# bibtab

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

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

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

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

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


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

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


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

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

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


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

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


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

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

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


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

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

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


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


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


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

entry:
@Article{Majithia:1971:CAN,
  author =       "J. C. Majithia and R. Kitai",
  title =        "A Cellular Array for the Nonrestoring Extraction of
                 Square Roots",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1617--1618",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223191",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
  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: Matta:1971:UCE
author: F. Matta and A. Reichel
title: Uniform Computation of the Error Function and Other Related Functions
journal: j-MATH-COMPUT
volume: 25
number: 114
pages: 339--344
month: apr
monthnumber: 4
year: 1971
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1971-0295538-4
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0295538-4
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: F. Matta and A. Reichel
rawtitle: Uniform Computation of the Error Function and Other Related Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database

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


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

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

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


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

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


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

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

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

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


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


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

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

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


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


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


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

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

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


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

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


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

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

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

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


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


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

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

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

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


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

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

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

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

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


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

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


bibtype: article
filename: elefunt.bib
label: Chen:1972:ACE
author: Tien Chi Chen
title: Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots
journal: j-IBM-JRD
volume: 16
number: 4
pages: 380--388
month: jul
monthnumber: 7
year: 1972
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65D20
MRnumber: 49 \#1738
bibdate: Tue Mar 25 14:26:59 MST 1997
bibtimestamp: 1997.03.25 14:26:59 MST
URL: http://www.research.ibm.com/journal/rd/164/chen.pdf
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: IBM, San Jose, CA, USA
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: F. Gotze
treatment: P Practical
rawauthor: Tien Chi Chen
rawtitle: Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots
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

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

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

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

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


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

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


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

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

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

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


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

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


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

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


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

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


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

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

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


bibtype: article
filename: elefunt.bib
label: Kolbig:1972:PCL
author: K. S. Kolbig
journal: j-COMP-PHYS-COMM
volume: 4
number: 2
pages: 221--226
month: nov
monthnumber: 11
year: 1972
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(72)90012-4
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Oct 30 08:33:42 2010
bibtimestamp: 2010.10.30 08:33:42 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: K. S. K{\"o}lbig
title:
Programs for Computing the Logarithm of the Gamma Function, and the Digamma Function, for Complex Argument

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

rawtitle:
Programs for Computing the Logarithm of the Gamma Function, and the Digamma Function, for Complex Argument

entry:
@Article{Kolbig:1972:PCL,
  author =       "K. S. K{\"o}lbig",
  title =        "Programs for Computing the Logarithm of the Gamma
                 Function, and the Digamma Function, for Complex
                 Argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "4",
  number =       "2",
  pages =        "221--226",
  month =        nov,
  year =         "1972",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(72)90012-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 08:33:42 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1972:RCC
author: K. S. Kolbig
title: Remarks on the Computation of Coulomb Wavefunctions
journal: j-COMP-PHYS-COMM
volume: 4
number: 2
pages: 214--220
month: nov
monthnumber: 11
year: 1972
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(72)90011-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Oct 30 08:35:38 2010
bibtimestamp: 2010.10.30 08:35:38 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: K. S. K{\"o}lbig
rawtitle: Remarks on the Computation of {Coulomb} Wavefunctions
entry:
@Article{Kolbig:1972:RCC,
  author =       "K. S. K{\"o}lbig",
  title =        "Remarks on the Computation of {Coulomb}
                 Wavefunctions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "4",
  number =       "2",
  pages =        "214--220",
  month =        nov,
  year =         "1972",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(72)90011-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 08:35:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1972:ZIG
author: K. S. Kolbig
title: On the Zeros of the Incomplete Gamma Function
journal: j-MATH-COMPUT
volume: 26
number: 119
pages: 751--755
month: jul
monthnumber: 7
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: CERN, Geneva, Switzerland
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: K. S. Kolbig
rawtitle: On the Zeros of the Incomplete Gamma Function
keywords:
asymptotic formulae; complex w plane; function approximation; incomplete gamma function; poles and zeros; zeros

entry:
@Article{Kolbig:1972:ZIG,
  author =       "K. S. Kolbig",
  title =        "On the Zeros of the Incomplete Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "119",
  pages =        "751--755",
  month =        jul,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "CERN, Geneva, Switzerland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic formulae; complex w plane; function
                 approximation; incomplete gamma function; poles and
                 zeros; zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Kuki:1972:AAC
author: Hirondo Kuki
title: ACM Algorithm 421: Complex Gamma Function with Error Control [S14]
journal: j-CACM
volume: 15
number: 4
pages: 271--272
month: apr
monthnumber: 4
year: 1972
CODEN: CACMA2
DOI: https://doi.org/10.1145/361284.361296
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65D20
MRnumber: 47 1249
MRreviewer: L. Fox
bibdate: Mon Jan 22 06:56:30 MST 2001
bibtimestamp: 2001.01.22 06:56:30 MST
fjournal: Communications of the ACM
remark: Fullerton: 100-line FORTRAN routine with double complex accuracy to $ 10^-14 $.
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation); C7310 (Mathematics computing)
corpsource: Univ. Chicago, IL, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: Hirondo Kuki
rawtitle: {ACM Algorithm 421}: Complex Gamma Function with Error Control [{S14}]
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
algorithm; complex; complex gamma function; complex loggamma; error control; FORTRAN; function; function approximation; loggamma function; programme; subroutines

entry:
@Article{Kuki:1972:AAC,
  author =       "Hirondo Kuki",
  title =        "{ACM Algorithm 421}: Complex Gamma Function with Error
                 Control [{S14}]",
  journal =      j-CACM,
  volume =       "15",
  number =       "4",
  pages =        "271--272",
  month =        apr,
  year =         "1972",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/361284.361296",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65D20",
  MRnumber =     "47 1249",
  MRreviewer =   "L. Fox",
  bibdate =      "Mon Jan 22 06:56:30 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics computing)",
  corpsource =   "Univ. Chicago, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; complex; complex gamma function; complex
                 loggamma; error control; FORTRAN; function; function
                 approximation; loggamma function; programme;
                 subroutines",
  oldlabel =     "Kuki72a",
  remark =       "Fullerton: 100-line FORTRAN routine with double
                 complex accuracy to $ 10^{-14} $.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}


bibtype: article
filename: elefunt.bib
label: Kuki:1972:CGF
author: Hirondo Kuki
title: Complex Gamma Function with Error Control [S14]
journal: j-CACM
volume: 15
number: 4
pages: 262--267
month: apr
monthnumber: 4
year: 1972
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65D20
MRnumber: 47 1249
MRreviewer: L. Fox
bibdate: Mon Jan 22 06:56:30 MST 2001
bibtimestamp: 2001.01.22 06:56:30 MST
fjournal: Communications of the ACM
remark: Fullerton: Description of a FORTRAN routine with some math details.
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation); C7310 (Mathematics computing)
corpsource: Univ. Chicago, IL, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: Hirondo Kuki
rawtitle: Complex Gamma Function with Error Control [{S14}]
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
algorithm; complex; complex gamma function; complex loggamma; error control; FORTRAN; function; function approximation; loggamma function; programme; subroutines

entry:
@Article{Kuki:1972:CGF,
  author =       "Hirondo Kuki",
  title =        "Complex Gamma Function with Error Control [{S14}]",
  journal =      j-CACM,
  volume =       "15",
  number =       "4",
  pages =        "262--267",
  month =        apr,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65D20",
  MRnumber =     "47 1249",
  MRreviewer =   "L. Fox",
  bibdate =      "Mon Jan 22 06:56:30 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics computing)",
  corpsource =   "Univ. Chicago, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; complex; complex gamma function; complex
                 loggamma; error control; FORTRAN; function; function
                 approximation; loggamma function; programme;
                 subroutines",
  oldlabel =     "Kuki72a",
  remark =       "Fullerton: Description of a FORTRAN routine with some
                 math details.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}


bibtype: book
filename: elefunt.bib
label: Lebedev:1972:SFT
author: N. N. (Nikolai Nikolaevich) Lebedev
title: Special functions and their applications
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xii + 308
year: 1972
ISBN: 0-486-60624-4 (paperback) OR 0486606244 (paperback)
ISBN13: 978-0-486-60624-8 (paperback) OR 9780486606248 (paperback)
LCCN: QA351 .L3613 1972
bibdate: Sat Oct 30 16:25:05 MDT 2010
bibtimestamp: 2010.10.30 16:25:05 MDT
note: Translated to English and edited by Richard A. Silverman.
URL: http://www.loc.gov/catdir/description/dover031/72086228.html
remark: Translation of Speetisialnye funketisii i ikh prilozhenieiia.
subject: Functions, Special; Mathematical physics
acknowledgement: ack-nhfb
rawauthor: N. N. (Nikolai Nikolaevich) Lebedev
rawnote: Translated to English and edited by Richard A. Silverman.
rawtitle: Special functions and their applications
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager

TOC:
1 The Gamma Function 1.1. Definition of the Gamma Function 1.2. Some Relations Satisfied by the Gamma Function 1.3. The Logarithmic Derivative of the Gamma Function 1.4. Asymptotic Representation of the Gamma Function for Large $|z|$ 1.5. Definite Integrals Related to the Gamma Function Problems 2 The Probability Integral and Related Functions 2.1. The Probability Integral and Its Basic Properties 2.2. Asymptotic Representation of the Probability Integral for Large $|z|$ 2.3. The Probability Integral of Imaginary Argument. The Function $F(z)$ 2.4. The Probability Integral of Argument $sqrt i x$. The Fresnel Integrals, 21. 2.5. Application to Probability Theory 2.6. Application to the Theory of Heat Conduction. Cooling of the Surface of a Heated Object 2.7. Application to the Theory of Vibrations. Transverse Vibrations of an Infinite Rod under the Action of a Suddenly Applied Concentrated Force Problems 3 The Exponential Integral and Related Functions 3.1. The Exponential Integral and its Basic Properties 3.2. Asymptotic Representation of the Exponential Integral for Large $|z|$ 3.3. The Exponential Integral of Imaginary Argument. The Sine and Cosine Integrals 3.4. The Logarithmic Integral 3.5. Application to Electromagnetic Theory, Radiation of a Linear Half-Wave Oscillator Problems 4 Orthogonal Polynomials 4.1. Introductory Remarks 4.2. Definition and Generating Function of the Legendre Polynomials 4.3. Recurrence Relations and Differential Equation for the Legendre Polynomials 4.4. Integral Representations of the Legendre Polynomials 4.5. Orthogonality of the Legendre Polynomials 4.6. Asymptotic Representation of the Legendre Polynomials for Large $n$ 4.7. Expansion of Functions in Series of Legendre Polynomials 4.8. Examples of Expansions in Series of Legendre Polynomials 4.9. Definition and Generating Function of the Hermite Polynomials 4.10. Recurrence Relations and Differential Equation for the Hermite Polynomials 4.11. Integral Representations of the Hermite Polynomials 4.12. Integral Equations Satisfied by the Hermite Polynomials 4.13. Orthogonality of the Hermite Polynomials 4.14. Asymptotic Representation of the Hermite Polynomials for Large n 4.15. Expansion of Functions in Series of Hermite Polynomials 4.16. Examples of Expansions in Series of Hermite Polynomials 4.17. Definition and Generating Function of the Laguerre Polynomials 4.18. Recurrence Relations and Differential Equation for the Laguerre Polynomials 4.19. An Integral Representation of the Laguerre Polynomials. Relation between the Laguerre and Hermite Polynomials 4.20. An Integral Equation Satisfied by the Laguerre Polynomials 4.21. Orthogonality of the Laguerre Polynomials 4.22. Asymptotic Representation of the Laguerre Polynomials for Large $n$ 4.23. Expansion of Functions in Series of Laguerre Polynomials 4.24. Examples of Expansions in Series of Laguerre Polynomials 4.25. Application to the Theory of Propagation of Electromagnetic Waves. Reflection from the End of a Long Transmission Line Terminated by a Lumped Inductance Problems 5 Cylinder Functions: Theory 5.1. Introductory Remarks 5.2. Bessel Functions of Nonnegative Integral Order 5.3. Bessel Functions of Arbitrary Order 5.4. General Cylinder Functions. Bessel Functions of the Second Kind 5.5. Series Expansion of the Function $Y_n(z)$ 5.6. Bessel Functions of the Third Kind 5.7. Bessel Functions of Imaginary Argument 5.8. Cylinder Functions of Half-Integral Order 5.9. Wronskians of Pairs of Solutions of Bessel s Equation 5.10. Integral Representations of the Cylinder Functions 5.11. Asymptotic Representations of the Cylinder Functions for Large $|z|$ 5.12. Addition Theorems for the Cylinder Functions, 124.Zeros of the Cylinder Functions 5.13. Expansions in Series and Integrals Involving Cylinder Functions 5.14. Definite Integrals Involving Cylinder Functions 5.15. Cylinder Functions of Nonnegative Argument and Order 5.16. Airy Functions Problems 6 Cylinder Functions: Applications 6.1. Introductory Remarks 6.2. Separation of Variables in Cylindrical Coordinates 6.3. The Boundary Value Problems of Potential Theory. The Dirichlet Problem for a Cylinder 6.4. The Dirichlet Problem for a Domain Bounded by Two Parallel Planes 6.5. The Dirichlet Problem for a Wedge 6.6. The Field of a Point Charge near the Edge of a Conducting Sheet 6.7. Cooling of a Heated Cylinder 6.8. Diffraction by a Cylinder Problems 7 Spherical Harmonics: Theory 7.1. Introductory Remarks 7.2. The Hypergeometric Equation and Its Series Solution 7.3. Legendre Functions 7.4. Integral Representations of the Legendre Functions 7.5. Some Relations Satisfied by the Legendre Functions 7.6. Series Representations of the Legendre Functions 7.7. Wronskians of Pairs of Solutions of Legend-re s Equation 7.8. Recurrence Relations for the Legendre Functions 7.9. Legendre Functions of Nonnegative Integral Degree and Their Relation to Legendre Polynomials 7.10. Legendre Functions of Half-Integral Degree 7.11. Asymptotic Representations of the Legendre Functions for Large $|v|$ 7.12. Associated Legendre Functions Problems 8 Spherical Harmonics: Applications 8.1. Introductory Remarks 8.2. Solution of Laplace s Equation in Spherical Coordinates 8.3. The Dirichlet Problem for a Sphere 8.4. The Field of a Point Charge Inside a Hollow Conducting Sphere 8.5. The Dirichlet Problem for a Cone 8.6. Solution of Laplace s Equation in Spheroidal Coordinates 8.7. The Dirichlet Problem for a Spheroid 8.8. The Gravitational Attraction of a Homogeneous Solid Spheroid 8.9. The Dirichlet Problem for a Hyperboloid of Revolution 8.10. Solution of Laplace s Equation in Toroidal Coordinates 8.11. The Dirichlet Problem for a Torus 8.12. The Dirichlet Problem for a Domain Bounded by Two Intersecting Spheres 8.13. Solution of Laplace s Equation in Bipolar Coordinates 8.14. Solution of Helmholtz s Equation in Spherical Coordinates Problems 9 Hypergeometric Functions 9.1. The Hypergeometric Series and Its Analytic Continuation 9.2. Elementary Properties of the Hypergeometric Function 9.3. Evaluation of $F(alpha , beta ; gamma ; z)$ for $Re (gamma alpha beta ) > 0$, 243. 9.4. $F(alpha , beta ; gamma ; z)$ as a Function of its Parameters 9.5. Linear Transformations of the Hypergeometric Function 9.6. Quadratic Transformations of the Hypergeometric Function 9.7. Formulas for Analytic Continuation of $F(alpha , beta ; gamma ; z)$ in Exceptional Cases 9.8. Representation of Various Functions in Terms of the Hypergeometric Function 9.9. The Confluent Hypergeometric Function 9.10. The Differential Equation for the Confluent Hypergeometric Function and Its Solution. The Confluent Hypergeometric Function of the Second Kind 9.11. Integral Representations of the Confluent Hypergeometric Functions 9.12. Asymptotic Representations of the Confluent Hypergeometric Functions for Large $|z|$ 9.13. Representation of Various Functions in Terms of the Confluent Hypergeometric Functions 9.14. Generalized Hypergeometric Functions Problems 10 Parabolic Cylinder Functions 10.1. Separation of Variables in Laplace s Equation in Parabolic Coordinates 10.2. Hermite Functions 10.3. Some Relations Satisfied by the Hermite Functions 10.4. Recurrence Relations for the Hermite Functions 10.5. Integral Representations of the Hermite Functions 10.6. Asymptotic Representations of the Hermite Functions for Large $|z|$ 10.7. The Dirichlet Problem for a Parabolic Cylinder 10.8. Application to Quantum Mechanics Problems Bibliography Index

