78 \\ 4.3 Legendre Functions of the Second Kind / 83 \\ 4.4 Associated Legendre Functions of the First Kind / 89 \\ 4.5 Associated Legendre Functions of the Second Kind / 96 \\ 4.6 Legendre Functions with an Arbitrary Degree / 104 \\ 4.7 Mathematical Tables / 113 \\ References and Further Reading / 125 \\ 5: Bessel Functions / 126 \\ 5.1 Introduction / 126 \\ 5.2 Computation of $J_0(x)$, $J_1(x)$, $Y_0(x)$, and $Y_1(x)$ / 131 \\ 5.3 Computation of $J_n(x)$ and $Y_n(x)$ with Real Arguments / 140 \\ 5.4 Computation of $Y_n(z)$ and$ Y_n(z)$ with Complex Arguments / 149 \\ 5.5 Computation of $J_\nu(z)$ and $J_\nu(z)$ with an Arbitrary Order / 161 \\ 5.6 Assessment of Validity and Accuracy of Computation / 175 \\ 5.7 Zeros of Bessel Functions / 180 \\ 5.8 Lambda Functions / 182 \\ 5.9 Mathematical Tables / 184 \\ References and Further Reading / 201 \\ 6: Modified Bessel Functions / 202 \\ 6.1 Introduction / 202 \\ 6.2 Computation of $I_0(x)$, $I_1(x)$, $K_0(x)$, and $K_1(x)$ / 207 \\ 6.3 Computation of $I_n(x)$ and $K_n(x)$ with Real Arguments / 213 \\ 6.4 Computation of $I_n(z)$ and $K_n(z)$ with Complex Arguments / 217 \\ 6.5 Computation of $I_\nu(z)$ and $K_\nu(z)$ with an Arbitrary Order / 225 \\ 6.6 Computation of $H_\nu^{(1)}(z)$ and $H_\nu^{(2)}(z)$ for Complex Arguments / 235 \\ 6.7 Mathematical Tables / 239 \\ References and Further Reading / 251 \\ 7: Integrals of Bessel Functions / 252 \\ 7.1 Simple Integrals of Bessel Functions / 252 \\ 7.2 Simple Integrals of Modified Bessel Functions / 261 \\ 7.3 Curves and Tables / 268 \\ References / 272 \\ 8: Spherical Bessel Functions / 273 \\ 8.1 Spherical Bessel Functions / 273 \\ 8.2 Riccati--Bessel Functions / 283 \\ 8.3 Modified Spherical Bessel Functions / 286 \\ 8.4 Mathematical Tables / 295 \\ References and Further Reading / 306 \\ 9: Kelvin Functions / 307 \\ 9.1 Introduction / 307 \\ 9.2 Mathematical Properties / 311 \\ 9.3 Asymptotic Expansions / 312 \\ 9.4 Numerical Computation / 315 \\ 9.5 Zeros of Kelvin Functions / 321 \\ 9.6 Mathematical Tables / 321 \\ Reference / 324 \\ 10: Airy Functions / 325 \\ 10.1 Introduction / 325 \\ 10.2 Numerical Computation / 329 \\ 10.3 Mathematical Tables / 336 \\ References / 340 \\ 11: Struve Functions / 341 \\ 11.1 Struve Functions / 341 \\ 11.2 Modified Struve Functions / 353 \\ 11.3 Mathematical Tables / 362 \\ References / 365 \\ 12: Hypergeometric and Confluent Hypergeometric Functions / 366 \\ 12.1 Definition of Hypergeometric Functions / 366 \\ 12.2 Properties of Hypergeometric Functions / 368 \\ 12.3 Linear Transformation Formulas / 369 \\ 12.4 Recurrence Relations for Hypergeometric Functions / 372 \\ 12.5 Special Functions Expressed as Hypergeometric Functions / 373 \\ 12.6 Numerical Computation of Hypergeometric Functions / 374 \\ 12.7 Definition of Confluent Hypergeometric Functions / 385 \\ 12.8 Properties of Confluent Hypergeometric Functions / 387 \\ 12.9 Recurrence Relations for Confluent Hypergeometric Functions / 389 \\ 12.10 Special Functions Expressed as Confluent Hypergeometric Functions / 394 \\ 12.11 Definition of Whittaker Functions / 395 \\ 12.12 Numerical Computation of Confluent Hypergeometric Functions / 398 \\ 12.13 Mathematical Tables / 411 \\ References and Further Reading / 424 \\ 13: Parabolic Cylinder Functions / 425 \\ 13.1 Introduction / 425 \\ 13.2 Definitions of Parabolic Cylinder Functions / 428 \\ 13.3 Basic Properties / 432 \\ 13.4 Series and Asymptotic Expansions / 437 \\ 13.5 Numerical Computation / 438 \\ 13.6 Mathematical Tables / 455 \\ References and Further Reading / 474 \\ 14: Mathieu Functions / 475 \\ 14.1 Definition of Mathieu Functions / 475 \\ 14.2 Determination of Expansion Coefficients and Characteristic Values / 477 \\ 14.3 Approximate Calculation of Characteristic Values / 482 \\ 14.4 Expansion of Mathieu Functions When $|q| < 1$ / 485 \\ 14.5 Properties of Mathieu Functions / 487 \\ 14.6 Definition of Modified Mathieu Functions / 489 \\ 14.7 Properties of Modified Mathieu Functions / 496 \\ 14.8 Numerical Computation: Algorithms and Computer Programs / 501 \\ 14.9 Mathematical Tables / 520 \\ References and Further Reading / 535 \\ 15: Spheroidal Wave Functions / 536 \\ 15.1 Spheroidal Coordinate Systems / 536 \\ 15.2 Wave Equation and Its Solution in Spheroidal Coordinates / 540 \\ 15.3 Definitions of Angular and Radial Prolate Spheroidal Wave Functions / 542 \\ 15.4 Determination of Characteristic Values and Expansion Coefficients / 550 \\ 15.5 Evaluation of Prolate Radial Wave Functions of the Second Kind for Small $c \xi$ / 556 \\ 15.6 Definitions of Angular and Radial Oblate Spheroidal Wave Functions / 559 \\ 15.7 Evaluation of Oblate Radial Wave Functions of the Second Kind for Small $c \xi$ / 561 \\ 15.8 Numerical Computation: Algorithms and Computer Programs / 569 \\ 15.9 Mathematical Tables / 594 \\ References / 619 \\ 16: Error Function and Fresnel Integrals / 620 \\ 16.1 Introduction to Error Function / 620 \\ 16.2 Numerical Computation of Error Function / 621 \\ 16.3 Gaussian Probability Integral / 624 \\ 16.4 Introduction to Fresnel Integrals / 625 \\ 16.5 Series and Asymptotic Expansions of Fresnel Integrals / 629 \\ 16.6 Numerical Computation of Fresnel Integrals / 630 \\ 16.7 Zeros of Error Function and Fresnel Integrals / 635 \\ 16.8 Mathematical Tables / 636 \\ References and Further Reading / 643 \\ 17: Cosine and Sine Integrals / 644 \\ 17.1 Introduction / 644 \\ 17.2 Series and Asymptotic Expansions / 646 \\ 17.3 Numerical Computation / 647 \\ 17.4 Mathematical Table / 651 \\ References and Further Readings / 653 \\ 18: Elliptic Integrals and Jacobian Elliptic Functions / 654 \\ 18.1 Introduction to Elliptic Integrals / 654 \\ 18.2 Series Expansion of Elliptic Integrals / 659 \\ 18.3 Numerical Computation of Elliptic Integrals / 661 \\ 18.4 Introduction to Jacobian Elliptic Functions / 666 \\ 18.5 Numerical Computation of Jacobian Elliptic Functions / 670 \\ 18.6 Mathematical Tables / 672 \\ References and Further Reading / 679 \\ 19: Exponential Integrals / 680 \\ 19.1 Introduction / 680 \\ 19.2 Series, Asymptotic, and Continued Fraction Expressions / 682 \\ 19.3 Rational Approximations / 683 \\ 19.4 Numerical Computation / 684 \\ 19.5 Mathematical Tables / 688 \\ References / 693 \\ 20: Summary of Methods for Computing Special Functions / 694 \\ Appendix A: Derivation of Some Special Differential Equations / 697 \\ A.1 Helmholtz Equation and Separation of Variables / 697 \\ A.2 Circular Cylindrical Coordinates / 698 \\ A.3 Elliptic Cylindrical Coordinates / 700 \\ A.4 Parabolic Cylindrical Coordinates / 700 \\ A.5 Spherical Coordinates / 701 \\ A.6 Prolate Spheroidal Coordinates / 701 \\ A.7 Oblate Spheroidal Coordinates / 702 \\ A.8 Parabolic Coordinates / 703 \\ References / 703 \\ Appendix B: Root-Finding Methods / 704 \\ B.1 Newton's Method / 704 \\ B.2 Modified Newton's Method / 706 \\ B.3 Secant Method / 706 \\ Reference / 706 \\ Appendix C: About the Software / 707 \\ Index / 709 \\ Index of Computer Programs / 715