rawTOC:
1 The Gamma Function \\ \\ 1.1. Definition of the Gamma Function \\ 1.2. Some Relations Satisfied by the Gamma Function \\ 1.3. The Logarithmic Derivative of the Gamma Function \\ 1.4. Asymptotic Representation of the Gamma Function for Large $|z|$ \\ 1.5. Definite Integrals Related to the Gamma Function \\ Problems \\ \\ 2 The Probability Integral and Related Functions \\ \\ 2.1. The Probability Integral and Its Basic Properties \\ 2.2. Asymptotic Representation of the Probability Integral for Large $|z|$ \\ 2.3. The Probability Integral of Imaginary Argument. The Function $F(z)$ \\ 2.4. The Probability Integral of Argument $\sqrt{i} x$. The Fresnel Integrals, 21. \\ 2.5. Application to Probability Theory \\ 2.6. Application to the Theory of Heat Conduction. Cooling of the Surface of a Heated Object \\ 2.7. Application to the Theory of Vibrations. Transverse Vibrations of an Infinite Rod under the Action of a Suddenly Applied Concentrated Force \\ Problems \\ \\ 3 The Exponential Integral and Related Functions \\ \\ 3.1. The Exponential Integral and its Basic Properties \\ 3.2. Asymptotic Representation of the Exponential Integral for Large $|z|$ \\ 3.3. The Exponential Integral of Imaginary Argument. The Sine and Cosine Integrals \\ 3.4. The Logarithmic Integral \\ 3.5. Application to Electromagnetic Theory, Radiation of a Linear Half-Wave Oscillator Problems \\ \\ 4 Orthogonal Polynomials \\ \\ 4.1. Introductory Remarks \\ 4.2. Definition and Generating Function of the Legendre Polynomials \\ 4.3. Recurrence Relations and Differential Equation for the Legendre Polynomials \\ 4.4. Integral Representations of the Legendre Polynomials \\ 4.5. Orthogonality of the Legendre Polynomials \\ 4.6. Asymptotic Representation of the Legendre Polynomials for Large $n$ \\ 4.7. Expansion of Functions in Series of Legendre Polynomials \\ 4.8. Examples of Expansions in Series of Legendre Polynomials \\ 4.9. Definition and Generating Function of the Hermite Polynomials \\ 4.10. Recurrence Relations and Differential Equation for the Hermite Polynomials \\ 4.11. Integral Representations of the Hermite Polynomials \\ 4.12. Integral Equations Satisfied by the Hermite Polynomials \\ 4.13. Orthogonality of the Hermite Polynomials \\ 4.14. Asymptotic Representation of the Hermite Polynomials for Large n \\ 4.15. Expansion of Functions in Series of Hermite Polynomials \\ 4.16. Examples of Expansions in Series of Hermite Polynomials \\ 4.17. Definition and Generating Function of the Laguerre Polynomials \\ 4.18. Recurrence Relations and Differential Equation for the Laguerre Polynomials \\ 4.19. An Integral Representation of the Laguerre Polynomials. Relation between the Laguerre and Hermite Polynomials \\ 4.20. An Integral Equation Satisfied by the Laguerre Polynomials \\ 4.21. Orthogonality of the Laguerre Polynomials \\ 4.22. Asymptotic Representation of the Laguerre Polynomials for Large $n$ \\ 4.23. Expansion of Functions in Series of Laguerre Polynomials \\ 4.24. Examples of Expansions in Series of Laguerre Polynomials \\ 4.25. Application to the Theory of Propagation of Electromagnetic Waves. Reflection from the End of a Long Transmission Line Terminated by a Lumped Inductance \\ Problems \\ \\ 5 Cylinder Functions: Theory \\ \\ 5.1. Introductory Remarks \\ 5.2. Bessel Functions of Nonnegative Integral Order \\ 5.3. Bessel Functions of Arbitrary Order \\ 5.4. General Cylinder Functions. Bessel Functions of the Second Kind \\ 5.5. Series Expansion of the Function $Y_n(z)$ \\ 5.6. Bessel Functions of the Third Kind \\ 5.7. Bessel Functions of Imaginary Argument \\ 5.8. Cylinder Functions of Half-Integral Order \\ 5.9. Wronskians of Pairs of Solutions of Bessel s Equation \\ 5.10. Integral Representations of the Cylinder Functions \\ 5.11. Asymptotic Representations of the Cylinder Functions for Large $|z|$ \\ 5.12. Addition Theorems for the Cylinder Functions, 124.Zeros of the Cylinder Functions \\ 5.13. Expansions in Series and Integrals Involving Cylinder Functions \\ 5.14. Definite Integrals Involving Cylinder Functions \\ 5.15. Cylinder Functions of Nonnegative Argument and Order \\ 5.16. Airy Functions \\ Problems \\ \\ 6 Cylinder Functions: Applications \\ \\ 6.1. Introductory Remarks \\ 6.2. Separation of Variables in Cylindrical Coordinates \\ 6.3. The Boundary Value Problems of Potential Theory. The Dirichlet Problem for a Cylinder \\ 6.4. The Dirichlet Problem for a Domain Bounded by Two Parallel Planes \\ 6.5. The Dirichlet Problem for a Wedge \\ 6.6. The Field of a Point Charge near the Edge of a Conducting Sheet \\ 6.7. Cooling of a Heated Cylinder \\ 6.8. Diffraction by a Cylinder \\ Problems \\ \\ 7 Spherical Harmonics: Theory \\ \\ 7.1. Introductory Remarks \\ 7.2. The Hypergeometric Equation and Its Series Solution \\ 7.3. Legendre Functions \\ 7.4. Integral Representations of the Legendre Functions \\ 7.5. Some Relations Satisfied by the Legendre Functions \\ 7.6. Series Representations of the Legendre Functions \\ 7.7. Wronskians of Pairs of Solutions of Legend-re s Equation \\ 7.8. Recurrence Relations for the Legendre Functions \\ 7.9. Legendre Functions of Nonnegative Integral Degree and Their Relation to Legendre Polynomials \\ 7.10. Legendre Functions of Half-Integral Degree \\ 7.11. Asymptotic Representations of the Legendre Functions for Large $|v|$ \\ 7.12. Associated Legendre Functions \\ Problems \\ \\ 8 Spherical Harmonics: Applications \\ \\ 8.1. Introductory Remarks \\ 8.2. Solution of Laplace s Equation in Spherical Coordinates \\ 8.3. The Dirichlet Problem for a Sphere \\ 8.4. The Field of a Point Charge Inside a Hollow Conducting Sphere \\ 8.5. The Dirichlet Problem for a Cone \\ 8.6. Solution of Laplace s Equation in Spheroidal Coordinates \\ 8.7. The Dirichlet Problem for a Spheroid \\ 8.8. The Gravitational Attraction of a Homogeneous Solid Spheroid \\ 8.9. The Dirichlet Problem for a Hyperboloid of Revolution \\ 8.10. Solution of Laplace s Equation in Toroidal Coordinates \\ 8.11. The Dirichlet Problem for a Torus \\ 8.12. The Dirichlet Problem for a Domain Bounded by Two Intersecting Spheres \\ 8.13. Solution of Laplace s Equation in Bipolar Coordinates \\ 8.14. Solution of Helmholtz s Equation in Spherical Coordinates \\ Problems \\ \\ 9 Hypergeometric Functions \\ \\ 9.1. The Hypergeometric Series and Its Analytic Continuation \\ 9.2. Elementary Properties of the Hypergeometric Function \\ 9.3. Evaluation of $F(\alpha, \beta; \gamma; z)$ for $\Re(\gamma \alpha \beta) > 0$, 243. \\ 9.4. $F(\alpha, \beta; \gamma; z)$ as a Function of its Parameters \\ 9.5. Linear Transformations of the Hypergeometric Function \\ 9.6. Quadratic Transformations of the Hypergeometric Function \\ 9.7. Formulas for Analytic Continuation of $F(\alpha, \beta; \gamma; z)$ in Exceptional Cases \\ 9.8. Representation of Various Functions in Terms of the Hypergeometric Function \\ 9.9. The Confluent Hypergeometric Function \\ 9.10. The Differential Equation for the Confluent Hypergeometric Function and Its Solution. The Confluent Hypergeometric Function of the Second Kind \\ 9.11. Integral Representations of the Confluent Hypergeometric Functions \\ 9.12. Asymptotic Representations of the Confluent Hypergeometric Functions for Large $|z|$ \\ 9.13. Representation of Various Functions in Terms of the Confluent Hypergeometric Functions \\ 9.14. Generalized Hypergeometric Functions \\ Problems \\ \\ 10 Parabolic Cylinder Functions \\ \\ 10.1. Separation of Variables in Laplace s Equation in Parabolic Coordinates \\ 10.2. Hermite Functions \\ 10.3. Some Relations Satisfied by the Hermite Functions \\ 10.4. Recurrence Relations for the Hermite Functions \\ 10.5. Integral Representations of the Hermite Functions \\ 10.6. Asymptotic Representations of the Hermite Functions for Large $|z|$ \\ 10.7. The Dirichlet Problem for a Parabolic Cylinder \\ 10.8. Application to Quantum Mechanics \\ Problems \\ \\ Bibliography \\ \\ Index

entry:
@Book{Lebedev:1972:SFT,
  author =       "N. N. (Nikolai Nikolaevich) Lebedev",
  title =        "Special functions and their applications",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xii + 308",
  year =         "1972",
  ISBN =         "0-486-60624-4 (paperback)",
  ISBN-13 =      "978-0-486-60624-8 (paperback)",
  LCCN =         "QA351 .L3613 1972",
  bibdate =      "Sat Oct 30 16:25:05 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translated to English and edited by Richard A.
                 Silverman.",
  URL =          "http://www.loc.gov/catdir/description/dover031/72086228.html",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Spe{\"e}t{\`\i}sial\S{}nye
                 funk{\"e}t{\`\i}sii i ikh prilozheni{\"e}i{\`\i}a.",
  subject =      "Functions, Special; Mathematical physics",
  tableofcontents = "1 The Gamma Function \\
                 \\
                 1.1. Definition of the Gamma Function \\
                 1.2. Some Relations Satisfied by the Gamma Function \\
                 1.3. The Logarithmic Derivative of the Gamma Function
                 \\
                 1.4. Asymptotic Representation of the Gamma Function
                 for Large $|z|$ \\
                 1.5. Definite Integrals Related to the Gamma Function
                 \\
                 Problems \\
                 \\
                 2 The Probability Integral and Related Functions \\
                 \\
                 2.1. The Probability Integral and Its Basic Properties
                 \\
                 2.2. Asymptotic Representation of the Probability
                 Integral for Large $|z|$ \\
                 2.3. The Probability Integral of Imaginary Argument.
                 The Function $F(z)$ \\
                 2.4. The Probability Integral of Argument $\sqrt{i} x$.
                 The Fresnel Integrals, 21. \\
                 2.5. Application to Probability Theory \\
                 2.6. Application to the Theory of Heat Conduction.
                 Cooling of the Surface of a Heated Object \\
                 2.7. Application to the Theory of Vibrations.
                 Transverse Vibrations of an Infinite Rod under the
                 Action of a Suddenly Applied Concentrated Force \\
                 Problems \\
                 \\
                 3 The Exponential Integral and Related Functions \\
                 \\
                 3.1. The Exponential Integral and its Basic Properties
                 \\
                 3.2. Asymptotic Representation of the Exponential
                 Integral for Large $|z|$ \\
                 3.3. The Exponential Integral of Imaginary Argument.
                 The Sine and Cosine Integrals \\
                 3.4. The Logarithmic Integral \\
                 3.5. Application to Electromagnetic Theory, Radiation
                 of a Linear Half-Wave Oscillator Problems \\
                 \\
                 4 Orthogonal Polynomials \\
                 \\
                 4.1. Introductory Remarks \\
                 4.2. Definition and Generating Function of the Legendre
                 Polynomials \\
                 4.3. Recurrence Relations and Differential Equation for
                 the Legendre Polynomials \\
                 4.4. Integral Representations of the Legendre
                 Polynomials \\
                 4.5. Orthogonality of the Legendre Polynomials \\
                 4.6. Asymptotic Representation of the Legendre
                 Polynomials for Large $n$ \\
                 4.7. Expansion of Functions in Series of Legendre
                 Polynomials \\
                 4.8. Examples of Expansions in Series of Legendre
                 Polynomials \\
                 4.9. Definition and Generating Function of the Hermite
                 Polynomials \\
                 4.10. Recurrence Relations and Differential Equation
                 for the Hermite Polynomials \\
                 4.11. Integral Representations of the Hermite
                 Polynomials \\
                 4.12. Integral Equations Satisfied by the Hermite
                 Polynomials \\
                 4.13. Orthogonality of the Hermite Polynomials \\
                 4.14. Asymptotic Representation of the Hermite
                 Polynomials for Large n \\
                 4.15. Expansion of Functions in Series of Hermite
                 Polynomials \\
                 4.16. Examples of Expansions in Series of Hermite
                 Polynomials \\
                 4.17. Definition and Generating Function of the
                 Laguerre Polynomials \\
                 4.18. Recurrence Relations and Differential Equation
                 for the Laguerre Polynomials \\
                 4.19. An Integral Representation of the Laguerre
                 Polynomials. Relation between the Laguerre and Hermite
                 Polynomials \\
                 4.20. An Integral Equation Satisfied by the Laguerre
                 Polynomials \\
                 4.21. Orthogonality of the Laguerre Polynomials \\
                 4.22. Asymptotic Representation of the Laguerre
                 Polynomials for Large $n$ \\
                 4.23. Expansion of Functions in Series of Laguerre
                 Polynomials \\
                 4.24. Examples of Expansions in Series of Laguerre
                 Polynomials \\
                 4.25. Application to the Theory of Propagation of
                 Electromagnetic Waves. Reflection from the End of a
                 Long Transmission Line Terminated by a Lumped
                 Inductance \\
                 Problems \\
                 \\
                 5 Cylinder Functions: Theory \\
                 \\
                 5.1. Introductory Remarks \\
                 5.2. Bessel Functions of Nonnegative Integral Order \\
                 5.3. Bessel Functions of Arbitrary Order \\
                 5.4. General Cylinder Functions. Bessel Functions of
                 the Second Kind \\
                 5.5. Series Expansion of the Function $Y_n(z)$ \\
                 5.6. Bessel Functions of the Third Kind \\
                 5.7. Bessel Functions of Imaginary Argument \\
                 5.8. Cylinder Functions of Half-Integral Order \\
                 5.9. Wronskians of Pairs of Solutions of Bessel s
                 Equation \\
                 5.10. Integral Representations of the Cylinder
                 Functions \\
                 5.11. Asymptotic Representations of the Cylinder
                 Functions for Large $|z|$ \\
                 5.12. Addition Theorems for the Cylinder Functions,
                 124.Zeros of the Cylinder Functions \\
                 5.13. Expansions in Series and Integrals Involving
                 Cylinder Functions \\
                 5.14. Definite Integrals Involving Cylinder Functions
                 \\
                 5.15. Cylinder Functions of Nonnegative Argument and
                 Order \\
                 5.16. Airy Functions \\
                 Problems \\
                 \\
                 6 Cylinder Functions: Applications \\
                 \\
                 6.1. Introductory Remarks \\
                 6.2. Separation of Variables in Cylindrical Coordinates
                 \\
                 6.3. The Boundary Value Problems of Potential Theory.
                 The Dirichlet Problem for a Cylinder \\
                 6.4. The Dirichlet Problem for a Domain Bounded by Two
                 Parallel Planes \\
                 6.5. The Dirichlet Problem for a Wedge \\
                 6.6. The Field of a Point Charge near the Edge of a
                 Conducting Sheet \\
                 6.7. Cooling of a Heated Cylinder \\
                 6.8. Diffraction by a Cylinder \\
                 Problems \\
                 \\
                 7 Spherical Harmonics: Theory \\
                 \\
                 7.1. Introductory Remarks \\
                 7.2. The Hypergeometric Equation and Its Series
                 Solution \\
                 7.3. Legendre Functions \\
                 7.4. Integral Representations of the Legendre Functions
                 \\
                 7.5. Some Relations Satisfied by the Legendre Functions
                 \\
                 7.6. Series Representations of the Legendre Functions
                 \\
                 7.7. Wronskians of Pairs of Solutions of Legend-re s
                 Equation \\
                 7.8. Recurrence Relations for the Legendre Functions
                 \\
                 7.9. Legendre Functions of Nonnegative Integral Degree
                 and Their Relation to Legendre Polynomials \\
                 7.10. Legendre Functions of Half-Integral Degree \\
                 7.11. Asymptotic Representations of the Legendre
                 Functions for Large $|v|$ \\
                 7.12. Associated Legendre Functions \\
                 Problems \\
                 \\
                 8 Spherical Harmonics: Applications \\
                 \\
                 8.1. Introductory Remarks \\
                 8.2. Solution of Laplace s Equation in Spherical
                 Coordinates \\
                 8.3. The Dirichlet Problem for a Sphere \\
                 8.4. The Field of a Point Charge Inside a Hollow
                 Conducting Sphere \\
                 8.5. The Dirichlet Problem for a Cone \\
                 8.6. Solution of Laplace s Equation in Spheroidal
                 Coordinates \\
                 8.7. The Dirichlet Problem for a Spheroid \\
                 8.8. The Gravitational Attraction of a Homogeneous
                 Solid Spheroid \\
                 8.9. The Dirichlet Problem for a Hyperboloid of
                 Revolution \\
                 8.10. Solution of Laplace s Equation in Toroidal
                 Coordinates \\
                 8.11. The Dirichlet Problem for a Torus \\
                 8.12. The Dirichlet Problem for a Domain Bounded by Two
                 Intersecting Spheres \\
                 8.13. Solution of Laplace s Equation in Bipolar
                 Coordinates \\
                 8.14. Solution of Helmholtz s Equation in Spherical
                 Coordinates \\
                 Problems \\
                 \\
                 9 Hypergeometric Functions \\
                 \\
                 9.1. The Hypergeometric Series and Its Analytic
                 Continuation \\
                 9.2. Elementary Properties of the Hypergeometric
                 Function \\
                 9.3. Evaluation of $F(\alpha, \beta; \gamma; z)$ for
                 $\Re(\gamma \alpha \beta) > 0$, 243. \\
                 9.4. $F(\alpha, \beta; \gamma; z)$ as a Function of its
                 Parameters \\
                 9.5. Linear Transformations of the Hypergeometric
                 Function \\
                 9.6. Quadratic Transformations of the Hypergeometric
                 Function \\
                 9.7. Formulas for Analytic Continuation of $F(\alpha,
                 \beta; \gamma; z)$ in Exceptional Cases \\
                 9.8. Representation of Various Functions in Terms of
                 the Hypergeometric Function \\
                 9.9. The Confluent Hypergeometric Function \\
                 9.10. The Differential Equation for the Confluent
                 Hypergeometric Function and Its Solution. The Confluent
                 Hypergeometric Function of the Second Kind \\
                 9.11. Integral Representations of the Confluent
                 Hypergeometric Functions \\
                 9.12. Asymptotic Representations of the Confluent
                 Hypergeometric Functions for Large $|z|$ \\
                 9.13. Representation of Various Functions in Terms of
                 the Confluent Hypergeometric Functions \\
                 9.14. Generalized Hypergeometric Functions \\
                 Problems \\
                 \\
                 10 Parabolic Cylinder Functions \\
                 \\
                 10.1. Separation of Variables in Laplace s Equation in
                 Parabolic Coordinates \\
                 10.2. Hermite Functions \\
                 10.3. Some Relations Satisfied by the Hermite Functions
                 \\
                 10.4. Recurrence Relations for the Hermite Functions
                 \\
                 10.5. Integral Representations of the Hermite Functions
                 \\
                 10.6. Asymptotic Representations of the Hermite
                 Functions for Large $|z|$ \\
                 10.7. The Dirichlet Problem for a Parabolic Cylinder
                 \\
                 10.8. Application to Quantum Mechanics \\
                 Problems \\
                 \\
                 Bibliography \\
                 \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: Ling:1972:EM
author: Chih-Bing Ling and Jung Lin
title: On Evaluation of Moments of $ K_nu (t) / I_nu (t) $
journal: j-MATH-COMPUT
volume: 26
number: 118
pages: 529--537
month: apr
monthnumber: 4
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: evaluation; K/sub nu/(t)/I/sub; moments; nu/(t); numerical methods; Watson's method
acknowledgement: ack-nhfb
classcodes: C4190 (Other numerical methods)
corpsource: Virginia Politech. Inst., Blacksburg, VA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Chih-Bing Ling and Jung Lin
rawtitle: On Evaluation of Moments of $ {K}_\nu (t) / {I}_\nu (t) $
entry:
@Article{Ling:1972:EM,
  author =       "Chih-Bing Ling and Jung Lin",
  title =        "On Evaluation of Moments of $ {K}_\nu (t) / {I}_\nu
                 (t) $",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "529--537",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods)",
  corpsource =   "Virginia Politech. Inst., Blacksburg, VA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "evaluation; K/sub nu/(t)/I/sub; moments; nu/(t);
                 numerical methods; Watson's method",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Linz:1972:MCB
author: Peter Linz
title: A Method for Computing Bessel Function Integrals
journal: j-MATH-COMPUT
volume: 26
number: 118
pages: 509--513
month: apr
monthnumber: 4
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4160 (Numerical integration and differentiation)
corpsource: Univ. California, Davis, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Peter Linz
rawtitle: A Method for Computing {Bessel} Function Integrals
keywords:
Abel; Bessel function integrals; Fourier integrals; infinite integrals; integration; numerical computation; transform