entry:
@Book{Zhang:1996:CSF,
  author =       "Shanjie Zhang and Jianming Jin",
  title =        "Computation of Special Functions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xxvi + 717",
  year =         "1996",
  ISBN =         "0-471-11963-6",
  ISBN-13 =      "978-0-471-11963-0",
  LCCN =         "QA351.C45 1996",
  bibdate =      "Wed Mar 22 14:39:04 2000",
  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",
  price =        "US\$94.00",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Preface / xi \\
                 Acknowledgments / xvii \\
                 List of Computer Programs / xix \\
                 1: Bernoulli and Euler Numbers / 1 \\
                 2: Orthogonal Polynomials / 12 \\
                 3: Gamma, Beta, and Psi Functions / 44 \\
                 4: Legendre Functions / 77 \\
                 5: Bessel Functions / 126 \\
                 6: Modified Bessel Functions / 202 \\
                 7: Integrals of Bessel Functions / 252 \\
                 8: Spherical Bessel Functions / 273 \\
                 9: Kelvin Functions / 307 \\
                 10: Airy Functions / 325 \\
                 11: Struve Functions / 341 \\
                 12: Hypergeometric and Confluent Hypergeometric / 366
                 \\
                 13: Parabolic Cylinder Functions / 425 \\
                 14: Mathieu Functions / 475 \\
                 15: Spheroidal Wave Functions / 536 \\
                 16: Error Function and Fresnel Integrals / 620 \\
                 17: Cosine and Sine Integrals / 644 \\
                 18: Elliptic Integrals and Jacobian Elliptic Functions
                 19: Exponential Integrals / 680 \\
                 20: Summary of Methods for Computing Special Functions
                 Appendix A: Derivation of Some Special Differential
                 Appendix B: Root-Finding Methods / 704 \\
                 Reference / 706 \\
                 Appendix C: About the Software / 707 \\
                 Index / 709 \\
                 Index of Computer Programs / 715",
  tableofcontents = "Preface / xi \\
                 Acknowledgments / xvii \\
                 List of Computer Programs / xix \\
                 1: Bernoulli and Euler Numbers / 1 \\
                 1.1 Bernoulli Numbers / 1 \\
                 1.2 Euler Numbers / 6 \\
                 1.3 Mathematical Table / 10 \\
                 References / 11 \\
                 2: Orthogonal Polynomials / 12 \\
                 2.1 Introduction / 12 \\
                 2.2 Chebyshev Polynomials / 13 \\
                 2.3 Laguerre Polynomials / 18 \\
                 2.4 Hermite Polynomials / 20 \\
                 2.5 Numerical Computation / 23 \\
                 2.6 Application in Numerical Integration / 27 \\
                 References / 43 \\
                 3: Gamma, Beta, and Psi Functions / 44 \\
                 3.1 Gamma Function / 44 \\
                 3.2 Beta Function / 53 \\
                 3.3 Psi Function / 55 \\
                 3.4 Incomplete Gamma Function / 61 \\
                 3.5 Incomplete Beta Function / 64 \\
                 3.6 Mathematical Tables / 66 \\
                 References and Further Reading / 76 \\
                 4: Legendre Functions / 77 \\
                 4.1 Introduction / 77 \\
                 4.2 Legendre Functions of the First Kind / 78 \\
                 4.3 Legendre Functions of the Second Kind / 83 \\
                 4.4 Associated Legendre Functions of the First Kind /
                 89 \\
                 4.5 Associated Legendre Functions of the Second Kind /
                 96 \\
                 4.6 Legendre Functions with an Arbitrary Degree / 104
                 \\
                 4.7 Mathematical Tables / 113 \\
                 References and Further Reading / 125 \\
                 5: Bessel Functions / 126 \\
                 5.1 Introduction / 126 \\
                 5.2 Computation of $J_0(x)$, $J_1(x)$, $Y_0(x)$, and
                 $Y_1(x)$ / 131 \\
                 5.3 Computation of $J_n(x)$ and $Y_n(x)$ with Real
                 Arguments / 140 \\
                 5.4 Computation of $Y_n(z)$ and$ Y_n(z)$ with Complex
                 Arguments / 149 \\
                 5.5 Computation of $J_\nu(z)$ and $J_\nu(z)$ with an
                 Arbitrary Order / 161 \\
                 5.6 Assessment of Validity and Accuracy of Computation
                 / 175 \\
                 5.7 Zeros of Bessel Functions / 180 \\
                 5.8 Lambda Functions / 182 \\
                 5.9 Mathematical Tables / 184 \\
                 References and Further Reading / 201 \\
                 6: Modified Bessel Functions / 202 \\
                 6.1 Introduction / 202 \\
                 6.2 Computation of $I_0(x)$, $I_1(x)$, $K_0(x)$, and
                 $K_1(x)$ / 207 \\
                 6.3 Computation of $I_n(x)$ and $K_n(x)$ with Real
                 Arguments / 213 \\
                 6.4 Computation of $I_n(z)$ and $K_n(z)$ with Complex
                 Arguments / 217 \\
                 6.5 Computation of $I_\nu(z)$ and $K_\nu(z)$ with an
                 Arbitrary Order / 225 \\
                 6.6 Computation of $H_\nu^{(1)}(z)$ and
                 $H_\nu^{(2)}(z)$ for Complex Arguments / 235 \\
                 6.7 Mathematical Tables / 239 \\
                 References and Further Reading / 251 \\
                 7: Integrals of Bessel Functions / 252 \\
                 7.1 Simple Integrals of Bessel Functions / 252 \\
                 7.2 Simple Integrals of Modified Bessel Functions / 261
                 \\
                 7.3 Curves and Tables / 268 \\
                 References / 272 \\
                 8: Spherical Bessel Functions / 273 \\
                 8.1 Spherical Bessel Functions / 273 \\
                 8.2 Riccati--Bessel Functions / 283 \\
                 8.3 Modified Spherical Bessel Functions / 286 \\
                 8.4 Mathematical Tables / 295 \\
                 References and Further Reading / 306 \\
                 9: Kelvin Functions / 307 \\
                 9.1 Introduction / 307 \\
                 9.2 Mathematical Properties / 311 \\
                 9.3 Asymptotic Expansions / 312 \\
                 9.4 Numerical Computation / 315 \\
                 9.5 Zeros of Kelvin Functions / 321 \\
                 9.6 Mathematical Tables / 321 \\
                 Reference / 324 \\
                 10: Airy Functions / 325 \\
                 10.1 Introduction / 325 \\
                 10.2 Numerical Computation / 329 \\
                 10.3 Mathematical Tables / 336 \\
                 References / 340 \\
                 11: Struve Functions / 341 \\
                 11.1 Struve Functions / 341 \\
                 11.2 Modified Struve Functions / 353 \\
                 11.3 Mathematical Tables / 362 \\
                 References / 365 \\
                 12: Hypergeometric and Confluent Hypergeometric
                 Functions / 366 \\
                 12.1 Definition of Hypergeometric Functions / 366 \\
                 12.2 Properties of Hypergeometric Functions / 368 \\
                 12.3 Linear Transformation Formulas / 369 \\
                 12.4 Recurrence Relations for Hypergeometric Functions
                 / 372 \\
                 12.5 Special Functions Expressed as Hypergeometric
                 Functions / 373 \\
                 12.6 Numerical Computation of Hypergeometric Functions
                 / 374 \\
                 12.7 Definition of Confluent Hypergeometric Functions /
                 385 \\
                 12.8 Properties of Confluent Hypergeometric Functions /
                 387 \\
                 12.9 Recurrence Relations for Confluent Hypergeometric
                 Functions / 389 \\
                 12.10 Special Functions Expressed as Confluent
                 Hypergeometric Functions / 394 \\