entry:
@Article{Linz:1972:MCB,
  author =       "Peter Linz",
  title =        "A Method for Computing {Bessel} Function Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "509--513",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. California, Davis, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Abel; Bessel function integrals; Fourier integrals;
                 infinite integrals; integration; numerical computation;
                 transform",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Luke:1972:MTB
author: Yudell L. Luke
title: Miniaturized Tables of Bessel Functions. III
journal: j-MATH-COMPUT
volume: 26
number: 117
pages: 237--240
month: jan
monthnumber: 1
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; miniaturized tables; numerical methods
acknowledgement: ack-nhfb
classcodes: C4190 (Other numerical methods)
corpsource: Univ. Missouri, Kansas City, KS, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Yudell L. Luke
rawtitle: Miniaturized Tables of {Bessel} Functions. {III}
entry:
@Article{Luke:1972:MTB,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions. {III}",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "117",
  pages =        "237--240",
  month =        jan,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods)",
  corpsource =   "Univ. Missouri, Kansas City, KS, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; miniaturized tables; numerical
                 methods",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: MacKinnon:1972:AEH
author: Robert F. MacKinnon
title: The asymptotic expansions of Hankel transforms and related integrals
journal: j-MATH-COMPUT
volume: 26
number: 118
pages: 515--527
month: apr
monthnumber: 4
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: asymptotic expansions; Bessel; functions; Hankel transforms; integrals; transforms
acknowledgement: ack-nhfb
classcodes: B0230 (Integral transforms); C1130 (Integral transforms)
corpsource: Defence Res. Establ., Pacific, Victoria, BC, Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Robert F. MacKinnon
rawtitle: The asymptotic expansions of {Hankel} transforms and related integrals
entry:
@Article{MacKinnon:1972:AEH,
  author =       "Robert F. MacKinnon",
  title =        "The asymptotic expansions of {Hankel} transforms and
                 related integrals",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "515--527",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0230 (Integral transforms); C1130 (Integral
                 transforms)",
  corpsource =   "Defence Res. Establ., Pacific, Victoria, BC, Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic expansions; Bessel; functions; Hankel
                 transforms; integrals; transforms",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Majithia:1972:CAE
author: J. C. Majithia
title: Cellular Array for Extraction of Squares and Square Roots of Binary Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 9
pages: 1023--1024
month: sep
monthnumber: 9
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009084
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:46 MDT 2011
bibtimestamp: 2011.07.12 18:58:46 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. C. Majithia
rawtitle: Cellular Array for Extraction of Squares and Square Roots of Binary Numbers
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

entry:
@Article{Majithia:1972:CAE,
  author =       "J. C. Majithia",
  title =        "Cellular Array for Extraction of Squares and Square
                 Roots of Binary Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "9",
  pages =        "1023--1024",
  month =        sep,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009084",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: elefunt.bib
label: Manos:1972:CCA
author: Paul Manos and L. Richard Turner
type: NASA Technical Note
number: TN D-6698
institution: pub-NASA
address: pub-NASA:adr
pages: iii + 68
month: mar
monthnumber: 3
year: 1972
bibdate: Mon May 22 11:27:24 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2006.05.22 11:27:24 ???
URL: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf
acknowledgement: ack-nhfb
rawauthor: Paul Manos and L. Richard Turner
title:
Constrained Chebyshev approximations to some elementary functions suitable for evaluation with floating-point arithmetic

rawtitle:
Constrained {Chebyshev} approximations to some elementary functions suitable for evaluation with floating-point arithmetic

entry:
@TechReport{Manos:1972:CCA,
  author =       "Paul Manos and L. Richard Turner",
  title =        "Constrained {Chebyshev} approximations to some
                 elementary functions suitable for evaluation with
                 floating-point arithmetic",
  type =         "{NASA} Technical Note",
  number =       "TN D-6698",
  institution =  pub-NASA,
  address =      pub-NASA:adr,
  pages =        "iii + 68",
  month =        mar,
  year =         "1972",
  bibdate =      "Mon May 22 11:27:24 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Marino:1972:NAA
author: D. Marino
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 12
pages: 1416--1421
month: dec
monthnumber: 12
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1972.223516
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 08 08:05:51 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 08:05:51 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Marino
title:
New Algorithms for the Approximate Evaluation in Hardware of Binary Logarithms and Elementary Functions

rawtitle:
New Algorithms for the Approximate Evaluation in Hardware of Binary Logarithms and Elementary Functions

entry:
@Article{Marino:1972:NAA,
  author =       "D. Marino",
  title =        "New Algorithms for the Approximate Evaluation in
                 Hardware of Binary Logarithms and Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "12",
  pages =        "1416--1421",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223516",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 08:05:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Morita:1972:CAG
author: Tohru Morita and Tsuyoshi Horiguchi
journal: j-NUM-MATH
volume: 20
number: 5
pages: 425--430
month: oct
monthnumber: 10
year: 1972
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01402565
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Thu Jan 13 10:01:46 MST 2011
bibtimestamp: 2011.01.13 10:01:46 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=20&issue=5&spage=425
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Tohru Morita and Tsuyoshi Horiguchi
title:
Convergence of the arithmetic-geometric mean procedure for the complex variables and the calculation of the complete elliptic integrals with complex modulus

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=20&issue=5; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
The convergence of the arithmetic-geometric mean procedure is checked for complex variables. The procedure is shown to be useful for the evaluation of the complete elliptic integrals of the first and second kinds with complex modulus. It is suggested that the procedure will be useful also for the numerical calculation of the elliptic integrals and the Jacobian elliptic functions with complex modulus in general.

rawabstract:
The convergence of the arithmetic-geometric mean procedure is checked for complex variables. The procedure is shown to be useful for the evaluation of the complete elliptic integrals of the first and second kinds with complex modulus. It is suggested that the procedure will be useful also for the numerical calculation of the elliptic integrals and the Jacobian elliptic functions with complex modulus in general.

rawtitle:
Convergence of the arithmetic-geometric mean procedure for the complex variables and the calculation of the complete elliptic integrals with complex modulus

entry:
@Article{Morita:1972:CAG,
  author =       "Tohru Morita and Tsuyoshi Horiguchi",
  title =        "Convergence of the arithmetic-geometric mean procedure
                 for the complex variables and the calculation of the
                 complete elliptic integrals with complex modulus",
  journal =      j-NUM-MATH,
  volume =       "20",
  number =       "5",
  pages =        "425--430",
  month =        oct,
  year =         "1972",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01402565",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Thu Jan 13 10:01:46 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=20&issue=5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=20&issue=5&spage=425",
  abstract =     "The convergence of the arithmetic-geometric mean
                 procedure is checked for complex variables. The
                 procedure is shown to be useful for the evaluation of
                 the complete elliptic integrals of the first and second
                 kinds with complex modulus. It is suggested that the
                 procedure will be useful also for the numerical
                 calculation of the elliptic integrals and the Jacobian
                 elliptic functions with complex modulus in general.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Moses:1972:TGT
author: Joel Moses
title: Toward a General Theory of Special Functions
journal: j-CACM
volume: 15
number: 7
pages: 550--554
month: jul
monthnumber: 7
year: 1972
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 34-02 12H05
MRnumber: 53 3384
MRreviewer: K. Okugawa
bibdate: Mon Jan 22 07:06:21 MST 2001
bibtimestamp: 2001.01.22 07:06:21 MST
note: Twenty-fifth anniversary of the Association for Computing Machinery.
fjournal: Communications of the ACM
keywords: general theory; mathematics; special functions
acknowledgement: ack-nhfb
classcodes: C1100 (Mathematical techniques)
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: Joel Moses
rawnote: Twenty-fifth anniversary of the Association for Computing Machinery.
rawtitle: Toward a General Theory of Special Functions
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Moses72; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/macsyma.bib

entry:
@Article{Moses:1972:TGT,
  author =       "Joel Moses",
  title =        "Toward a General Theory of Special Functions",
  journal =      j-CACM,
  volume =       "15",
  number =       "7",
  pages =        "550--554",
  month =        jul,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "34-02 12H05",
  MRnumber =     "53 3384",
  MRreviewer =   "K. Okugawa",
  bibdate =      "Mon Jan 22 07:06:21 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Moses72;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/macsyma.bib",
  note =         "Twenty-fifth anniversary of the Association for
                 Computing Machinery.",
  acknowledgement = ack-nhfb,
  classcodes =   "C1100 (Mathematical techniques)",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "general theory; mathematics; special functions",
  oldlabel =     "Moses72",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Moses72",
}


bibtype: article
filename: elefunt.bib
label: Olver:1972:NBR
author: F. W. J. Olver and D. J. Sookne
title: Note on Backward Recurrence Algorithms
journal: j-MATH-COMPUT
volume: 26
number: 120
pages: 941--947
month: oct
monthnumber: 10
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290Z (Other numerical methods); C4190 (Other numerical methods)
corpsource: Univ. Maryland, College Park, MD, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: F. W. J. Olver and D. J. Sookne
rawtitle: Note on Backward Recurrence Algorithms
keywords:
backward recurrence algorithms; Bessel; Bessel functions; difference equations; functions; recessive solution; second order linear difference equation

entry:
@Article{Olver:1972:NBR,
  author =       "F. W. J. Olver and D. J. Sookne",
  title =        "Note on Backward Recurrence Algorithms",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "941--947",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290Z (Other numerical methods); C4190 (Other
                 numerical methods)",
  corpsource =   "Univ. Maryland, College Park, MD, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "backward recurrence algorithms; Bessel; Bessel
                 functions; difference equations; functions; recessive
                 solution; second order linear difference equation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Parnes:1972:CZM
author: R. Parnes
title: Complex zeros of the modified Bessel function $ K_n(Z) $
journal: j-MATH-COMPUT
volume: 26
number: 120
pages: 949--953
month: oct
monthnumber: 10
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: City Univ., New York, NY, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: R. Parnes
rawtitle: Complex zeros of the modified {Bessel} function {$ K_n(Z) $}
keywords:
and zeros; Bessel functions; complex zeros; interpolation; interpolation scheme; iterative; iterative methods; modified Bessel function; poles

entry:
@Article{Parnes:1972:CZM,
  author =       "R. Parnes",
  title =        "Complex zeros of the modified {Bessel} function {$
                 K_n(Z) $}",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "949--953",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "City Univ., New York, NY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "and zeros; Bessel functions; complex zeros;
                 interpolation; interpolation scheme; iterative;
                 iterative methods; modified Bessel function; poles",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Rabin:1972:FEP
author: Michael O. Rabin and Shmuel Winograd
title: Fast evaluation of polynomials by rational preparation
journal: j-COMM-PURE-APPL-MATH
volume: 25
number: 4
pages: 433--458
month: jul
monthnumber: 7
year: 1972
CODEN: CPAMAT, CPMAMV
DOI: https://doi.org/10.1002/cpa.3160250405
ISSN: 0010-3640 (print), 1097-0312 (electronic) OR 00103640 (print), 10970312 (electronic)
ISSNL: 0010-3640 OR 00103640
bibdate: Fri Oct 20 09:03:28 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 09:03:28 ???
fjournal: Communications on Pure and Applied Mathematics (New York)
keywords: number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
ajournal: Comm. Pure Appl. Math.
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312
rawauthor: Michael O. Rabin and Shmuel Winograd
rawtitle: Fast evaluation of polynomials by rational preparation
entry:
@Article{Rabin:1972:FEP,
  author =       "Michael O. Rabin and Shmuel Winograd",
  title =        "Fast evaluation of polynomials by rational
                 preparation",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "25",
  number =       "4",
  pages =        "433--458",
  month =        jul,
  year =         "1972",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160250405",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  bibdate =      "Fri Oct 20 09:03:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Pure Appl. Math.",
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  keywords =     "number of multiplications to evaluate a polynomial",
}


bibtype: article
filename: elefunt.bib
label: Ramamoorthy:1972:SPI
author: C. V. Ramamoorthy and James R. Goodman and K. H. Kim
title: Some Properties of Iterative Square-Rooting Methods Using High-Speed Multiplication
journal: j-IEEE-TRANS-COMPUT
volume: C-21
number: 8
pages: 837--847
month: aug
monthnumber: 8
year: 1972
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1972.5009039
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 18:58:45 MDT 2011
bibtimestamp: 2011.07.12 18:58:45 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: C. V. Ramamoorthy and James R. Goodman and K. H. Kim
rawtitle: Some Properties of Iterative Square-Rooting Methods Using High-Speed Multiplication
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

entry:
@Article{Ramamoorthy:1972:SPI,
  author =       "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
  title =        "Some Properties of Iterative Square-Rooting Methods
                 Using High-Speed Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "837--847",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:45 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Samet:1972:CDL
author: P. A. Samet and D. W. Honey
journal: j-COMP-J
volume: 15
number: 2
pages: 116--116
month: may
monthnumber: 5
year: 1972
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/15.2.116
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:49 MST 2012
bibtimestamp: 2012.12.04 14:47:49 MST
fjournal: The Computer Journal
keywords: digital arithmetic; double length; precision techniques; single; square root
acknowledgement: ack-nhfb
classcodes: C5230 (Digital arithmetic methods)
corpsource: Univ. Coll., London, UK
journalURL: http://comjnl.oxfordjournals.org/
treatment: T Theoretical or Mathematical
rawauthor: P. A. Samet and D. W. Honey
title:
Calculation of a Double-Length Square Root from Double-Length Number using Single Precision Techniques

bibsource:
http://comjnl.oxfordjournals.org/content/15/2.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/; https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif

rawtitle:
Calculation of a Double-Length Square Root from Double-Length Number using Single Precision Techniques