                 12.11 Definition of Whittaker Functions / 395 \\
                 12.12 Numerical Computation of Confluent Hypergeometric
                 Functions / 398 \\
                 12.13 Mathematical Tables / 411 \\
                 References and Further Reading / 424 \\
                 13: Parabolic Cylinder Functions / 425 \\
                 13.1 Introduction / 425 \\
                 13.2 Definitions of Parabolic Cylinder Functions / 428
                 \\
                 13.3 Basic Properties / 432 \\
                 13.4 Series and Asymptotic Expansions / 437 \\
                 13.5 Numerical Computation / 438 \\
                 13.6 Mathematical Tables / 455 \\
                 References and Further Reading / 474 \\
                 14: Mathieu Functions / 475 \\
                 14.1 Definition of Mathieu Functions / 475 \\
                 14.2 Determination of Expansion Coefficients and
                 Characteristic Values / 477 \\
                 14.3 Approximate Calculation of Characteristic Values /
                 482 \\
                 14.4 Expansion of Mathieu Functions When $|q| < 1$ /
                 485 \\
                 14.5 Properties of Mathieu Functions / 487 \\
                 14.6 Definition of Modified Mathieu Functions / 489 \\
                 14.7 Properties of Modified Mathieu Functions / 496 \\
                 14.8 Numerical Computation: Algorithms and Computer
                 Programs / 501 \\
                 14.9 Mathematical Tables / 520 \\
                 References and Further Reading / 535 \\
                 15: Spheroidal Wave Functions / 536 \\
                 15.1 Spheroidal Coordinate Systems / 536 \\
                 15.2 Wave Equation and Its Solution in Spheroidal
                 Coordinates / 540 \\
                 15.3 Definitions of Angular and Radial Prolate
                 Spheroidal Wave Functions / 542 \\
                 15.4 Determination of Characteristic Values and
                 Expansion Coefficients / 550 \\
                 15.5 Evaluation of Prolate Radial Wave Functions of the
                 Second Kind for Small $c \xi$ / 556 \\
                 15.6 Definitions of Angular and Radial Oblate
                 Spheroidal Wave Functions / 559 \\
                 15.7 Evaluation of Oblate Radial Wave Functions of the
                 Second Kind for Small $c \xi$ / 561 \\
                 15.8 Numerical Computation: Algorithms and Computer
                 Programs / 569 \\
                 15.9 Mathematical Tables / 594 \\
                 References / 619 \\
                 16: Error Function and Fresnel Integrals / 620 \\
                 16.1 Introduction to Error Function / 620 \\
                 16.2 Numerical Computation of Error Function / 621 \\
                 16.3 Gaussian Probability Integral / 624 \\
                 16.4 Introduction to Fresnel Integrals / 625 \\
                 16.5 Series and Asymptotic Expansions of Fresnel
                 Integrals / 629 \\
                 16.6 Numerical Computation of Fresnel Integrals / 630
                 \\
                 16.7 Zeros of Error Function and Fresnel Integrals /
                 635 \\
                 16.8 Mathematical Tables / 636 \\
                 References and Further Reading / 643 \\
                 17: Cosine and Sine Integrals / 644 \\
                 17.1 Introduction / 644 \\
                 17.2 Series and Asymptotic Expansions / 646 \\
                 17.3 Numerical Computation / 647 \\
                 17.4 Mathematical Table / 651 \\
                 References and Further Readings / 653 \\
                 18: Elliptic Integrals and Jacobian Elliptic Functions
                 / 654 \\
                 18.1 Introduction to Elliptic Integrals / 654 \\
                 18.2 Series Expansion of Elliptic Integrals / 659 \\
                 18.3 Numerical Computation of Elliptic Integrals / 661
                 \\
                 18.4 Introduction to Jacobian Elliptic Functions / 666
                 \\
                 18.5 Numerical Computation of Jacobian Elliptic
                 Functions / 670 \\
                 18.6 Mathematical Tables / 672 \\
                 References and Further Reading / 679 \\
                 19: Exponential Integrals / 680 \\
                 19.1 Introduction / 680 \\
                 19.2 Series, Asymptotic, and Continued Fraction
                 Expressions / 682 \\
                 19.3 Rational Approximations / 683 \\
                 19.4 Numerical Computation / 684 \\
                 19.5 Mathematical Tables / 688 \\
                 References / 693 \\
                 20: Summary of Methods for Computing Special Functions
                 / 694 \\
                 Appendix A: Derivation of Some Special Differential
                 Equations / 697 \\
                 A.1 Helmholtz Equation and Separation of Variables /
                 697 \\
                 A.2 Circular Cylindrical Coordinates / 698 \\
                 A.3 Elliptic Cylindrical Coordinates / 700 \\
                 A.4 Parabolic Cylindrical Coordinates / 700 \\
                 A.5 Spherical Coordinates / 701 \\
                 A.6 Prolate Spheroidal Coordinates / 701 \\
                 A.7 Oblate Spheroidal Coordinates / 702 \\
                 A.8 Parabolic Coordinates / 703 \\
                 References / 703 \\
                 Appendix B: Root-Finding Methods / 704 \\
                 B.1 Newton's Method / 704 \\
                 B.2 Modified Newton's Method / 706 \\
                 B.3 Secant Method / 706 \\
                 Reference / 706 \\
                 Appendix C: About the Software / 707 \\
                 Index / 709 \\
                 Index of Computer Programs / 715",
  xxauthor =     "Shan-chieh Chang and Shanjie Zhang and Jianming Jin",
  xxnote =       "There is online bookstore and library catalog
                 confusion over the authors of this book. The
                 publisher's Web page at
                 http://catalog.wiley.com/remsrch.cgi has Shan-jie Zhang
                 (Nanjing Univ., China) / Jianming Jin (Univ. of
                 Illinois at Urbana-Champaign), and a price of
                 US\$125.00. It looks like Shan-chieh Chang is merely a
                 different English transcription of Shanjie Zhang.
                 http://www.fatbrain.com/ lists this book for US\$99.95.
                 My copy of the book lists the authors as Shanjie Zhang
                 and Jianming Jin in four places.",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1996:NTM
author: J. Zhang
title: A note on the tau-method approximations for the Bessel functions $ Y_0 (z) $ and $ Y_1 (z) $
journal: j-COMPUT-MATH-APPL
volume: 31
number: 9
pages: 63--70
month: may
monthnumber: 5
year: 1996
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(96)00043-0
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sun Jun 12 08:43:36 2011
bibtimestamp: 2011.06.12 08:43:36 ???
URL: http://www.sciencedirect.com/science/article/pii/0898122196000430
fjournal: Computers and Mathematics with Applications
keywords: Automated $tau $-method; Bessel functions; Chebyshev series; Symbolic Faber polynomials
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. Zhang
rawtitle: A note on the tau-method approximations for the {Bessel} functions {$ Y_0 (z) $} and {$ Y_1 (z) $}
abstract:
This paper is to complete and improve the work reported in [1,2], using the Lanczos $ tau $-method (in Coleman's version) to approximate the Bessel functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane. These Faber polynomials are used as the perturbation terms in the $ tau $-method. Numerical comparison among the power series, the Chebyshev series and the $ tau $-method are conducted to show the accuracy improvement achieved by this new version of the $ tau $-method. Some concluding remarks and suggestions on future research are given.

rawabstract:
This paper is to complete and improve the work reported in [1,2], using the Lanczos $ \tau $-method (in Coleman's version) to approximate the Bessel functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane. These Faber polynomials are used as the perturbation terms in the $ \tau $-method. Numerical comparison among the power series, the Chebyshev series and the $ \tau $-method are conducted to show the accuracy improvement achieved by this new version of the $ \tau $-method. Some concluding remarks and suggestions on future research are given.

entry:
@Article{Zhang:1996:NTM,
  author =       "J. Zhang",
  title =        "A note on the tau-method approximations for the
                 {Bessel} functions {$ Y_0 (z) $} and {$ Y_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "31",
  number =       "9",
  pages =        "63--70",
  month =        may,
  year =         "1996",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(96)00043-0",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 08:43:36 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122196000430",
  abstract =     "This paper is to complete and improve the work
                 reported in [1,2], using the Lanczos $ \tau $-method
                 (in Coleman's version) to approximate the Bessel
                 functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce
                 symbolic representations of the scaled Faber
                 polynomials on any fan-shaped section of the complex
                 plane. These Faber polynomials are used as the
                 perturbation terms in the $ \tau $-method. Numerical
                 comparison among the power series, the Chebyshev series
                 and the $ \tau $-method are conducted to show the
                 accuracy improvement achieved by this new version of
                 the $ \tau $-method. Some concluding remarks and
                 suggestions on future research are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Automated $\tau$-method; Bessel functions; Chebyshev
                 series; Symbolic Faber polynomials",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1996:SNC
author: Jun Zhang
title: Symbolic and numerical computation on Bessel functions of complex argument and large magnitude
journal: j-J-COMPUT-APPL-MATH
volume: 75
number: 1
pages: 99--118
day: 12
month: nov
monthnumber: 11
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796000635
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jun Zhang
rawtitle: Symbolic and numerical computation on {Bessel} functions of complex argument and large magnitude
entry:
@Article{Zhang:1996:SNC,
  author =       "Jun Zhang",
  title =        "Symbolic and numerical computation on {Bessel}
                 functions of complex argument and large magnitude",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "1",
  pages =        "99--118",
  day =          "12",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000635",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Abad:1997:NEC
author: Julio Abad and Javier Sesma
title: A new expansion of the confluent hypergeometric function in terms of modified Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 78
number: 1
pages: 97--101
day: 3
month: feb
monthnumber: 2
year: 1997
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:59 MST 2017
bibtimestamp: 2017.02.25 12:35:59 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796001331
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Julio Abad and Javier Sesma
rawtitle: A new expansion of the confluent hypergeometric function in terms of modified {Bessel} functions
entry:
@Article{Abad:1997:NEC,
  author =       "Julio Abad and Javier Sesma",
  title =        "A new expansion of the confluent hypergeometric
                 function in terms of modified {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "78",
  number =       "1",
  pages =        "97--101",
  day =          "3",
  month =        feb,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:59 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001331",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1997:HMI
author: Horst Alzer
title: A harmonic mean inequality for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 87
number: 2
pages: 195--198
day: 23
month: dec
monthnumber: 12
year: 1997
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:06 MST 2017
bibtimestamp: 2017.02.25 12:36:06 MST
note: See corrigendum cite Alzer:1998:CHM.
URL: http://www.sciencedirect.com/science/article/pii/S0377042796001811
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Horst Alzer
rawnote: See corrigendum \cite{Alzer:1998:CHM}.
rawtitle: A harmonic mean inequality for the gamma function
entry:
@Article{Alzer:1997:HMI,
  author =       "Horst Alzer",
  title =        "A harmonic mean inequality for the gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "87",
  number =       "2",
  pages =        "195--198",
  day =          "23",
  month =        dec,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  note =         "See corrigendum \cite{Alzer:1998:CHM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001811",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1997:SIG
author: Horst Alzer
title: On some inequalities for the gamma and psi functions
journal: j-MATH-COMPUT
volume: 66
number: 217
pages: 373--389
month: jan
monthnumber: 1
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B15 (26D07)
MRnumber: 97e:33004
MRreviewer: Peter Schroth
bibdate: Fri Jul 16 10:38:40 MDT 1999
bibsource: http://www.ams.org/mcom/1997-66-217; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:40 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Horst Alzer
rawtitle: On some inequalities for the gamma and psi functions
entry:
@Article{Alzer:1997:SIG,
  author =       "Horst Alzer",
  title =        "On some inequalities for the gamma and psi functions",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "373--389",
  month =        jan,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (26D07)",
  MRnumber =     "97e:33004",
  MRreviewer =   "Peter Schroth",
  bibdate =      "Fri Jul 16 10:38:40 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-217;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1997:SII
author: Horst Alzer
title: On some inequalities for the incomplete gamma function
journal: j-MATH-COMPUT
volume: 66
number: 218
pages: 771--778
month: apr
monthnumber: 4
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B20 (26D07)
MRnumber: 97h:33004
bibdate: Fri Jul 16 10:38:42 MDT 1999
bibsource: http://www.ams.org/mcom/1997-66-218; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:42 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Horst Alzer
rawtitle: On some inequalities for the incomplete gamma function
entry:
@Article{Alzer:1997:SII,
  author =       "Horst Alzer",
  title =        "On some inequalities for the incomplete gamma
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "218",
  pages =        "771--778",
  month =        apr,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B20 (26D07)",
  MRnumber =     "97h:33004",
  bibdate =      "Fri Jul 16 10:38:42 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-218;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Bailey:1997:RCV
author: David Bailey and Peter Borwein and Simon Plouffe
title: On the rapid computation of various polylogarithmic constants
journal: j-MATH-COMPUT
volume: 66
number: 218
pages: 903--913
month: apr
monthnumber: 4
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Yxx
MRnumber: 1 415 794
bibdate: Fri Jul 16 10:38:42 MDT 1999
bibtimestamp: 1999.07.16 10:38:42 MDT
URL: http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf
fjournal: Mathematics of Computation
keywords: BBP formula
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: David Bailey and Peter Borwein and Simon Plouffe
rawtitle: On the rapid computation of various polylogarithmic constants
bibsource:
http://www.ams.org/mcom/1997-66-218; http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