entry:
@Article{Samet:1972:CDL,
  author =       "P. A. Samet and D. W. Honey",
  title =        "Calculation of a Double-Length Square Root from
                 Double-Length Number using Single Precision
                 Techniques",
  journal =      j-COMP-J,
  volume =       "15",
  number =       "2",
  pages =        "116--116",
  month =        may,
  year =         "1972",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/15.2.116",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:49 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/15/2.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. Coll., London, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "digital arithmetic; double length; precision
                 techniques; single; square root",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Strecok:1972:HPE
author: A. J. Strecok and J. A. Gregory
title: High Precision Evaluation of the Irregular Coulomb Wave Functions
journal: j-MATH-COMPUT
volume: 26
number: 120
pages: 955--961 + s1--s10
month: oct
monthnumber: 10
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Argonne Nat. Lab., IL, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: A. J. Strecok and J. A. Gregory
rawtitle: High Precision Evaluation of the Irregular {Coulomb} Wave Functions
keywords:
function approximation; high precision evaluation; irregular Coulomb wave functions; numerical methods; wave functions

classcodes:
A0365G (Solutions of wave equations: bound state in quantum theory); B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)

entry:
@Article{Strecok:1972:HPE,
  author =       "A. J. Strecok and J. A. Gregory",
  title =        "High Precision Evaluation of the Irregular {Coulomb}
                 Wave Functions",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "955--961 + s1--s10",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "A0365G (Solutions of wave equations: bound state in
                 quantum theory); B0290F (Interpolation and function
                 approximation); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function approximation; high precision evaluation;
                 irregular Coulomb wave functions; numerical methods;
                 wave functions",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Turunov:1972:EFD
author: M. Turunov
title: Elementary functions of a discrete real and complex argument. (Russian)
journal: Taskent. Gos. Univ. Naucn. Trudy
volume: 418 Voprosy Mat.
pages: 263--271, 386
year: 1972
MRclass: 30A95
MRnumber: 50 \#13556
MRreviewer: G. Berzsenyi
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: M. Turunov
rawtitle: Elementary functions of a discrete real and complex argument. ({Russian})
entry:
@Article{Turunov:1972:EFD,
  author =       "M. Turunov",
  title =        "Elementary functions of a discrete real and complex
                 argument. ({Russian})",
  journal =      "Ta{\v{s}}kent. Gos. Univ. Nau{\v{c}}n. Trudy",
  volume =       "418 Voprosy Mat.",
  pages =        "263--271, 386",
  year =         "1972",
  MRclass =      "30A95",
  MRnumber =     "50 \#13556",
  MRreviewer =   "G. Berzsenyi",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Wimp:1972:CPE
author: Jet Wimp
journal: j-MATH-COMPUT
volume: 26
number: 117
pages: 309--309
month: jan
monthnumber: 1
year: 1972
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Sat Dec 22 06:54:10 MST 2018
bibtimestamp: 2018.12.22 06:54:10 MST
note: See cite Wimp:1962:PEB.
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Jet Wimp
rawnote: See \cite{Wimp:1962:PEB}.
title:
Corrigendum: booktitle Polynomial expansions of Bessel functions and some associated functions (Math. Comp. bf 16 (1962), 446--458)

bibsource:
http://www.ams.org/mcom/1972-26-117; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib

URL:
http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X; http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X/S0025-5718-1972-0400659-X.pdf; https://www.ams.org/mathscinet-getitem?mr=400659; https://www.ams.org/mathscinet/search/authors.html?authorName=Wimp%2C%20Jet

rawtitle:
Corrigendum: {{\booktitle{Polynomial expansions of Bessel functions and some associated functions}} (Math. Comp. {\bf 16} (1962), 446--458)}

entry:
@Article{Wimp:1972:CPE,
  author =       "Jet Wimp",
  title =        "Corrigendum: {{\booktitle{Polynomial expansions of
                 Bessel functions and some associated functions}} (Math.
                 Comp. {\bf 16} (1962), 446--458)}",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "117",
  pages =        "309--309",
  month =        jan,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Dec 22 06:54:10 MST 2018",
  bibsource =    "http://www.ams.org/mcom/1972-26-117;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
  note =         "See \cite{Wimp:1962:PEB}.",
  URL =          "http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X;
                 http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X/S0025-5718-1972-0400659-X.pdf;
                 https://www.ams.org/mathscinet-getitem?mr=400659;
                 https://www.ams.org/mathscinet/search/authors.html?authorName=Wimp%2C%20Jet",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Wynn:1972:CAM
author: Peter Wynn
title: Convergence Acceleration by a Method of Intercalation
journal: j-COMPUTING
volume: 9
number: 4
pages: 267--273
year: 1972
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:51 MST 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; INSPEC Axiom database (1968--date)
bibtimestamp: 2001.01.02 17:40:51 MST
fjournal: Computing
keywords: convergence acceleration; method of intercalation; series of real terms
acknowledgement: ack-ec
affiliation: Louisiana State Univ., New Orleans, LA, USA
journalURL: http://link.springer.com/journal/607
rawauthor: Peter Wynn
rawtitle: Convergence Acceleration by a Method of Intercalation
entry:
@Article{Wynn:1972:CAM,
  author =       "Peter Wynn",
  title =        "Convergence Acceleration by a Method of
                 Intercalation",
  journal =      j-COMPUTING,
  volume =       "9",
  number =       "4",
  pages =        "267--273",
  year =         "1972",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-ec # " and " # ack-nhfb,
  affiliation =  "Louisiana State Univ., New Orleans, LA, USA",
  classification = "B0290Z; C4190",
  description =  "convergence; series (mathematics)",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "convergence acceleration; method of intercalation;
                 series of real terms",
}


bibtype: article
filename: elefunt.bib
label: Amos:1973:BIC
author: D. E. Amos
title: Bounds on Iterated Coerror Functions and Their Ratios
journal: j-MATH-COMPUT
volume: 27
number: 122
pages: 413--427
month: apr
monthnumber: 4
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: D. E. Amos
rawtitle: Bounds on Iterated Coerror Functions and Their Ratios
entry:
@Article{Amos:1973:BIC,
  author =       "D. E. Amos",
  title =        "Bounds on Iterated Coerror Functions and Their
                 Ratios",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "413--427",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Baker:1973:PAS
author: P. W. Baker
title: Predictive algorithms for some elementary functions in radix 2
journal: j-ELECT-LETTERS
volume: 9
number: 21
pages: 493--494
month: oct
monthnumber: 10
year: 1973
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19730363
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
MRclass: 68A10
MRnumber: 57 \#18203
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Electronics Letters
acknowledgement: ack-nhfb
rawauthor: P. W. Baker
rawtitle: Predictive algorithms for some elementary functions in radix 2
journalURL:
https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220; https://digital-library.theiet.org/journal/el

entry:
@Article{Baker:1973:PAS,
  author =       "P. W. Baker",
  title =        "Predictive algorithms for some elementary functions in
                 radix 2",
  journal =      j-ELECT-LETTERS,
  volume =       "9",
  number =       "21",
  pages =        "493--494",
  month =        oct,
  year =         "1973",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19730363",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  MRclass =      "68A10",
  MRnumber =     "57 \#18203",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 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: Besslich:1973:MDS
author: P. W. Besslich and S. Raman
title: Multiplication, Division and Square Root Extraction Methods for Electronic Desk Calculators
journal: Journal of the Institution of Telecommunication Engineers (India)
volume: 19
number: 4
pages: 493--494
month: apr
monthnumber: 4
year: 1973
bibdate: Thu Sep 1 10:16:11 1994
bibtimestamp: 1994.09.01 10:16:11 ???
acknowledgement: ack-nj
rawauthor: P. W. Besslich and S. Raman
rawtitle: Multiplication, Division and Square Root Extraction Methods for Electronic Desk Calculators
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

entry:
@Article{Besslich:1973:MDS,
  author =       "P. W. Besslich and S. Raman",
  title =        "Multiplication, Division and Square Root Extraction
                 Methods for Electronic Desk Calculators",
  journal =      "Journal of the Institution of Telecommunication
                 Engineers (India)",
  volume =       "19",
  number =       "4",
  month =        apr,
  year =         "1973",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Braithwaite:1973:ALP
author: W. J. Braithwaite
title: Associated Legendre Polynomials, Ordinary and Modified Spherical Harmonics
journal: j-COMP-PHYS-COMM
volume: 5
number: 5
pages: 390--394
month: may
monthnumber: 5
year: 1973
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(73)90065-9
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Fri Oct 29 21:45:41 2010
bibtimestamp: 2010.10.29 21:45:41 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: W. J. Braithwaite
rawtitle: Associated {Legendre} Polynomials, Ordinary and Modified Spherical Harmonics
entry:
@Article{Braithwaite:1973:ALP,
  author =       "W. J. Braithwaite",
  title =        "Associated {Legendre} Polynomials, Ordinary and
                 Modified Spherical Harmonics",
  journal =      j-COMP-PHYS-COMM,
  volume =       "5",
  number =       "5",
  pages =        "390--394",
  month =        may,
  year =         "1973",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(73)90065-9",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Oct 29 21:45:41 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Cody:1973:CAP
author: W. J. Cody and Anthony J. Strecok and Henry C. Thacher, Jr.
title: Chebyshev Approximations for the Psi Function
journal: j-MATH-COMPUT
volume: 27
number: 121
pages: 123--127
month: jan
monthnumber: 1
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65-06 (68-06)
MRnumber: 50 6095
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Chebyshev approximation; Chebyshev approximations; digamma function; psi function
remark: Fullerton: Relative errors down to $ 10^-20 $
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: Argonne Nat. Lab., IL, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: W. J. Cody and Anthony J. Strecok and Henry C. {Thacher, Jr.}
rawtitle: {Chebyshev} Approximations for the Psi Function
entry:
@Article{Cody:1973:CAP,
  author =       "W. J. Cody and Anthony J. Strecok and Henry C.
                 {Thacher, Jr.}",
  title =        "{Chebyshev} Approximations for the Psi Function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "121",
  pages =        "123--127",
  month =        jan,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65-06 (68-06)",
  MRnumber =     "50 6095",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev approximation; Chebyshev approximations;
                 digamma function; psi function",
  remark =       "Fullerton: Relative errors down to $ 10^{-20} $",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: elefunt.bib
label: Dingle:1973:AET
author: Robert B. Dingle
title: Asymptotic expansions: their derivation and interpretation
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xv + 521
year: 1973
ISBN: 0-12-216550-0 OR 0122165500
ISBN13: 978-0-12-216550-4 OR 9780122165504
LCCN: QA295 .D45
bibdate: Sat Feb 18 14:52:17 MST 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.02.18 14:52:17 MST
subject: Asymptotic expansions; Power series
acknowledgement: ack-nhfb
rawauthor: Robert B. Dingle
rawtitle: Asymptotic expansions: their derivation and interpretation
entry:
@Book{Dingle:1973:AET,
  author =       "Robert B. Dingle",
  title =        "Asymptotic expansions: their derivation and
                 interpretation",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 521",
  year =         "1973",
  ISBN =         "0-12-216550-0",
  ISBN-13 =      "978-0-12-216550-4",
  LCCN =         "QA295 .D45",
  bibdate =      "Sat Feb 18 14:52:17 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Asymptotic expansions; Power series",
}


bibtype: article
filename: elefunt.bib
label: Ercegovac:1973:REC
author: Milos D. Ercegovac
title: Radix-16 Evaluation of Certain Elementary Functions
journal: j-IEEE-TRANS-COMPUT
volume: C-22
number: 6
pages: 561--566
month: jun
monthnumber: 6
year: 1973
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1973.5009107
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:39 1994
bibtimestamp: 1994.09.01 10:15:39 ???
fjournal: IEEE Transactions on Computers
keywords: ARITH-2
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Milo{\v{s}} D. Ercegovac
rawtitle: Radix-16 Evaluation of Certain Elementary Functions
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

URL:
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf; https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009107

entry:
@Article{Ercegovac:1973:REC,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "Radix-16 Evaluation of Certain Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "561--566",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009107",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009107",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1973:CZE
author: Henry E. Fettis and James C. Caslin and Kenneth R. Cramer
title: Complex zeros of the error function and of the complementary error function
journal: j-MATH-COMPUT
volume: 27
number: 122
pages: 401--407
month: apr
monthnumber: 4
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Wright-Patterson Air Force Base, OH, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Henry E. Fettis and James C. Caslin and Kenneth R. Cramer
rawtitle: Complex zeros of the error function and of the complementary error function
keywords:
asymptotic formula; complementary error function; complex zeros; error function; errors; first one hundred zeros; function evaluation; poles and zeros

entry:
@Article{Fettis:1973:CZE,
  author =       "Henry E. Fettis and James C. Caslin and Kenneth R.
                 Cramer",
  title =        "Complex zeros of the error function and of the
                 complementary error function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "401--407",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Wright-Patterson Air Force Base, OH, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic formula; complementary error function;
                 complex zeros; error function; errors; first one
                 hundred zeros; function evaluation; poles and zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1973:SPC
author: Henry E. Fettis and James C. Caslin and Kenneth R. Cramer
title: Saddle Points of the Complementary Error Function
journal: j-MATH-COMPUT
volume: 27
number: 122
pages: 409--412
month: apr
monthnumber: 4
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Sandia Labs., Albuquerque, NM, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Henry E. Fettis and James C. Caslin and Kenneth R. Cramer
rawtitle: Saddle Points of the Complementary Error Function
keywords:
asymptotic; complementary error function; errors; formula; function evaluation; poles and zeros; saddle points

entry:
@Article{Fettis:1973:SPC,
  author =       "Henry E. Fettis and James C. Caslin and Kenneth R.
                 Cramer",
  title =        "Saddle Points of the Complementary Error Function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "409--412",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Sandia Labs., Albuquerque, NM, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic; complementary error function; errors;
                 formula; function evaluation; poles and zeros; saddle
                 points",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Fisher:1973:NEI
author: N. I. Fisher
title: A note on the evaluation of the incomplete gamma function
journal: j-J-STAT-COMPUT-SIMUL
volume: 2
number: 4
pages: 325--332
year: 1973
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949657308810058
ISSNL: 0094-9655 OR 00949655
bibdate: Tue Apr 22 09:10:34 MDT 2014
bibtimestamp: 2014.04.22 09:10:34 MDT
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
rawauthor: N. I. Fisher
rawtitle: A note on the evaluation of the incomplete gamma function
ISSN:
0094-9655 (print), 1026-7778 (electronic), 1563-5163 OR 00949655 (print), 10267778 (electronic), 15635163

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

entry:
@Article{Fisher:1973:NEI,
  author =       "N. I. Fisher",
  title =        "A note on the evaluation of the incomplete gamma
                 function",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "2",
  number =       "4",
  pages =        "325--332",
  year =         "1973",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657308810058",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:10:34 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}


bibtype: techreport
filename: elefunt.bib
label: Franke:1973:AAH
author: R. Franke
title: An analysis of algorithms for hardware evaluation of elementary functions
type: Report
number: NPS-53FE73051A
institution: Naval Post-Graduate School
address: Monterey, CA, USA
pages: 325--332
month: may
monthnumber: 5
year: 1973
bibdate: Mon Nov 10 14:43:43 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.11.10 14:43:43 ???
acknowledgement: ack-nhfb
rawauthor: R. Franke
rawtitle: An analysis of algorithms for hardware evaluation of elementary functions
entry:
@TechReport{Franke:1973:AAH,
  author =       "R. Franke",
  title =        "An analysis of algorithms for hardware evaluation of
                 elementary functions",
  type =         "Report",
  number =       "NPS-53FE73051A",
  institution =  "Naval Post-Graduate School",
  address =      "Monterey, CA, USA",
  month =        may,
  year =         "1973",
  bibdate =      "Mon Nov 10 14:43:43 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  xxnumber =     "AD-761519",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1973:AAE
author: Walter Gautschi
title: ACM Algorithm 471: Exponential Integrals [S13]
journal: j-CACM
volume: 16
number: 12
pages: 761--763
month: dec
monthnumber: 12
year: 1973
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:43:23 MST 2001
bibtimestamp: 2001.01.22 06:43:23 MST
fjournal: Communications of the ACM
remark: Fullerton: Algol-language routine for $ E_n(x) = int _1^infty e^-x t t^n d t, x > 0 $.
acknowledgement: ack-nhfb
corpsource: Purdue Univ., Lafayette, IN, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: A Application; T Theoretical or Mathematical
rawauthor: Walter Gautschi
rawtitle: {ACM Algorithm 471}: Exponential Integrals [{S13}]
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Gautschi73; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
ALGOL; computation; continued fractions; exponential integrals; integration; recurrence relations; recursive; subroutine; subroutines

classcodes:
B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation); C7310 (Mathematics computing)

entry:
@Article{Gautschi:1973:AAE,
  author =       "Walter Gautschi",
  title =        "{ACM Algorithm 471}: Exponential Integrals [{S13}]",
  journal =      j-CACM,
  volume =       "16",
  number =       "12",
  pages =        "761--763",
  month =        dec,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:43:23 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Gautschi73;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation);
                 C7310 (Mathematics computing)",
  corpsource =   "Purdue Univ., Lafayette, IN, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "ALGOL; computation; continued fractions; exponential
                 integrals; integration; recurrence relations;
                 recursive; subroutine; subroutines",
  oldlabel =     "Gautschi73",
  remark =       "Fullerton: Algol-language routine for $ E_n(x) =
                 \int_1^\infty e^{-x t} t^n \, d t, x > 0 $.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gautschi73",
}


bibtype: techreport
filename: elefunt.bib
label: Hemker:1973:SDL
author: P. W. Hemker and W. Hoffmann and S. P. N. van Kampen and H. L. Oudshoorn and D. T. Winter
title: Single- and double-length computation of elementary functions
number: NW 7
institution: Mathematical Centre
address: Amsterdam
pages: 761--763
year: 1973
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
acknowledgement: ack-nhfb
rawauthor: P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen} and H. L. Oudshoorn and D. T. Winter
rawtitle: Single- and double-length computation of elementary functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{Hemker:1973:SDL,
  author =       "P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen}
                 and H. L. Oudshoorn and D. T. Winter",
  title =        "Single- and double-length computation of elementary
                 functions",
  number =       "NW 7",
  institution =  "Mathematical Centre",
  address =      "Amsterdam",
  year =         "1973",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Hill:1973:AAN
author: G. W. Hill and A. W. Davis
title: ACM Algorithm 442: Normal Deviate [S14]
journal: j-CACM
volume: 16
number: 1
pages: 51--52
month: jan
monthnumber: 1
year: 1973
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:49:54 MST 2001
bibtimestamp: 2001.01.22 06:49:54 MST
fjournal: Communications of the ACM
remark: Fullerton: Short Algol-language procedure with accuracy to 24 digits.
acknowledgement: ack-nhfb
classcodes: C7310 (Mathematics computing)
corpsource: CSIRO, Glen Osmond, Australia
journalURL: https://dl.acm.org/loi/cacm
treatment: P Practical
rawauthor: G. W. Hill and A. W. Davis
rawtitle: {ACM Algorithm 442}: Normal Deviate [{S14}]
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1973.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#HillD73; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
ALGOL; normal deviate; normal distribution inverse; probit; statistics; subroutines; Taylor series approximation; transform

entry:
@Article{Hill:1973:AAN,
  author =       "G. W. Hill and A. W. Davis",
  title =        "{ACM Algorithm 442}: Normal Deviate [{S14}]",
  journal =      j-CACM,
  volume =       "16",
  number =       "1",
  pages =        "51--52",
  month =        jan,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:49:54 MST 2001",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1973.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#HillD73;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "CSIRO, Glen Osmond, Australia",
  country =      "USA",
  descriptors =  "RVG",
  enum =         "7393",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "ALGOL; normal deviate; normal distribution inverse;
                 probit; statistics; subroutines; Taylor series
                 approximation; transform",
  oldlabel =     "HillD73",
  references =   "0",
  remark =       "Fullerton: Short Algol-language procedure with
                 accuracy to 24 digits.",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/HillD73",
}


bibtype: article
filename: elefunt.bib
label: Hill:1973:AAS
author: G. W. Hill
title: ACM Algorithm 465: Student's $t$ Frequency [S14]
journal: j-CACM
volume: 16
number: 11
pages: 690--690
month: nov
monthnumber: 11
year: 1973
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:49:52 MST 2001
bibtimestamp: 2001.01.22 06:49:52 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C7310 (Mathematics computing)
corpsource: CSIRO, Glen Osmond, SA, Australia
journalURL: https://dl.acm.org/loi/cacm
treatment: P Practical
rawauthor: G. W. Hill
rawtitle: {ACM Algorithm 465}: {Student}'s $t$ Frequency [{S14}]
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Hill73a; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
ALGOL; approximation; density function; series; statistics; student's t statistic; subroutine; subroutines

remark:
Fullerton: Algol-language routine for $ f(t | n) = frac Gamma (n / 2 + 1 / 2)(pi n)^1 / 2 Gamma (n / 2) (1 + t^2 / n)^n / 2 + 1 / 2 $.

entry:
@Article{Hill:1973:AAS,
  author =       "G. W. Hill",
  title =        "{ACM Algorithm 465}: {Student}'s $t$ Frequency
                 [{S14}]",
  journal =      j-CACM,
  volume =       "16",
  number =       "11",
  pages =        "690--690",
  month =        nov,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:49:52 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Hill73a;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "CSIRO, Glen Osmond, SA, Australia",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "ALGOL; approximation; density function; series;
                 statistics; student's t statistic; subroutine;
                 subroutines",
  oldlabel =     "Hill73a",
  remark =       "Fullerton: Algol-language routine for $ f(t | n) =
                 \frac {\Gamma (n / 2 + 1 / 2)}{(\pi n)^{1 / 2} \Gamma
                 (n / 2)} (1 + t^2 / n)^{n / 2 + 1 / 2} $.",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Hill73a",
}


bibtype: article
filename: elefunt.bib
label: Hill:1973:SAA
author: I. D. Hill
title: Statistical Algorithms: Algorithm AS 66: The Normal Integral
journal: j-APPL-STAT
volume: 22
number: 3
pages: 424--427
month: sep
monthnumber: 9
year: 1973
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
bibdate: Sat Apr 21 10:20:49 MDT 2001
bibtimestamp: 2001.04.21 10:20:49 MDT
URL: http://lib.stat.cmu.edu/apstat/66
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: I. D. Hill
rawtitle: Statistical Algorithms: {Algorithm AS 66}: The Normal Integral
bibsource:
https://www.math.utah.edu/pub/tex/bib/as1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

entry:
@Article{Hill:1973:SAA,
  author =       "I. D. Hill",
  title =        "Statistical Algorithms: {Algorithm AS 66}: The Normal
                 Integral",
  journal =      j-APPL-STAT,
  volume =       "22",
  number =       "3",
  pages =        "424--427",
  month =        sep,
  year =         "1973",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:20:49 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://lib.stat.cmu.edu/apstat/66",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: article
filename: elefunt.bib
label: Hwang:1973:RRS
author: W. G. Hwang and John Todd
title: A recurrence relation for the square root
journal: j-J-APPROX-THEORY
volume: 9
pages: 299--306
year: 1973
CODEN: JAXTAZ
DOI: https://doi.org/10.1016/0021-9045(73)90075-0
ISSN: 0021-9045,1096-0430 OR 00219045,10960430
ISSNL: 0021-9045 OR 00219045
MRclass: 65H05
MRnumber: 373270
MRreviewer: L. Fox
bibdate: Sat Oct 21 14:25:01 2023
bibtimestamp: 2023.10.21 14:25:01 ???
fjournal: Journal of Approximation Theory
ZMnumber: 0271.65032
acknowledgement: ack-nhfb
authordates: John Todd (16 May 1911--21 June 2007)
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: W. G. Hwang and John Todd
rawtitle: A recurrence relation for the square root
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Hwang:1973:RRS,
  author =       "W. G. Hwang and John Todd",
  title =        "A recurrence relation for the square root",
  journal =      j-J-APPROX-THEORY,
  volume =       "9",
  pages =        "299--306",
  year =         "1973",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/0021-9045(73)90075-0",
  ISSN =         "0021-9045,1096-0430",
  ISSN-L =       "0021-9045",
  MRclass =      "65H05",
  MRnumber =     "373270",
  MRreviewer =   "L. Fox",
  bibdate =      "Sat Oct 21 14:25:01 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0271.65032",
  acknowledgement = ack-nhfb,
  author-dates = "John Todd (16 May 1911--21 June 2007)",
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  received =     "19 April 1971",
  ZBmath =       "3426800",
}


bibtype: article
filename: elefunt.bib
label: Laurenzi:1973:DWF
author: Bernard J. Laurenzi
title: Derivatives of Whittaker Functions $ W_k, 1 / 2 $ and $ M_k, 1 / 2 $ with Respect to Order $ K $
journal: j-MATH-COMPUT
volume: 27
number: 121
pages: 129--132
month: jan
monthnumber: 1
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Bernard J. Laurenzi
rawtitle:
Derivatives of {Whittaker} Functions $ {W}_{k, 1 / 2} $ and $ {M}_{k, 1 / 2} $ with Respect to Order $ {K} $

entry:
@Article{Laurenzi:1973:DWF,
  author =       "Bernard J. Laurenzi",
  title =        "Derivatives of {Whittaker} Functions $ {W}_{k, 1 / 2}
                 $ and $ {M}_{k, 1 / 2} $ with Respect to Order $ {K}
                 $",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "121",
  pages =        "129--132",
  month =        jan,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Levin:1973:DNL
author: D. Levin
title: Development of non-linear transformations for improving convergence of sequences
journal: j-INT-J-COMPUT-MATH
volume: 3
number: 1--4
pages: 371--388
year: 1973
CODEN: IJCMAT
DOI: https://doi.org/10.1080/00207167308803075
ISSN: 0020-7160 OR 00207160
ISSNL: 0020-7160 OR 00207160
bibdate: Thu Dec 01 10:27:34 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:27:34 ???
fjournal: International Journal of Computer Mathematics
keywords: convergence acceleration
ZMnumber: 0274.65004
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gcom20
rawauthor: D. Levin
rawtitle: Development of non-linear transformations for improving convergence of sequences
entry:
@Article{Levin:1973:DNL,
  author =       "D. Levin",
  title =        "Development of non-linear transformations for
                 improving convergence of sequences",
  journal =      j-INT-J-COMPUT-MATH,
  volume =       "3",
  number =       "1--4",
  pages =        "371--388",
  month =        "????",
  year =         "1973",
  CODEN =        "IJCMAT",
  DOI =          "https://doi.org/10.1080/00207167308803075",
  ISSN =         "0020-7160",
  ISSN-L =       "0020-7160",
  bibdate =      "Thu Dec 01 10:27:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0274.65004",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Computer Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/gcom20",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Linz:1973:NCI
author: Peter Linz and T. E. Kropp
title: A note on the computation of integrals involving products of trigonometric and Bessel functions
journal: j-MATH-COMPUT
volume: 27
number: 124
pages: 871--872
month: oct
monthnumber: 10
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; computation; integration; numerical; numerical methods; products; trigonometric
acknowledgement: ack-nhfb
corpsource: Univ. California, Davies, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Peter Linz and T. E. Kropp
rawtitle: A note on the computation of integrals involving products of trigonometric and {Bessel} functions
classcodes:
B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)

entry:
@Article{Linz:1973:NCI,
  author =       "Peter Linz and T. E. Kropp",
  title =        "A note on the computation of integrals involving
                 products of trigonometric and {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "124",
  pages =        "871--872",
  month =        oct,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. California, Davies, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; computation; integration; numerical;
                 numerical methods; products; trigonometric",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Lozier:1973:BCP
author: D. W. Lozier and L. C. Maximon and W. L. Sadowski
title: A bit comparison program for algorithm testing
journal: j-COMP-J
volume: 16
number: 2
pages: 111--117
month: may
monthnumber: 5
year: 1973
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:52:11 MDT 2000
bibtimestamp: 2000.09.29 08:52:11 MDT
fjournal: The Computer Journal
keywords: accuracy; algorithm testing; bit comparison program; computer algorithms; program debugging
acknowledgement: ack-nhfb
classcodes: C6150G (Diagnostic, testing, debugging and evaluating systems)
corpsource: Nat. Bur. Stand., Washington, DC, USA
journalURL: http://comjnl.oxfordjournals.org/
treatment: P Practical
rawauthor: D. W. Lozier and L. C. Maximon and W. L. Sadowski
rawtitle: A bit comparison program for algorithm testing
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif

entry:
@Article{Lozier:1973:BCP,
  author =       "D. W. Lozier and L. C. Maximon and W. L. Sadowski",
  title =        "A bit comparison program for algorithm testing",
  journal =      j-COMP-J,
  volume =       "16",
  number =       "2",
  pages =        "111--117",
  month =        may,
  year =         "1973",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:52:11 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  corpsource =   "Nat. Bur. Stand., Washington, DC, USA",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "accuracy; algorithm testing; bit comparison program;
                 computer algorithms; program debugging",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: McNolty:1973:SPD
author: Frank McNolty
title: Some probability density functions and their characteristic functions
journal: j-MATH-COMPUT
volume: 27
number: 123
pages: 495--504
month: jul
monthnumber: 7
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0240 (Probability and statistics); C1140 (Probability and statistics)
corpsource: Lockheed Palo Alto Res. Lab., CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Frank McNolty
rawtitle: Some probability density functions and their characteristic functions
keywords:
Bessel function; characteristic functions; functions; hypergeometric function; probability; probability density functions

entry:
@Article{McNolty:1973:SPD,
  author =       "Frank McNolty",
  title =        "Some probability density functions and their
                 characteristic functions",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "123",
  pages =        "495--504",
  month =        jul,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0240 (Probability and statistics); C1140 (Probability
                 and statistics)",
  corpsource =   "Lockheed Palo Alto Res. Lab., CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; characteristic functions; functions;
                 hypergeometric function; probability; probability
                 density functions",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Meinardus:1973:OSA
author: Gunter Meinardus and G. D. Taylor
title: Optimal starting approximations for iterative schemes
journal: j-J-APPROX-THEORY
volume: 9
number: 1
pages: 1--19
month: sep
monthnumber: 9
year: 1973
CODEN: JAXTAZ
DOI: https://doi.org/10.1016/0021-9045(73)90108-1
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Mon Nov 10 09:49:33 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.11.10 09:49:33 ???
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: G{\"u}nter Meinardus and G. D. Taylor
rawtitle: Optimal starting approximations for iterative schemes
entry:
@Article{Meinardus:1973:OSA,
  author =       "G{\"u}nter Meinardus and G. D. Taylor",
  title =        "Optimal starting approximations for iterative
                 schemes",
  journal =      j-J-APPROX-THEORY,
  volume =       "9",
  number =       "1",
  pages =        "1--19",
  month =        sep,
  year =         "1973",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/0021-9045(73)90108-1",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Mon Nov 10 09:49:33 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
}


bibtype: article
filename: elefunt.bib
label: Rice:1973:EEI
author: S. O. Rice
title: Efficient Evaluation of Integrals of Analytic Functions by the Trapezoidal Rule
journal: j-BELL-SYST-TECH-J
volume: 52
number: 5
pages: 707--722
month: may
monthnumber: 5
year: 1973
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:55 MST 2010
bibtimestamp: 2010.11.09 11:15:55 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol52/bstj52-5-707.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: S. O. Rice
rawtitle: Efficient Evaluation of Integrals of Analytic Functions by the Trapezoidal Rule
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1973/BSTJ.1973.5205.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Rice:1973:EEI,
  author =       "S. O. Rice",
  title =        "Efficient Evaluation of Integrals of Analytic
                 Functions by the Trapezoidal Rule",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "52",
  number =       "5",
  pages =        "707--722",
  month =        may # "--" # jun,
  year =         "1973",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1973/BSTJ.1973.5205.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol52/bstj52-5-707.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: elefunt.bib
label: Schmid:1973:BLVa
author: H. Schmid
title: BCD logic V: BCD square root
journal: j-ELECTRONIC-DESIGN
volume: 21
number: 17
pages: 62--69
month: aug
monthnumber: 8
year: 1973
CODEN: ELODAW
ISSN: 0013-4872 (print), 1944-9550 (electronic) OR 00134872 (print), 19449550 (electronic)
ISSNL: 0013-4872 OR 00134872
bibdate: Thu Sep 1 10:16:11 1994
bibtimestamp: 1994.09.01 10:16:11 ???
fjournal: Electronic Design
keywords: decimal fixed-point arithmetic
acknowledgement: ack-nj
rawauthor: H. Schmid
rawtitle: {BCD} logic {V}: {BCD} square root
entry:
@Article{Schmid:1973:BLVa,
  author =       "H. Schmid",
  title =        "{BCD} logic {V}: {BCD} square root",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "17",
  pages =        "62--69",
  month =        aug,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
  keywords =     "decimal fixed-point arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Sookne:1973:BFC
author: D. J. Sookne
title: Bessel Functions $I$ and $J$ of Complex Argument and Integer Order
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 77B
number: 3--4
pages: 111--114
month: jul
monthnumber: 7
year: 1973
ISSN: 0091-0635 OR 00910635
bibdate: Sat Oct 30 10:49:13 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:49:13 ???
fjournal: Journal of Research of the National Bureau of Standards (1934)
remark: Fullerton: A program is described but not published.
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: D. J. Sookne
rawtitle: {Bessel} Functions {$I$} and {$J$} of Complex Argument and Integer Order
entry:
@Article{Sookne:1973:BFC,
  author =       "D. J. Sookne",
  title =        "{Bessel} Functions {$I$} and {$J$} of Complex Argument
                 and Integer Order",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "77B",
  number =       "3--4",
  pages =        "111--114",
  month =        jul,
  year =         "1973",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:49:13 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: A program is described but not published.",
}


bibtype: article
filename: elefunt.bib
label: Sookne:1973:BFR
author: D. J. Sookne
title: Bessel Functions of Real Argument and Integer Order
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 77A
number: 3--4
pages: 125--132
month: jul
monthnumber: 7
year: 1973
ISSN: 0091-0635 OR 00910635
bibdate: Sat Oct 30 10:51:18 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:51:18 ???
fjournal: Journal of Research of the National Bureau of Standards (1934)
remark: Fullerton: Sequences of $ I_n(x) $ and $ J_n(x) $ are computed with a FORTRAN routine.
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: D. J. Sookne
rawtitle: {Bessel} Functions of Real Argument and Integer Order
entry:
@Article{Sookne:1973:BFR,
  author =       "D. J. Sookne",
  title =        "{Bessel} Functions of Real Argument and Integer
                 Order",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "77A",
  number =       "3--4",
  pages =        "125--132",
  month =        jul,
  year =         "1973",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:51:18 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Sequences of $ I_n(x) $ and $ J_n(x) $ are
                 computed with a FORTRAN routine.",
}