entry:
@Article{Bailey:1997:RCV,
  author =       "David Bailey and Peter Borwein and Simon Plouffe",
  title =        "On the rapid computation of various polylogarithmic
                 constants",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "218",
  pages =        "903--913",
  month =        apr,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Yxx",
  MRnumber =     "1 415 794",
  bibdate =      "Fri Jul 16 10:38:42 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-218;
                 http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "BBP formula",
  xxnote =       "See \cite{Adamchik:1997:SF}.",
}


bibtype: article
filename: elefunt.bib
label: Blinn:1997:JBC
author: James F. Blinn
title: Jim Blinn's Corner: Floating-Point Tricks
journal: j-IEEE-CGA
volume: 17
number: 4
pages: 80--84
month: jul
monthnumber: 7
year: 1997
CODEN: ICGADZ
DOI: https://doi.org/10.1109/38.595279
ISSN: 0272-1716 (print), 1558-1756 (electronic) OR 02721716 (print), 15581756 (electronic)
ISSNL: 0272-1716 OR 02721716
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Computer Graphics and Applications
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/portal/web/csdl/magazines/cga
rawauthor: James F. Blinn
rawtitle: {Jim Blinn}'s Corner: Floating-Point Tricks
note:
Discusses use of IEEE 754 single-precision floating-point bit patterns as integers for implementations of fast, but low-accuracy, functions useful in computer graphics.

rawnote:
Discusses use of IEEE 754 single-precision floating-point bit patterns as integers for implementations of fast, but low-accuracy, functions useful in computer graphics.

entry:
@Article{Blinn:1997:JBC,
  author =       "James F. Blinn",
  title =        "{Jim Blinn}'s Corner: Floating-Point Tricks",
  journal =      j-IEEE-CGA,
  volume =       "17",
  number =       "4",
  pages =        "80--84",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/38.595279",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Discusses use of IEEE 754 single-precision
                 floating-point bit patterns as integers for
                 implementations of fast, but low-accuracy, functions
                 useful in computer graphics.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
  summary =      "The author discusses IEEE floating point
                 representation that stores numbers in what amounts to
                 scientific notation. He considers the sign bit, the
                 logarithm function, function approximations, errors and
                 refinements \ldots{}",
}


bibtype: incollection
filename: elefunt.bib
label: Borwein:1997:AGMa
author: J. M. Borwein and P. B. Borwein
title: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
crossref: Berggren:1997:PSB
pages: 537--552
year: 1997
DOI: https://doi.org/10.1007/978-1-4757-2736-4_56
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1984:AGM.
URL: http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawnote: Reprint of \cite{Borwein:1984:AGM}.
rawtitle: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InCollection{Borwein:1997:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:1997:PSB",
  pages =        "537--552",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: elefunt.bib
label: Bshouty:1997:TBA
author: Nader H. Bshouty and Yishay Mansour and Baruch Schieber and Prasoon Tiwari
title: A tight bound for approximating the square root
journal: j-INFO-PROC-LETT
volume: 63
number: 4
pages: 211--213
day: 10
month: sep
monthnumber: 9
year: 1997
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68Q25 (65B15 68Q40)
MRnumber: 1 477 306
bibdate: Sat Nov 7 17:55:54 MST 1998
bibtimestamp: 1998.11.07 17:55:54 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Nader H. Bshouty and Yishay Mansour and Baruch Schieber and Prasoon Tiwari
rawtitle: A tight bound for approximating the square root
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Bshouty:1997:TBA,
  author =       "Nader H. Bshouty and Yishay Mansour and Baruch
                 Schieber and Prasoon Tiwari",
  title =        "A tight bound for approximating the square root",
  journal =      j-INFO-PROC-LETT,
  volume =       "63",
  number =       "4",
  pages =        "211--213",
  day =          "10",
  month =        sep,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68Q25 (65B15 68Q40)",
  MRnumber =     "1 477 306",
  bibdate =      "Sat Nov 7 17:55:54 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: article
filename: elefunt.bib
label: El-Gabali:1997:MTA
author: Magdi A. El-Gabali
title: Multiple-term approximations for Appell's $ F_1 $ function
journal: j-J-AUSTRAL-MATH-SOC-SER-B
volume: 39
number: 1
pages: 135--148
month: jul
monthnumber: 7
year: 1997
CODEN: JAMMDU
DOI: https://doi.org/10.1017/S0334270000009267
ISSN: 0334-2700 OR 03342700
ISSNL: 0334-2700 OR 03342700
bibdate: Fri Apr 26 16:13:39 MDT 2019
bibtimestamp: 2019.04.26 16:13:39 MDT
fjournal: Journal of the Australian Mathematical Society. Series B, Applied Mathematics
acknowledgement: ack-nhfb
ajournal: J. Austral Math. Soc. Ser. B
journalURL: http://journals.cambridge.org/action/displayJournal?jid=ANZ
onlinedate: 17 February 2009
rawauthor: Magdi A. El-Gabali
rawtitle: Multiple-term approximations for {Appell}'s {$ F_1 $} function
bibsource:
https://www.math.utah.edu/pub/tex/bib/anziamj.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
https://www.cambridge.org/core/journals/anziam-journal/article/multipleterm-approximations-for-appells-f1-function/8E218109899D68FD0DC15B6E9D61E8BD

entry:
@Article{El-Gabali:1997:MTA,
  author =       "Magdi A. El-Gabali",
  title =        "Multiple-term approximations for {Appell}'s {$ F_1 $}
                 function",
  journal =      j-J-AUSTRAL-MATH-SOC-SER-B,
  volume =       "39",
  number =       "1",
  pages =        "135--148",
  month =        jul,
  year =         "1997",
  CODEN =        "JAMMDU",
  DOI =          "https://doi.org/10.1017/S0334270000009267",
  ISSN =         "0334-2700",
  ISSN-L =       "0334-2700",
  bibdate =      "Fri Apr 26 16:13:39 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/journals/anziam-journal/article/multipleterm-approximations-for-appells-f1-function/8E218109899D68FD0DC15B6E9D61E8BD",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Austral Math. Soc. Ser. B",
  fjournal =     "Journal of the Australian Mathematical Society. Series
                 B, Applied Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  onlinedate =   "17 February 2009",
}


bibtype: article
filename: elefunt.bib
label: Fdil:1997:SRC
author: A. Fdil
title: Some results of convergence acceleration for a general $ Theta $-type algorithm
journal: j-APPL-NUM-MATH
volume: 23
number: 2
pages: 219--240
day: 21
month: mar
monthnumber: 3
year: 1997
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65B10 (65D32)
MRnumber: 1 437 884
bibdate: Wed Jul 28 14:36:42 MDT 1999
bibtimestamp: 1999.07.28 14:36:42 MDT
URL: http://www.elsevier.com/cas/tree/store/apnum/sub/1997/23/2/738.pdf
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: A. Fdil
rawtitle: Some results of convergence acceleration for a general {$ \Theta $}-type algorithm
bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1997&volume=23&issue=2; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Fdil:1997:SRC,
  author =       "A. Fdil",
  title =        "Some results of convergence acceleration for a general
                 {$ \Theta $}-type algorithm",
  journal =      j-APPL-NUM-MATH,
  volume =       "23",
  number =       "2",
  pages =        "219--240",
  day =          "21",
  month =        mar,
  year =         "1997",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B10 (65D32)",
  MRnumber =     "1 437 884",
  bibdate =      "Wed Jul 28 14:36:42 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1997&volume=23&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cas/tree/store/apnum/sub/1997/23/2/738.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Forrey:1997:CHF
author: Robert C. Forrey
title: Computing the hypergeometric function
journal: j-J-COMPUT-PHYS
volume: 137
number: 1
pages: 79--100
month: oct
monthnumber: 10
year: 1997
CODEN: JCTPAH
DOI: https://doi.org/10.1006/jcph.1997.5794
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
MRclass: 33C05 (33-04 65D20)
MRnumber: MR1481885 (99g:33004)
bibdate: Thu Dec 01 09:06:55 2011
bibtimestamp: 2011.12.01 09:06:55 ???
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Robert C. Forrey
rawtitle: Computing the hypergeometric function
remark:
The author gives a FORTRAN program for computing $_2 F_1$ for real variable and parameters, using rapidly-convergent power series in six separate intervals.

entry:
@Article{Forrey:1997:CHF,
  author =       "Robert C. Forrey",
  title =        "Computing the hypergeometric function",
  journal =      j-J-COMPUT-PHYS,
  volume =       "137",
  number =       "1",
  pages =        "79--100",
  month =        oct,
  year =         "1997",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1997.5794",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  MRclass =      "33C05 (33-04 65D20)",
  MRnumber =     "MR1481885 (99g:33004)",
  bibdate =      "Thu Dec 01 09:06:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "The author gives a FORTRAN program for computing $_2
                 F_1$ for real variable and parameters, using
                 rapidly-convergent power series in six separate
                 intervals.",
}