bibtype: article
filename: elefunt.bib
label: Sookne:1973:CABa
author: D. J. Sookne
title: Certification of an Algorithm for Bessel Functions of Real Argument
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 77B
number: 3--4
pages: 115--124
month: jul
monthnumber: 7
year: 1973
ISSN: 0091-0635 OR 00910635
bibdate: Sat Oct 30 10:55:03 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:55:03 ???
fjournal: Journal of Research of the National Bureau of Standards (1934)
remark: Fullerton: An algorithm is shown to lose at most about 3 bits of precision.
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: D. J. Sookne
rawtitle: Certification of an Algorithm for {Bessel} Functions of Real Argument
entry:
@Article{Sookne:1973:CABa,
  author =       "D. J. Sookne",
  title =        "Certification of an Algorithm for {Bessel} Functions
                 of Real Argument",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "77B",
  number =       "3--4",
  pages =        "115--124",
  month =        jul,
  year =         "1973",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:55:03 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: An algorithm is shown to lose at most about
                 3 bits of precision.",
}


bibtype: article
filename: elefunt.bib
label: Sookne:1973:CABb
author: D. J. Sookne
title: Certification of an Algorithm for Bessel Functions of Complex Argument
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 77B
number: 3
pages: 133--136
month: jul
monthnumber: 7
year: 1973
ISSN: 0091-0635 OR 00910635
bibdate: Sat Oct 30 10:53:39 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:53:39 ???
fjournal: Journal of Research of the National Bureau of Standards (1934)
remark: Fullerton: The algorithm is shown to lose at most about 3 bits of precision.
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: D. J. Sookne
rawtitle: Certification of an Algorithm for {Bessel} Functions of Complex Argument
entry:
@Article{Sookne:1973:CABb,
  author =       "D. J. Sookne",
  title =        "Certification of an Algorithm for {Bessel} Functions
                 of Complex Argument",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "77B",
  number =       "3",
  pages =        "133--136",
  month =        jul,
  year =         "1973",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:53:39 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: The algorithm is shown to lose at most
                 about 3 bits of precision.",
}


bibtype: article
filename: elefunt.bib
label: Vos:1973:RAC
author: H. Vos
title: Remark on ``Algorithm 300: Coulomb Wave Functions''
journal: j-CACM
volume: 16
number: 5
pages: 308--309
month: may
monthnumber: 5
year: 1973
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:27:34 MST 2001
bibtimestamp: 2001.01.22 07:27:34 MST
note: See cite Gunn:1967:ACW.
fjournal: Communications of the ACM
keywords: Coulomb wave functions; function evaluation; mathematics; wave functions
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis); C7310 (Mathematics computing)
corpsource: Vrije Univ., Amsterdam, Netherlands
journalURL: https://dl.acm.org/loi/cacm
treatment: A Application; T Theoretical or Mathematical
rawauthor: H. Vos
rawnote: See \cite{Gunn:1967:ACW}.
rawtitle: Remark on ``{Algorithm 300}: {Coulomb} Wave Functions''
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Vos73; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
Fullerton: Algol-language accuracy monitor for Algorithm 300, which is generally accurate only to 3 digits.

entry:
@Article{Vos:1973:RAC,
  author =       "H. Vos",
  title =        "Remark on ``{Algorithm 300}: {Coulomb} Wave
                 Functions''",
  journal =      j-CACM,
  volume =       "16",
  number =       "5",
  pages =        "308--309",
  month =        may,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:27:34 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Vos73;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gunn:1967:ACW}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis); C7310 (Mathematics computing)",
  corpsource =   "Vrije Univ., Amsterdam, Netherlands",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; function evaluation;
                 mathematics; wave functions",
  oldlabel =     "Vos73",
  remark =       "Fullerton: Algol-language accuracy monitor for
                 Algorithm 300, which is generally accurate only to 3
                 digits.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Vos73",
}


bibtype: article
filename: elefunt.bib
label: Wong:1973:AEL
author: R. Wong
title: An Asymptotic Expansion of $ W_k, m(z) $ with Large Variable and Parameters
journal: j-MATH-COMPUT
volume: 27
number: 122
pages: 429--436
month: apr
monthnumber: 4
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: R. Wong
rawtitle: An Asymptotic Expansion of {$ W_{k, m}(z) $} with Large Variable and Parameters
entry:
@Article{Wong:1973:AEL,
  author =       "R. Wong",
  title =        "An Asymptotic Expansion of {$ W_{k, m}(z) $} with
                 Large Variable and Parameters",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "429--436",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Wong:1973:UAE
author: R. Wong
title: On uniform asymptotic expansion of definite integrals
journal: j-J-APPROX-THEORY
volume: 7
number: 1
pages: 76--86
month: jan
monthnumber: 1
year: 1973
CODEN: JAXTAZ
DOI: https://doi.org/10.1016/0021-9045(73)90055-5
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
MRclass: 41A60
MRnumber: 0340910
MRreviewer: L. Berg
bibdate: Sat Feb 18 15:20:40 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 15:20:40 ???
URL: http://www.sciencedirect.com/science/article/pii/0021904573900555
fjournal: Journal of Approximation Theory
keywords: incomplete gamma functions
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: R. Wong
rawtitle: On uniform asymptotic expansion of definite integrals
entry:
@Article{Wong:1973:UAE,
  author =       "R. Wong",
  title =        "On uniform asymptotic expansion of definite
                 integrals",
  journal =      j-J-APPROX-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "76--86",
  month =        jan,
  year =         "1973",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/0021-9045(73)90055-5",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "41A60",
  MRnumber =     "0340910",
  MRreviewer =   "L. Berg",
  bibdate =      "Sat Feb 18 15:20:40 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021904573900555",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  keywords =     "incomplete gamma functions",
}


bibtype: article
filename: elefunt.bib
label: Wrench:1973:ECT
author: John W. Wrench
title: Erratum: Concerning Two Series for the Gamma Function
journal: j-MATH-COMPUT
volume: 27
number: 123
pages: 681--682
month: jul
monthnumber: 7
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: Minor last-digit rounding errors are reported.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: John W. Wrench
rawtitle: Erratum: {Concerning Two Series for the Gamma Function}
entry:
@Article{Wrench:1973:ECT,
  author =       "John W. Wrench",
  title =        "Erratum: {Concerning Two Series for the Gamma
                 Function}",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "123",
  pages =        "681--682",
  month =        jul,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Minor last-digit rounding errors are
                 reported.",
}


bibtype: article
filename: elefunt.bib
label: Wrigge:1973:EII
author: H. S. Wrigge
title: An Elliptic Integral Identity
journal: j-MATH-COMPUT
volume: 27
number: 124
pages: 839--840
month: oct
monthnumber: 10
year: 1973
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: H. S. Wrigge
rawtitle: An Elliptic Integral Identity
entry:
@Article{Wrigge:1973:EII,
  author =       "H. S. Wrigge",
  title =        "An Elliptic Integral Identity",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "124",
  pages =        "839--840",
  month =        oct,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Yohe:1973:IBS
author: J. M. Yohe
title: Interval Bounds for Square Roots and Cube Roots
journal: j-COMPUTING
volume: 11
number: 1
pages: 51--57
month: mar
monthnumber: 3
year: 1973
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:51 MST 2001
bibtimestamp: 2001.01.02 17:40:51 MST
fjournal: Computing
acknowledgement: ack-jr
affiliation: Univ. Wisconsin, Madison, WI, USA
journalURL: http://link.springer.com/journal/607
rawauthor: J. M. Yohe
rawtitle: Interval Bounds for Square Roots and Cube Roots
bibsource:
https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date)

keywords:
binary computers; cube roots; error analysis; interval bounds; machine representable number; optimal upward directed rounding; smallest machine representable interval; square roots

entry:
@Article{Yohe:1973:IBS,
  author =       "J. M. Yohe",
  title =        "Interval Bounds for Square Roots and Cube Roots",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "1",
  pages =        "51--57",
  month =        mar,
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  affiliation =  "Univ. Wisconsin, Madison, WI, USA",
  classification = "C5230",
  description =  "digital arithmetic; error analysis",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "binary computers; cube roots; error analysis; interval
                 bounds; machine representable number; optimal upward
                 directed rounding; smallest machine representable
                 interval; square roots",
}


bibtype: article
filename: elefunt.bib
label: Acton:1974:RRF
author: Forman S. Acton
journal: j-CACM
volume: 17
number: 8
pages: 480--481
month: aug
monthnumber: 8
year: 1974
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65D20 (33A70)
MRnumber: 49 6554
bibdate: Mon Jan 22 06:20:27 MST 2001
bibtimestamp: 2001.01.22 06:20:27 MST
fjournal: Communications of the ACM
keywords: exponential integral; Fresnel integral; mathematical techniques; recurrence relations
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
journalabr: Commun ACM
rawauthor: Forman S. Acton
title:
Recurrence relations for the Fresnel integral $ int _0^infty exp ( - c t) d t / sqrt t (1 + t^2) $ and similar integrals

bibsource:
Compendex database; http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Acton74; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
The class of functions defined by $ int _0^infty [exp ( - c X)d t / (1 + Y)(t^1 / 2)^k] $ where $X$ and $Y$ are either $t$ or $ t^2 $ and $k$ is $ - 1 $, $0$, or $1$ can be evaluated by recurrences for all but small values of the parameter $c$. These recurrences, given here, are more efficient than the usual asymptotic series.

rawabstract:
The class of functions defined by $ \int_0^\infty [\exp ( - c X)d t / (1 + Y)(t^{1 / 2})^k] $ where $X$ and $Y$ are either $t$ or $ t^2 $ and $k$ is $ - 1 $, $0$, or $1$ can be evaluated by recurrences for all but small values of the parameter $c$. These recurrences, given here, are more efficient than the usual asymptotic series.

rawtitle:
Recurrence relations for the {Fresnel} integral $ \int_0^{\infty } \exp ( - c t) \, d t / \sqrt {t (1 + t^2)} $ and similar integrals

entry:
@Article{Acton:1974:RRF,
  author =       "Forman S. Acton",
  title =        "Recurrence relations for the {Fresnel} integral $
                 \int_0^{\infty } \exp ( - c t) \, d t / \sqrt {t (1 +
                 t^2)} $ and similar integrals",
  journal =      j-CACM,
  volume =       "17",
  number =       "8",
  pages =        "480--481",
  month =        aug,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65D20 (33A70)",
  MRnumber =     "49 6554",
  bibdate =      "Mon Jan 22 06:20:27 MST 2001",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Acton74;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The class of functions defined by $ \int_0^\infty
                 [\exp ( - c X)d t / (1 + Y)(t^{1 / 2})^k] $ where $X$
                 and $Y$ are either $t$ or $ t^2 $ and $k$ is $ - 1 $,
                 $0$, or $1$ can be evaluated by recurrences for all but
                 small values of the parameter $c$. These recurrences,
                 given here, are more efficient than the usual
                 asymptotic series.",
  acknowledgement = ack-nhfb,
  classification = "921",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "exponential integral; Fresnel integral; mathematical
                 techniques; recurrence relations",
  oldlabel =     "Acton74",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Acton74",
}


bibtype: article
filename: elefunt.bib
label: Amos:1974:CMB
author: D. E. Amos
title: Computation of modified Bessel functions and their ratios
journal: j-MATH-COMPUT
volume: 28
number: 125
pages: 239--251
month: jan
monthnumber: 1
year: 1974
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: Ratios $ I_nu + 1(x) / I_nu (x) $ are considered.
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Sandia Labs., Albuquerque, NM, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: D. E. Amos
rawtitle: Computation of modified {Bessel} functions and their ratios
keywords:
Bessel functions; computation; low order Bessel functions; modified Bessel functions; monotonicity; properties; ratios; recursion; relation

entry:
@Article{Amos:1974:CMB,
  author =       "D. E. Amos",
  title =        "Computation of modified {Bessel} functions and their
                 ratios",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "125",
  pages =        "239--251",
  month =        jan,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Sandia Labs., Albuquerque, NM, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; computation; low order Bessel
                 functions; modified Bessel functions; monotonicity;
                 properties; ratios; recursion; relation",
  remark =       "Fullerton: Ratios $ I_{\nu + 1}(x) / I_\nu (x) $ are
                 considered.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: elefunt.bib
label: Anonymous:1974:TCH
editor: Anonymous
title: Tables of Complex Hyperbolic and Circular Functions
volume: 23
publisher: Corona Pub. Co.
address: Tokyo, Japan
pages: 621
year: 1974
LCCN: QA55 .T172
bibdate: Sat Apr 1 14:49:41 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:49:41 MDT
series: Advanced series of mathematical and engineering tables
remark: Title and introduction also in Japanese: Fukuso saa okyokusen kansaa u hyaa o.
subject: Mathematics; Tables; Exponential functions; Trigonometrical functions
acknowledgement: ack-nhfb
raweditor: Anonymous
rawtitle: Tables of Complex Hyperbolic and Circular Functions
entry:
@Book{Anonymous:1974:TCH,
  editor =       "Anonymous",
  title =        "Tables of Complex Hyperbolic and Circular Functions",
  volume =       "23",
  publisher =    "Corona Pub. Co.",
  address =      "Tokyo, Japan",
  pages =        "621",
  year =         "1974",
  LCCN =         "QA55 .T172",
  bibdate =      "Sat Apr 1 14:49:41 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Advanced series of mathematical and engineering
                 tables",
  acknowledgement = ack-nhfb,
  remark =       "Title and introduction also in Japanese: Fukuso
                 s{\aa}okyokusen kans{\aa}u hy{\aa}o.",
  subject =      "Mathematics; Tables; Exponential functions;
                 Trigonometrical functions",
}


bibtype: article
filename: elefunt.bib
label: Barlow:1974:CCF
author: R. H. Barlow
title: Convergent Continued Fraction Approximants to Generalised Polylogarithms
journal: j-BIT
volume: 14
number: 1
pages: 112--116
month: mar
monthnumber: 3
year: 1974
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01933124
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:13 MST 2006
bibtimestamp: 2006.01.04 18:52:13 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=1&spage=112
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: R. H. Barlow
rawtitle: Convergent Continued Fraction Approximants to Generalised Polylogarithms
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=14&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
Fullerton: Nielsen's generalization $ S_n, p(z) = frac ( - 1)^n + p - 1(n - 1)! p! int _0^1 ln ^n - 1(t) ln ^p(1 - z t) / t d t $ is evaluated in the complex plane.

entry:
@Article{Barlow:1974:CCF,
  author =       "R. H. Barlow",
  title =        "Convergent Continued Fraction Approximants to
                 Generalised Polylogarithms",
  journal =      j-BIT,
  volume =       "14",
  number =       "1",
  pages =        "112--116",
  month =        mar,
  year =         "1974",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933124",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:13 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=14&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=1&spage=112",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: Nielsen's generalization $ S_{n, p}(z) =
                 \frac {( - 1)^{n + p - 1}(n - 1)! p!} \int_0^1 \ln^{n -
                 1}(t) \ln^p(1 - z t) / t \, d t $ is evaluated in the
                 complex plane.",
}


bibtype: article
filename: elefunt.bib
label: Barnett:1974:CWF
author: A. R. Barnett and D. H. Feng and J. W. Steed and L. J. B. Goldfarb
title: Coulomb wave functions for all real $ eta $ and $ rho $
journal: j-COMP-PHYS-COMM
volume: 8
number: 5
pages: 377--395
month: dec
monthnumber: 12
year: 1974
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(74)90013-7
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Jul 14 09:47:42 2008
bibtimestamp: 2008.07.14 09:47:42 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: A. R. Barnett and D. H. Feng and J. W. Steed and L. J. B. Goldfarb
rawtitle: {Coulomb} wave functions for all real $ \eta $ and $ \rho $
remark:
This paper may contain the first presentation of Steed's algorithm for computing continued fractions.

entry:
@Article{Barnett:1974:CWF,
  author =       "A. R. Barnett and D. H. Feng and J. W. Steed and L. J.
                 B. Goldfarb",
  title =        "{Coulomb} wave functions for all real $ \eta $ and $
                 \rho $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "8",
  number =       "5",
  pages =        "377--395",
  month =        dec,
  year =         "1974",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(74)90013-7",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Jul 14 09:47:42 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "This paper may contain the first presentation of
                 Steed's algorithm for computing continued fractions.",
}


bibtype: article
filename: elefunt.bib
label: Blair:1974:RCA
author: J. M. Blair
title: Rational Chebyshev approximations for the modified Bessel functions $ I_0 (x) $ and $ I_1 (x) $
journal: j-MATH-COMPUT
volume: 28
number: 126
pages: 581--583
month: apr
monthnumber: 4
year: 1974
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: With microfiche supplement. Relative errors down to $ 10^-23 $.
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: Atomic Energy Canada Ltd., Chalk River, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. M. Blair
keywords:
Chebyshev approximation; functions; modified Bessel; nearly best rational approximations; rational Chebyshev approximations; series (mathematics)

rawtitle:
Rational {Chebyshev} approximations for the modified {Bessel} functions {$ I_0 (x) $} and {$ I_1 (x) $}

entry:
@Article{Blair:1974:RCA,
  author =       "J. M. Blair",
  title =        "Rational {Chebyshev} approximations for the modified
                 {Bessel} functions {$ I_0 (x) $} and {$ I_1 (x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "581--583",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy Canada Ltd., Chalk River, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev approximation; functions; modified Bessel;
                 nearly best rational approximations; rational Chebyshev
                 approximations; series (mathematics)",
  remark =       "Fullerton: With microfiche supplement. Relative errors
                 down to $ 10^{-23} $.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Bosten:1974:RAI
author: Nancy E. Bosten and E. L. Battiste
title: Remark on ``Algorithm 179: Incomplete Beta Ratio''
journal: j-CACM
volume: 17
number: 3
pages: 156--157
month: mar
monthnumber: 3
year: 1974
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:27:36 MST 2001
bibtimestamp: 2001.01.22 06:27:36 MST
note: See cite Ludwig:1963:AIB,Pike:1976:RIB.
fjournal: Communications of the ACM
keywords: Algorithm 179; computer aided analysis; function approximation; incomplete beta ratio; subroutines
remark: Fullerton: FORTRAN routine with accuracy about $ 10^-6 $. See M. C. Pike (1976) for a Remark.
acknowledgement: ack-nhfb
corpsource: IMSL, Houston, TX, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: T Theoretical or Mathematical
rawauthor: Nancy E. Bosten and E. L. Battiste
rawnote: See \cite{Ludwig:1963:AIB,Pike:1976:RIB}.
rawtitle: Remark on ``{Algorithm 179}: {Incomplete} Beta Ratio''
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#BostenB74; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

classcodes:
B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation); C7310 (Mathematics computing)

entry:
@Article{Bosten:1974:RAI,
  author =       "Nancy E. Bosten and E. L. Battiste",
  title =        "Remark on ``{Algorithm 179}: {Incomplete} Beta
                 Ratio''",
  journal =      j-CACM,
  volume =       "17",
  number =       "3",
  pages =        "156--157",
  month =        mar,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:27:36 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#BostenB74;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Ludwig:1963:AIB,Pike:1976:RIB}.",
  acknowledgement = ack-nhfb,
  bdate =        "Mon Jan 22 06:27:36 MST 2001",
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation); C7310
                 (Mathematics computing)",
  corpsource =   "IMSL, Houston, TX, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Algorithm 179; computer aided analysis; function
                 approximation; incomplete beta ratio; subroutines",
  oldlabel =     "BostenB74",
  remark =       "Fullerton: FORTRAN routine with accuracy about $
                 10^{-6} $. See M. C. Pike (1976) for a Remark.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/BostenB74",
}


bibtype: article
filename: elefunt.bib
label: Brent:1974:AAG
author: Richard P. Brent
title: ACM Algorithm 488: a Gaussian pseudo-random number generator [G5]
journal: j-CACM
volume: 17
number: 12
pages: 704--706
month: dec
monthnumber: 12
year: 1974
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:28:05 MST 2001
bibtimestamp: 2001.01.22 06:28:05 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C7890 (Other special applications of computing)
corpsource: Australian Nat. Univ., Canberra, Australia
journalURL: https://dl.acm.org/loi/cacm
treatment: A Application; T Theoretical or Mathematical
rawauthor: Richard P. Brent
rawtitle: {ACM Algorithm 488}: a {Gaussian} pseudo-random number generator [{G5}]
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Brent74; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
distribution; FORTRAN; Gaussian; generator; GRAND; normal distribution; pseudo random numbers; random number generation; random numbers; subroutines

remark:
Fullerton: A FORTRAN routine that returns normally distributed numbers with zero mean and unit standard deviation.

entry:
@Article{Brent:1974:AAG,
  author =       "Richard P. Brent",
  title =        "{ACM Algorithm 488}: a {Gaussian} pseudo-random number
                 generator [{G5}]",
  journal =      j-CACM,
  volume =       "17",
  number =       "12",
  pages =        "704--706",
  month =        dec,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:28:05 MST 2001",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Brent74;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7890 (Other special applications of computing)",
  corpsource =   "Australian Nat. Univ., Canberra, Australia",
  country =      "USA",
  descriptors =  "RVG",
  enum =         "7061",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "distribution; FORTRAN; Gaussian; generator; GRAND;
                 normal distribution; pseudo random numbers; random
                 number generation; random numbers; subroutines",
  location =     "SEL: Wi",
  oldlabel =     "Brent74",
  references =   "0",
  remark =       "Fullerton: A FORTRAN routine that returns normally
                 distributed numbers with zero mean and unit standard
                 deviation.",
  revision =     "16/01/94",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Brent74",
}


bibtype: article
filename: elefunt.bib
label: Burrell:1974:AAE
author: Keith H. Burrell
journal: j-CACM
volume: 17
number: 9
pages: 524--526
month: sep
monthnumber: 9
year: 1974
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:28:58 MST 2001
bibtimestamp: 2001.01.22 06:28:58 MST
fjournal: Communications of the ACM
remark: Fullerton: 10-digit accuracy FORTRAN program.
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis); C7310 (Mathematics computing)
corpsource: California Inst. Technol., Pasadena, CA, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: A Application; T Theoretical or Mathematical
rawauthor: Keith H. Burrell
title:
ACM Algorithm 484: Evaluation of the Modified Bessel Functions $ K_0 (z) $ and $ K_1 (z) $ for Complex Arguments [S17]

bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Burrell74; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
algorithm; applications of computers; Bessel functions; complex arguments; function evaluation; Gauss-Hermite quadrature; Hankel functions; modified Bessel functions; natural sciences; subroutines

rawtitle:
{ACM Algorithm 484}: Evaluation of the Modified {Bessel} Functions {$ K_0 (z) $} and {$ K_1 (z) $} for Complex Arguments [{S17}]

entry:
@Article{Burrell:1974:AAE,
  author =       "Keith H. Burrell",
  title =        "{ACM Algorithm 484}: Evaluation of the Modified
                 {Bessel} Functions {$ K_0 (z) $} and {$ K_1 (z) $} for
                 Complex Arguments [{S17}]",
  journal =      j-CACM,
  volume =       "17",
  number =       "9",
  pages =        "524--526",
  month =        sep,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:28:58 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Burrell74;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis); C7310 (Mathematics computing)",
  corpsource =   "California Inst. Technol., Pasadena, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; applications of computers; Bessel
                 functions; complex arguments; function evaluation;
                 Gauss-Hermite quadrature; Hankel functions; modified
                 Bessel functions; natural sciences; subroutines",
  oldlabel =     "Burrell74",
  remark =       "Fullerton: 10-digit accuracy FORTRAN program.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Burrell74",
}


bibtype: article
filename: elefunt.bib
label: Buschman:1974:FSR
author: R. G. Buschman
title: Finite sum representations for partial derivatives of special functions with respect to parameters
journal: j-MATH-COMPUT
volume: 28
number: 127
pages: 817--824
month: jul
monthnumber: 7
year: 1974
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: Whittaker and Bessel functions are considered.
acknowledgement: ack-nhfb
corpsource: Univ. Wyoming, Laramie, WY, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: R. G. Buschman
rawtitle: Finite sum representations for partial derivatives of special functions with respect to parameters
keywords:
Bessel functions; differentiation; finite sum representations; finite sums; functions; G function; Gegenbauer functions; hypergeometric; Legendre; Mellin transformation; partial derivatives; special functions; Whittaker functions

classcodes:
B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)

entry:
@Article{Buschman:1974:FSR,
  author =       "R. G. Buschman",
  title =        "Finite sum representations for partial derivatives of
                 special functions with respect to parameters",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "127",
  pages =        "817--824",
  month =        jul,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. Wyoming, Laramie, WY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; differentiation; finite sum
                 representations; finite sums; functions; G function;
                 Gegenbauer functions; hypergeometric; Legendre; Mellin
                 transformation; partial derivatives; special functions;
                 Whittaker functions",
  remark =       "Fullerton: Whittaker and Bessel functions are
                 considered.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Carta:1974:HLR
author: David G. Carta
title: Help!!: The Lost Reference: (A Modified Newton Method for Square Roots)
journal: j-SIGNUM
volume: 9
number: 4
pages: 9--9
month: oct
monthnumber: 10
year: 1974
CODEN: SNEWD6
DOI: https://doi.org/10.1145/1206085.1206086
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Jun 17 18:47:00 MDT 2008
bibtimestamp: 2008.06.17 18:47:00 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: David G. Carta
rawtitle: Help!!: {The} Lost Reference: ({A} Modified {Newton} Method for Square Roots)
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib

abstract:
Around 1970 I saw a journal article describing a modified Newton iteration for square roots. It involved changing the usual factor of 0.5 in $ x_n + 1 = 0.5 (x_n + a / x_n) $ to $ c_n $ where $ c_n rightarrow 0.5 $, thereby increasing the asymptotic rate of convergence from $ e_n + 1 = 0.5 e_n^2 $ to $ e_n + 1 = 0.25 e_n^2 $.

rawabstract:
Around 1970 I saw a journal article describing a modified Newton iteration for square roots. It involved changing the usual factor of 0.5 in $ x_{n + 1} = 0.5 (x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow 0.5 $, thereby increasing the asymptotic rate of convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n + 1} = 0.25 e_n^2 $.

entry:
@Article{Carta:1974:HLR,
  author =       "David G. Carta",
  title =        "Help!!: {The} Lost Reference: ({A} Modified {Newton}
                 Method for Square Roots)",
  journal =      j-SIGNUM,
  volume =       "9",
  number =       "4",
  pages =        "9--9",
  month =        oct,
  year =         "1974",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1206085.1206086",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Jun 17 18:47:00 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  abstract =     "Around 1970 I saw a journal article describing a
                 modified Newton iteration for square roots. It involved
                 changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
                 (x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
                 0.5 $, thereby increasing the asymptotic rate of
                 convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
                 1} = 0.25 e_n^2 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1974:SAC
author: Henry E. Fettis
title: A stable algorithm for computing the inverse error function in the `tail-end' region
journal: j-MATH-COMPUT
volume: 28
number: 126
pages: 585--587
month: apr
monthnumber: 4
year: 1974
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Wright-Patterson Air Force Base, OH, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Henry E. Fettis
rawtitle: A stable algorithm for computing the inverse error function in the `tail-end' region
keywords:
function evaluation; inverse error function; iterative algorithm; stability; stable algorithm; tail end region

entry:
@Article{Fettis:1974:SAC,
  author =       "Henry E. Fettis",
  title =        "A stable algorithm for computing the inverse error
                 function in the `tail-end' region",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "585--587",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Wright-Patterson Air Force Base, OH, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function evaluation; inverse error function; iterative
                 algorithm; stability; stable algorithm; tail end
                 region",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Glasser:1974:SDI
author: M. L. Glasser
title: Some definite integrals of the product of two Bessel functions of the second kind: (order zero)
journal: j-MATH-COMPUT
volume: 28
number: 126
pages: 613--615
month: apr
monthnumber: 4
year: 1974
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Battelle Memorial Inst., Columbus, OH, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: M. L. Glasser
rawtitle: Some definite integrals of the product of two {Bessel} functions of the second kind: (order zero)
keywords:
Bessel functions; definite integrals; evaluate; function evaluation; integral representation; order; second kind; zero

entry:
@Article{Glasser:1974:SDI,
  author =       "M. L. Glasser",
  title =        "Some definite integrals of the product of two {Bessel}
                 functions of the second kind: (order zero)",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "613--615",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Battelle Memorial Inst., Columbus, OH, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; definite integrals; evaluate;
                 function evaluation; integral representation; order;
                 second kind; zero",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Hitotumatu:1974:NMC
author: Sin Hitotumatu
journal: Revue d'Analyse Numerique et de la Theorie de l'Approximation
volume: 3
number: 2
pages: 173--180
year: 1974
ISSN: 1010-3376 (print), 2457-8118 (electronic) OR 10103376 (print), 24578118 (electronic)
ISSNL: 1010-3376 OR 10103376
MRclass: 65D20
MRnumber: 381249
MRreviewer: L. Fox
bibdate: Tue Nov 14 17:19:58 2023
bibtimestamp: 2023.11.14 17:19:58 ???
URL: https://ictp.acad.ro/jnaat/journal/article/view/1974-vol3-no2-art7
fjournal: Revue d'Analyse Numerique et de la Theorie de l'Approximation
acknowledgement: ack-nhfb
ajournal: Rev. Anal. Numer. Theorie Approximation
journalURL: https://ictp.acad.ro/jnaat/journal
rawauthor: Sin Hitotumatu
title:
A new method for the computation of square root, exponential and logarithmic functions through hyperbolic CORDIC

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
A new method for the computation of square root, exponential and logarithmic functions through hyperbolic {CORDIC}

entry:
@Article{Hitotumatu:1974:NMC,
  author =       "Sin Hitotumatu",
  title =        "A new method for the computation of square root,
                 exponential and logarithmic functions through
                 hyperbolic {CORDIC}",
  journal =      "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
                 l'Approximation",
  volume =       "3",
  number =       "2",
  pages =        "173--180",
  year =         "1974",
  ISSN =         "1010-3376 (print), 2457-8118 (electronic)",
  ISSN-L =       "1010-3376",
  MRclass =      "65D20",
  MRnumber =     "381249",
  MRreviewer =   "L. Fox",
  bibdate =      "Tue Nov 14 17:19:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://ictp.acad.ro/jnaat/journal/article/view/1974-vol3-no2-art7",
  acknowledgement = ack-nhfb,
  ajournal =     "Rev. Anal. Num{\'e}r. Th{\'e}orie Approximation",
  fjournal =     "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
                 l'Approximation",
  journal-URL =  "https://ictp.acad.ro/jnaat/journal",
  reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}


bibtype: article
filename: elefunt.bib
label: Koppelaar:1974:CRA
author: Henk Koppelaar
title: Certification and Remark on ``Algorithm 191: Hypergeometric''
journal: j-CACM
volume: 17
number: 10
pages: 589--590
month: oct
monthnumber: 10
year: 1974
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:55:45 MST 2001
bibtimestamp: 2001.01.22 06:55:45 MST
note: See cite Relph:1963:AH.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: C7310 (Mathematics computing)
corpsource: Utrecht State Univ., Netherlands
journalURL: https://dl.acm.org/loi/cacm
treatment: G General Review; T Theoretical or Mathematical
rawauthor: Henk Koppelaar
rawnote: See \cite{Relph:1963:AH}.
rawtitle: Certification and Remark on ``{Algorithm 191}: Hypergeometric''
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Kopelaar74; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
algorithm; hypergeometric; improvements; inefficiency; natural sciences applications of computers; subroutines

remark:
Fullerton: Algol-language modifications for Algorithm 191, which does not appear to be accurate far from the origin.

entry:
@Article{Koppelaar:1974:CRA,
  author =       "Henk Koppelaar",
  title =        "Certification and Remark on ``{Algorithm 191}:
                 Hypergeometric''",
  journal =      j-CACM,
  volume =       "17",
  number =       "10",
  pages =        "589--590",
  month =        oct,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:55:45 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Kopelaar74;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Relph:1963:AH}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "Utrecht State Univ., Netherlands",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; hypergeometric; improvements; inefficiency;
                 natural sciences applications of computers;
                 subroutines",
  oldlabel =     "Kopelaar74",
  remark =       "Fullerton: Algol-language modifications for Algorithm
                 191, which does not appear to be accurate far from the
                 origin.",
  treatment =    "G General Review; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kopelaar74",
}


bibtype: article
filename: elefunt.bib
label: Kyriakopoulos:1974:GFH
author: E. Kyriakopoulos
title: Generating functions of the hypergeometric functions
journal: j-J-MATH-PHYS
volume: 15
number: 6
pages: 753--759
month: jun
monthnumber: 6
year: 1974
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.1666724
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Oct 28 16:40:13 MDT 2011
bibtimestamp: 2011.10.28 16:40:13 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v15/i6/p753_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
corpsource: Nuclear Res. Center 'Democritos', Athens, Greece
journalURL: http://jmp.aip.org/
onlinedate: 4 November 2003
treatment: T Theoretical or Mathematical
rawauthor: E. Kyriakopoulos
rawtitle: Generating functions of the hypergeometric functions
bibsource:
http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib

keywords:
functions; generating functions; hypergeometric functions; Lie groups; Lie theory; multiplier representation theory; Weisner's technique

entry:
@Article{Kyriakopoulos:1974:GFH,
  author =       "E. Kyriakopoulos",
  title =        "Generating functions of the hypergeometric functions",
  journal =      j-J-MATH-PHYS,
  volume =       "15",
  number =       "6",
  pages =        "753--759",
  month =        jun,
  year =         "1974",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1666724",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 16:40:13 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v15/i6/p753_s1",
  acknowledgement = ack-nhfb,
  classification = "A0210 (Algebra, set theory, and graph theory); A0220
                 (Group theory); A0230 (Function theory, analysis)",
  corpsource =   "Nuclear Res. Center 'Democritos', Athens, Greece",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "functions; generating functions; hypergeometric
                 functions; Lie groups; Lie theory; multiplier
                 representation theory; Weisner's technique",
  onlinedate =   "4 November 2003",
  pagecount =    "7",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Latham:1974:CPC
author: W. P. Latham and Rogers W. Redding
title: On the calculation of the parabolic cylinder functions
journal: j-J-COMPUT-PHYS
volume: 16
number: 1
pages: 66--75
month: sep
monthnumber: 9
year: 1974
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(74)90104-1
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:15 MST 2012
bibtimestamp: 2012.01.01 09:15:15 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999174901041
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: W. P. Latham and Rogers W. Redding
rawtitle: On the calculation of the parabolic cylinder functions
entry:
@Article{Latham:1974:CPC,
  author =       "W. P. Latham and Rogers W. Redding",
  title =        "On the calculation of the parabolic cylinder
                 functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "16",
  number =       "1",
  pages =        "66--75",
  month =        sep,
  year =         "1974",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(74)90104-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:15 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999174901041",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: McCabe:1974:CFE
author: J. H. McCabe
title: A continued fraction expansion, with a truncation error estimate, for Dawson's integral
journal: j-MATH-COMPUT
volume: 28
number: 127
pages: 811--816
month: jul
monthnumber: 7
year: 1974
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Univ. St. Andrews, Fife, UK
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. H. McCabe
rawtitle: A continued fraction expansion, with a truncation error estimate, for {Dawson}'s integral
keywords:
continued fraction expansion; convergents; Dawson's integral; error analysis; function approximation; rational approximations; truncation error estimate