bibtype: article
filename: elefunt.bib
label: Ghanem:1997:SBF
author: Riadh Ben Ghanem and Clement Frappier
title: Spherical Bessel functions and explicit quadrature formula
journal: j-MATH-COMPUT
volume: 66
number: 217
pages: 289--296
month: jan
monthnumber: 1
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33C10 (41A55 65D32)
MRnumber: 97c:33005
MRreviewer: N. Hayek Calil
bibdate: Fri Jul 16 10:38:40 MDT 1999
bibsource: http://www.ams.org/mcom/1997-66-217; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:40 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Riadh Ben Ghanem and Cl{\'e}ment Frappier
rawtitle: Spherical {Bessel} functions and explicit quadrature formula
entry:
@Article{Ghanem:1997:SBF,
  author =       "Riadh Ben Ghanem and Cl{\'e}ment Frappier",
  title =        "Spherical {Bessel} functions and explicit quadrature
                 formula",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "289--296",
  month =        jan,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33C10 (41A55 65D32)",
  MRnumber =     "97c:33005",
  MRreviewer =   "N. Hayek Calil",
  bibdate =      "Fri Jul 16 10:38:40 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-217;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Goano:1997:RA7
author: Michele Goano
title: Remark on Algorithm 745
journal: j-TOMS
volume: 23
number: 2
pages: 295--295
month: jun
monthnumber: 6
year: 1997
CODEN: ACMSCU
DOI: https://doi.org/10.1145/264029.643581
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 9 10:19:38 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.03.09 10:19:38 ???
note: See cite Goano:1995:ACC.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Michele Goano
rawnote: See \cite{Goano:1995:ACC}.
rawtitle: Remark on {Algorithm 745}
entry:
@Article{Goano:1997:RA7,
  author =       "Michele Goano",
  title =        "Remark on {Algorithm 745}",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "295--295",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.643581",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:19:38 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Goano:1995:ACC}.",
  acknowledgement = ack-rfb # " and " # ack-kr # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Hare:1997:CPB
author: D. E. G. Hare
title: Computing the Principal Branch of log-Gamma
journal: j-J-ALG
volume: 25
number: 2
pages: 221--236
month: nov
monthnumber: 11
year: 1997
CODEN: JOALDV
DOI: https://doi.org/10.1006/jagm.1997.0881
ISSN: 0196-6774 (print), 1090-2678 (electronic) OR 01966774 (print), 10902678 (electronic)
ISSNL: 0196-6774 OR 01966774
bibdate: Tue Dec 11 09:16:52 MST 2012
bibtimestamp: 2012.12.11 09:16:52 MST
URL: http://www.sciencedirect.com/science/article/pii/S0196677497908816
fjournal: Journal of Algorithms
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01966774
rawauthor: D. E. G. Hare
rawtitle: Computing the Principal Branch of {log-Gamma}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jalg.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib

abstract:
The log-Gamma function is an important special function of mathematics, and its principal branch is required in many applications. We develop here the mathematics required to evaluate the principal branch to arbitrary precision, including a new bound for the error in Stirling's asymptotic series. We conclude with a discussion of the implementation of the principal branch of the log-Gamma function in the Maple symbolic algebra system, starting with version Maple V, Release 3.

rawabstract:
The log-Gamma function is an important special function of mathematics, and its principal branch is required in many applications. We develop here the mathematics required to evaluate the principal branch to arbitrary precision, including a new bound for the error in Stirling's asymptotic series. We conclude with a discussion of the implementation of the principal branch of the log-Gamma function in the Maple symbolic algebra system, starting with version Maple V, Release 3.

entry:
@Article{Hare:1997:CPB,
  author =       "D. E. G. Hare",
  title =        "Computing the Principal Branch of {log-Gamma}",
  journal =      j-J-ALG,
  volume =       "25",
  number =       "2",
  pages =        "221--236",
  month =        nov,
  year =         "1997",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1006/jagm.1997.0881",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:16:52 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0196677497908816",
  abstract =     "The log-Gamma function is an important special
                 function of mathematics, and its principal branch is
                 required in many applications. We develop here the
                 mathematics required to evaluate the principal branch
                 to arbitrary precision, including a new bound for the
                 error in Stirling's asymptotic series. We conclude with
                 a discussion of the implementation of the principal
                 branch of the log-Gamma function in the Maple symbolic
                 algebra system, starting with version Maple V, Release
                 3.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}


bibtype: article
filename: elefunt.bib
label: Harris:1997:NAC
author: Frank E. Harris
title: New Approach to Calculation of the Leaky Aquifer Function
journal: j-IJQC
volume: 63
number: 5
pages: 913--916
year: 1997
CODEN: IJQCB2
DOI: https://doi.org/10.1002/(SICI)1097-461X(1997)63:5<913::AID-QUA1>3.0.CO%3B2-Z
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Tue Oct 4 06:59:09 MDT 2011
bibtimestamp: 2011.10.04 06:59:09 MDT
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Int. J. Quantum Chem.
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
journalabr: Int J Quant Chem
onlinedate: 6 Dec 1998
rawauthor: Frank E. Harris
rawtitle: New Approach to Calculation of the Leaky Aquifer Function
bibsource:
Compendex database; http://www.interscience.wiley.com/jpages/0020-7608; http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ijqc.bib; https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42641; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42641&PLACEBO=IE.pdf

entry:
@Article{Harris:1997:NAC,
  author =       "Frank E. Harris",
  title =        "New Approach to Calculation of the Leaky Aquifer
                 Function",
  journal =      j-IJQC,
  volume =       "63",
  number =       "5",
  pages =        "913--916",
  month =        "????",
  year =         "1997",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1997)63:5<913::AID-QUA1>3.0.CO%3B2-Z",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:09 MDT 2011",
  bibsource =    "Compendex database;
                 http://www.interscience.wiley.com/jpages/0020-7608;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42641;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42641&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  journalabr =   "Int J Quant Chem",
  onlinedate =   "6 Dec 1998",
}


bibtype: article
filename: elefunt.bib
label: Ito:1997:EIA
author: M. Ito and N. Takagi and S. Yajima
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 4
pages: 495--498
month: apr
monthnumber: 4
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.588066
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:22 MDT 2011
bibtimestamp: 2011.07.06 10:06:22 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Ito and N. Takagi and S. Yajima
title:
Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification

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/ieeetranscomput1990.bib

rawtitle:
Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification

entry:
@Article{Ito:1997:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  title =        "Efficient initial approximation for multiplicative
                 division and square root by a multiplication with
                 operand modification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "495--498",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588066",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 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/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An efficient initial approximation method for
                 multiplicative division and square root is proposed. It
                 is a modification of the piecewise linear
                 approximation. The multiplication and the addition
                 required for the linear approximation are replaced by
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Karp:1997:HPD
author: Alan H. Karp and Peter Markstein
title: High-Precision Division and Square Root
journal: j-TOMS
volume: 23
number: 4
pages: 561--589
month: dec
monthnumber: 12
year: 1997
CODEN: ACMSCU
DOI: https://doi.org/10.1145/279232.279237
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Nov 8 14:50:37 2007
bibtimestamp: 2007.11.08 14:50:37 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms, performance, division, quad precision, square root.
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Alan H. Karp and Peter Markstein
rawtitle: High-Precision Division and Square Root
bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.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/toms.bib

URL:
http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/

abstract:
We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.

subject:
G.1.0 [Numerical Analysis]: General -- computer arithmetic. G.4 [Mathematics of Computing]: Mathematical Software.

rawabstract:
We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.

entry:
@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.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/toms.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
  abstract =     "We present division and square root algorithms for
                 calculation with more bits than are handled by the
                 floating-point hardware. These algorithms avoid the
                 need to multiply two high-precision numbers, speeding
                 up the last iteration by as much as a factor of 10. We
                 also show how to produce the floating-point number
                 closest to the exact result with relatively few
                 additional operations.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, division, quad precision,
                 square root.",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic. G.4 [Mathematics of Computing]:
                 Mathematical Software.",
}


bibtype: book
filename: elefunt.bib
label: Khinchin:1997:CF
author: Aleksandr Yakovlevich Khinchin and Herbert Eagle
title: Continued Fractions
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xi + 95
year: 1997
ISBN: 0-486-69630-8 (paperback) OR 0486696308 (paperback)
ISBN13: 978-0-486-69630-0 (paperback) OR 9780486696300 (paperback)
LCCN: QA295 .K513 1997
bibdate: Wed Apr 15 16:52:20 MDT 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2009.04.15 16:52:20 MDT
subject: Continued fractions
acknowledgement: ack-nhfb
authordates: 1894--1959
rawauthor: Aleksandr Yakovlevich Khinchin and Herbert Eagle
rawtitle: Continued Fractions
URL:
http://www.loc.gov/catdir/description/dover032/97008056.html; http://www.loc.gov/catdir/toc/dover031/97008056.html

remark:
Translated from the Russian by Scripta Technica, Inc. Originally published: Chicago : University of Chicago Press, 1964. Edited by Herbert Eagle.

TOC:
Chapter I. Properties of the Apparatus 1. Introduction 2. Convergents 3. Infinite continued fractions 4. Continued fractions with natural elements Chapter II. The Representation of Numbers by Continued Fractions 5. Continued fractions as an apparatus for representing real numbers 6. Convergents as best approximations 7. The order of approximation 8. General approximation theorems 9. The approximation of algebraic irrational numbers and Liouville's transcendental numbers 10. Quadratic irrational numbers and periodic continued fractions Chapter III. The Measure Theory of Continued Fractions 11. Introduction 12. The elements as functions of the number represented 13. Measure-theoretic evaluation of the increase in the elements 14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation 15. Gauss's problem and Kuz'min's theorem 16. Average values Index

rawTOC:
Chapter I. Properties of the Apparatus\\ 1. Introduction\\ 2. Convergents\\ 3. Infinite continued fractions\\ 4. Continued fractions with natural elements\\ Chapter II. The Representation of Numbers by Continued Fractions\\ 5. Continued fractions as an apparatus for representing real numbers\\ 6. Convergents as best approximations\\ 7. The order of approximation\\ 8. General approximation theorems\\ 9. The approximation of algebraic irrational numbers and Liouville's transcendental numbers\\ 10. Quadratic irrational numbers and periodic continued fractions\\ Chapter III. The Measure Theory of Continued Fractions\\ 11. Introduction\\ 12. The elements as functions of the number represented\\ 13. Measure-theoretic evaluation of the increase in the elements\\ 14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation\\ 15. Gauss's problem and Kuz'min's theorem\\ 16. Average values\\ Index

entry:
@Book{Khinchin:1997:CF,
  author =       "Aleksandr Yakovlevich Khinchin and Herbert Eagle",
  title =        "Continued Fractions",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 95",
  year =         "1997",
  ISBN =         "0-486-69630-8 (paperback)",
  ISBN-13 =      "978-0-486-69630-0 (paperback)",
  LCCN =         "QA295 .K513 1997",
  bibdate =      "Wed Apr 15 16:52:20 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/97008056.html;
                 http://www.loc.gov/catdir/toc/dover031/97008056.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1959",
  remark =       "Translated from the Russian by Scripta Technica, Inc.
                 Originally published: Chicago : University of Chicago
                 Press, 1964. Edited by Herbert Eagle.",
  subject =      "Continued fractions",
  tableofcontents = "Chapter I. Properties of the Apparatus\\
                 1. Introduction\\
                 2. Convergents\\
                 3. Infinite continued fractions\\
                 4. Continued fractions with natural elements\\
                 Chapter II. The Representation of Numbers by Continued
                 Fractions\\
                 5. Continued fractions as an apparatus for representing
                 real numbers\\
                 6. Convergents as best approximations\\
                 7. The order of approximation\\
                 8. General approximation theorems\\
                 9. The approximation of algebraic irrational numbers
                 and Liouville's transcendental numbers\\
                 10. Quadratic irrational numbers and periodic continued
                 fractions\\
                 Chapter III. The Measure Theory of Continued
                 Fractions\\
                 11. Introduction\\
                 12. The elements as functions of the number
                 represented\\
                 13. Measure-theoretic evaluation of the increase in the
                 elements\\
                 14. Measure-theoretic evaluation of the increase in the
                 denominators of the convergents. The fundamental
                 theorem of the measure theory of approximation\\
                 15. Gauss's problem and Kuz'min's theorem\\
                 16. Average values\\
                 Index",
  xxURL =        "http://www.loc.gov/catdir/description/dover032/97008056.html;
                 http://www.loc.gov/catdir/toc/dover031/97008056.html",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1997:TEH
author: K. S. Kolbig
journal: j-MATH-COMPUT
volume: 66
number: 220
pages: 1767--1767
month: oct
monthnumber: 10
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 44-00 (33-00)
MRnumber: 1 434 945
bibdate: Tue Dec 2 11:25:56 MST 1997
bibtimestamp: 1997.12.02 11:25:56 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: K. S. K{\"o}lbig
title:
Table errata: booktitle Handbook of elliptic integrals for engineers and scientists [Second edition, Springer, New York, 1971, MR bf 43 #3506] by P. F. Byrd and M. D. Friedman

rawtitle:
Table errata: {{\booktitle{Handbook of elliptic integrals for engineers and scientists}} [Second edition, Springer, New York, 1971, MR {\bf 43} \#3506] by P. F. Byrd and M. D. Friedman}

entry:
@Article{Kolbig:1997:TEH,
  author =       "K. S. K{\"o}lbig",
  title =        "Table errata: {{\booktitle{Handbook of elliptic
                 integrals for engineers and scientists}} [Second
                 edition, Springer, New York, 1971, MR {\bf 43} \#3506]
                 by P. F. Byrd and M. D. Friedman}",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "220",
  pages =        "1767--1767",
  month =        oct,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "44-00 (33-00)",
  MRnumber =     "1 434 945",
  bibdate =      "Tue Dec 2 11:25:56 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