classcodes:
B0290B (Error analysis in numerical methods); B0290F (Interpolation and function approximation); C4110 (Error analysis in numerical methods); C4130 (Interpolation and function approximation)

entry:
@Article{McCabe:1974:CFE,
  author =       "J. H. McCabe",
  title =        "A continued fraction expansion, with a truncation
                 error estimate, for {Dawson}'s integral",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "127",
  pages =        "811--816",
  month =        jul,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Univ. St. Andrews, Fife, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "continued fraction expansion; convergents; Dawson's
                 integral; error analysis; function approximation;
                 rational approximations; truncation error estimate",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Nasell:1974:IMB
author: Ingemar Nasell
title: Inequalities for Modified Bessel Functions
journal: j-MATH-COMPUT
volume: 28
number: 125
pages: 253--256
month: jan
monthnumber: 1
year: 1974
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Bessel functions; inequalities; modified Bessel functions; sharp versions
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis)
corpsource: Bell Labs., Holmdel, NJ, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Ingemar Nasell
rawtitle: Inequalities for Modified {Bessel} Functions
entry:
@Article{Nasell:1974:IMB,
  author =       "Ingemar Nasell",
  title =        "Inequalities for Modified {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "125",
  pages =        "253--256",
  month =        jan,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Bell Labs., Holmdel, NJ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; inequalities; modified Bessel
                 functions; sharp versions",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: elefunt.bib
label: Olver:1974:ASF
author: F. W. J. Olver
title: Asymptotics and Special Functions
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xvi + 572
year: 1974
ISBN: 0-12-525850-X OR 012525850X
ISBN13: 978-0-12-525850-0 OR 9780125258500
LCCN: QA351 .O481 1974
bibdate: Wed Dec 15 10:40:06 1993
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1993.12.15 10:40:06 ???
acknowledgement: ack-nhfb
rawauthor: F. W. J. Olver
rawtitle: Asymptotics and Special Functions
entry:
@Book{Olver:1974:ASF,
  author =       "F. W. J. Olver",
  title =        "Asymptotics and Special Functions",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvi + 572",
  year =         "1974",
  ISBN =         "0-12-525850-X",
  ISBN-13 =      "978-0-12-525850-0",
  LCCN =         "QA351 .O481 1974",
  bibdate =      "Wed Dec 15 10:40:06 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Pisarskii:1974:QCD
author: A. V. Pisarskiui and A. F. Kurgaev and A. V. Palagin
journal: Kibernetika (Kiev)
volume: 4
pages: 147--149
year: 1974
CODEN: KBRNA5
ISSN: 0023-1274 OR 00231274
MRclass: 65D20
MRnumber: 53 \#1915
MRreviewer: V. V. Ivanov
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: A. V. Pisarski{\u\i} and A. F. Kurgaev and A. V. Palagin
title:
On the question of the convergence of the ``digit by digit'' methods of computing the elementary functions

rawtitle:
On the question of the convergence of the {``digit by digit''} methods of computing the elementary functions

entry:
@Article{Pisarskii:1974:QCD,
  author =       "A. V. Pisarski{\u\i} and A. F. Kurgaev and A. V.
                 Palagin",
  title =        "On the question of the convergence of the {``digit by
                 digit''} methods of computing the elementary
                 functions",
  journal =      "Kibernetika (Kiev)",
  volume =       "4",
  pages =        "147--149",
  year =         "1974",
  CODEN =        "KBRNA5",
  ISSN =         "0023-1274",
  MRclass =      "65D20",
  MRnumber =     "53 \#1915",
  MRreviewer =   "V. V. Ivanov",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Pomeranz:1974:AAE
author: John Pomeranz
journal: j-CACM
volume: 17
number: 12
pages: 703--704
month: dec
monthnumber: 12
year: 1974
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:12:56 MST 2001
bibtimestamp: 2001.01.22 07:12:56 MST
note: See also cite Pomeranz:1976:REC.
fjournal: Communications of the ACM
remark: Fullerton: FORTRAN routine accurate apparently to 5 digits.
acknowledgement: ack-nhfb
classcodes: C7310 (Mathematics computing)
corpsource: Purdue Univ., West Lafayette, IN, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: A Application; T Theoretical or Mathematical
rawauthor: John Pomeranz
rawnote: See also \cite{Pomeranz:1976:REC}.
title:
ACM Algorithm 487: Exact Cumulative Distribution of the Kolmogorov--Smirnov Statistic for Small Samples

bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Pomeranz74; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
algorithm; exact cumulative distribution; FORTRAN; Kolmogorov Smirnov test; natural sciences applications of computers; small samples; statistic; statistics; subroutines

rawtitle:
{ACM Algorithm 487}: Exact Cumulative Distribution of the {Kolmogorov--Smirnov} Statistic for Small Samples

entry:
@Article{Pomeranz:1974:AAE,
  author =       "John Pomeranz",
  title =        "{ACM Algorithm 487}: Exact Cumulative Distribution of
                 the {Kolmogorov--Smirnov} Statistic for Small Samples",
  journal =      j-CACM,
  volume =       "17",
  number =       "12",
  pages =        "703--704",
  month =        dec,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:12:56 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Pomeranz74;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Pomeranz:1976:REC}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "Purdue Univ., West Lafayette, IN, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; exact cumulative distribution; FORTRAN;
                 Kolmogorov Smirnov test; natural sciences applications
                 of computers; small samples; statistic; statistics;
                 subroutines",
  oldlabel =     "Pomeranz74",
  remark =       "Fullerton: FORTRAN routine accurate apparently to 5
                 digits.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Pomeranz74",
}


bibtype: article
filename: elefunt.bib
label: Shaw:1974:NME
author: Mary Shaw and J. F. Traub
title: On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives
journal: j-J-ACM
volume: 21
number: 1
pages: 161--167
month: jan
monthnumber: 1
year: 1974
CODEN: JACOAH
DOI: https://doi.org/10.1145/321796.321810
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Wed Jan 15 18:12:53 MST 1997
bibtimestamp: 1997.01.15 18:12:53 MST
fjournal: Journal of the Association for Computing Machinery
keywords: mathematical techniques; number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: Mary Shaw and J. F. Traub
rawtitle: On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives
bibsource:
Compendex database; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib

abstract:
A family of new algorithms is given for evaluating the first $m$ derivatives of a polynomial. In particular, it is shown that all derivatives may be evaluated in $ 3 n - 2 $ multiplications. The best previous result required $ (1 / 2) n (n + 1) $ multiplications. Some optimality results are presented.

rawabstract:
A family of new algorithms is given for evaluating the first $m$ derivatives of a polynomial. In particular, it is shown that all derivatives may be evaluated in $ 3 n - 2 $ multiplications. The best previous result required $ (1 / 2) n (n + 1) $ multiplications. Some optimality results are presented.

entry:
@Article{Shaw:1974:NME,
  author =       "Mary Shaw and J. F. Traub",
  title =        "On the Number of Multiplications for the Evaluation of
                 a Polynomial and Some of Its Derivatives",
  journal =      j-J-ACM,
  volume =       "21",
  number =       "1",
  pages =        "161--167",
  month =        jan,
  year =         "1974",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321796.321810",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "A family of new algorithms is given for evaluating the
                 first $m$ derivatives of a polynomial. In particular,
                 it is shown that all derivatives may be evaluated in $
                 3 n - 2 $ multiplications. The best previous result
                 required $ (1 / 2) n (n + 1) $ multiplications. Some
                 optimality results are presented.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "921",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  keywords =     "mathematical techniques; number of multiplications to
                 evaluate a polynomial",
}


bibtype: article
filename: elefunt.bib
label: Sheorey:1974:CEW
author: V. B. Sheorey
title: Chebyshev Expansions for Wavefunctions
journal: j-COMP-PHYS-COMM
volume: 7
number: 1
pages: 1--12
month: jan
monthnumber: 1
year: 1974
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(74)90053-8
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Oct 30 10:36:29 2010
bibtimestamp: 2010.10.30 10:36:29 ???
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: V. B. Sheorey
rawtitle: {Chebyshev} Expansions for Wavefunctions
entry:
@Article{Sheorey:1974:CEW,
  author =       "V. B. Sheorey",
  title =        "{Chebyshev} Expansions for Wavefunctions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "7",
  number =       "1",
  pages =        "1--12",
  month =        jan,
  year =         "1974",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(74)90053-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:36:29 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Stegun:1974:ACM
author: I. A. Stegun and R. Zucker
title: Automatic Computing Methods for Special Functions. Part II. The Exponential Integral $ E_n(x) $
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 78B
number: 4
pages: 199--216
month: oct
monthnumber: 10
year: 1974
ISSN: 0091-0635 OR 00910635
bibdate: Sat Oct 30 11:00:40 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 11:00:40 ???
fjournal: Journal of Research of the National Bureau of Standards (1934)
remark: Fullerton: Adjustable double precision FORTRAN routines for $ E_n(x) $ and $ e^x E_n(x) $.
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: I. A. Stegun and R. Zucker
rawtitle:
Automatic Computing Methods for Special Functions. {Part II}. {The} Exponential Integral {$ E_n(x) $}

entry:
@Article{Stegun:1974:ACM,
  author =       "I. A. Stegun and R. Zucker",
  title =        "Automatic Computing Methods for Special Functions.
                 {Part II}. {The} Exponential Integral {$ E_n(x) $}",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "78B",
  number =       "4",
  pages =        "199--216",
  month =        oct,
  year =         "1974",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 11:00:40 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Adjustable double precision FORTRAN
                 routines for $ E_n(x) $ and $ e^x E_n(x) $.",
}


bibtype: article
filename: elefunt.bib
label: Wang:1974:UEZ
author: Paul S. Wang
title: The Undecidability of the Existence of Zeros of Real Elementary Functions
journal: j-J-ACM
volume: 21
number: 4
pages: 586--589
month: oct
monthnumber: 10
year: 1974
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Wed Jan 15 18:12:53 MST 1997
bibtimestamp: 1997.01.15 18:12:53 MST
fjournal: Journal of the ACM
keywords: mathematical techniques
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: Paul S. Wang
rawtitle: The Undecidability of the Existence of Zeros of Real Elementary Functions
bibsource:
Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
From Richardson's undecidability results, it is shown that the predicate ``there exists a real number such that G(r) equals 0'' is recursively undecidable for G(x) in a class of functions which involves polynomials and the sine function. The deduction follows that the convergence of a class of improper integrals is recursively undecidable.

rawabstract:
From Richardson's undecidability results, it is shown that the predicate ``there exists a real number such that G(r) equals 0'' is recursively undecidable for G(x) in a class of functions which involves polynomials and the sine function. The deduction follows that the convergence of a class of improper integrals is recursively undecidable.

entry:
@Article{Wang:1974:UEZ,
  author =       "Paul S. Wang",
  title =        "The Undecidability of the Existence of Zeros of Real
                 Elementary Functions",
  journal =      j-J-ACM,
  volume =       "21",
  number =       "4",
  pages =        "586--589",
  month =        oct,
  year =         "1974",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "From Richardson's undecidability results, it is shown
                 that the predicate ``there exists a real number such
                 that G(r) equals 0'' is recursively undecidable for
                 G(x) in a class of functions which involves polynomials
                 and the sine function. The deduction follows that the
                 convergence of a class of improper integrals is
                 recursively undecidable.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "921",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  keywords =     "mathematical techniques",
}


bibtype: article
filename: elefunt.bib
label: Wimp:1974:CTP
author: J. Wimp
title: On the computation of Tricomi's Psi function
journal: j-COMPUTING
volume: 13
number: 3--4
pages: 195--203
year: 1974
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Jan 2 17:40:52 MST 2001
bibtimestamp: 2001.01.02 17:40:52 MST
fjournal: Computing
remark: Fullerton: Backward recursion methods are discussed.
acknowledgement: ack-nhfb
affiliation: Drexel Univ., Philadelphia, PA, USA
journalURL: http://link.springer.com/journal/607
journalabr: Comput (Vienna/NY)
rawauthor: J. Wimp
rawtitle: On the computation of {Tricomi}'s {Psi} function
bibsource:
Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; INSPEC Axiom database (1968--date)

keywords:
computation; computer programming --- Subroutines; confluent hypergeometric function; convergence; mathematical techniques; recurrence relations; Tricomi's

entry:
@Article{Wimp:1974:CTP,
  author =       "J. Wimp",
  title =        "On the computation of {Tricomi}'s {Psi} function",
  journal =      j-COMPUTING,
  volume =       "13",
  number =       "3--4",
  pages =        "195--203",
  year =         "1974",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:52 MST 2001",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nhfb,
  affiliation =  "Drexel Univ., Philadelphia, PA, USA",
  citedby =      "Fullerton:1980:BEM",
  classification = "723; 921; B0290D; C4120",
  description =  "convergence of numerical methods; function
                 evaluation",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "computation; computer programming --- Subroutines;
                 confluent hypergeometric function; convergence;
                 mathematical techniques; recurrence relations;
                 Tricomi's",
  remark =       "Fullerton: Backward recursion methods are discussed.",
}


bibtype: article
filename: elefunt.bib
label: Baker:1975:MER
author: P. W. Baker
title: More efficient radix-2 algorithms for some elementary functions
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 11
pages: 1049--1054
month: nov
monthnumber: 11
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224132
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 68A10
MRnumber: 52 \#7193
MRreviewer: I. Kaufmann
bibdate: Tue Jul 12 07:57:58 MDT 2011
bibtimestamp: 2011.07.12 07:57:58 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672725
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. W. Baker
rawtitle: More efficient radix-2 algorithms for some elementary functions
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/cordic.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib

entry:
@Article{Baker:1975:MER,
  author =       "P. W. Baker",
  title =        "More efficient radix-2 algorithms for some elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "11",
  pages =        "1049--1054",
  month =        nov,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224132",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68A10",
  MRnumber =     "52 \#7193",
  MRreviewer =   "I. Kaufmann",
  bibdate =      "Tue Jul 12 07:57:58 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672725",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  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: Baker:1975:PMA
author: P. W. Baker
title: Parallel Multiplicative Algorithms for Some Elementary Functions
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 3
pages: 322--325
month: mar
monthnumber: 3
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224215
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:51 MDT 2011
bibtimestamp: 2011.07.12 07:57:51 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672808
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. W. Baker
rawtitle: Parallel Multiplicative Algorithms for Some Elementary Functions
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/ieeetranscomput1970.bib

abstract:
This correspondence presents generalized higher radix algorithms for some elementary functions which use fast parallel $m$-bit multipliers where $ mathrm radix = 2^m $. These algorithms are extensions of those iterative schemes which are based on multiplications by $ (1 + 2^-i) $ and the use of prestored values of $ ln (1 + 2^-i) $ and $ tan ^-1(2^-i) $. The particular functions under consideration are $ y / x $, $ y / x^1 / 2 $, $ y exp (x) $, $ y + ln (x) $, $ sin (x) $ and $ cos (x) $ [and hence $ tan (x) $ ]. The extended algorithms rely on multiplication by $ (1 + mathrm dir^-k) $ where $ mathrm dir $, $ 0 leq mathrm dir $, is an $m$-bit integer. Using a simple selection procedure for $ mathrm dir $, simulations show that $p$ (radix $r$) digits of a function may be generated, on the average, in less than $ p + 1 $ iterations.

remark:
The final paragraph says: ``In order to obtain an answer with $p$ correct digits in radix $ 2^m$, an extra $ log _2 ((p + 1) m)$ guard digits ought to be used and $k$ should be taken to $ p + 2$ with the final result rounded to $p$ digits.'' That corresponds to 5 to 7 extra bits in the four IEEE 754 binary formats.

rawabstract:
This correspondence presents generalized higher radix algorithms for some elementary functions which use fast parallel $m$-bit multipliers where $ \mathrm {radix} = 2^m $. These algorithms are extensions of those iterative schemes which are based on multiplications by $ (1 + 2^{-i}) $ and the use of prestored values of $ \ln (1 + 2^{-i}) $ and $ \tan^{-1}(2^{-i}) $. The particular functions under consideration are $ y / x $, $ y / x^{1 / 2} $, $ y \exp (x) $, $ y + \ln (x) $, $ \sin (x) $ and $ \cos (x) $ [and hence $ \tan (x) $ ]. The extended algorithms rely on multiplication by $ (1 + \mathrm {dir}^{-k}) $ where $ \mathrm {dir} $, $ 0 \leq \mathrm {dir} $, is an $m$-bit integer. Using a simple selection procedure for $ \mathrm {dir} $, simulations show that $p$ (radix $r$) digits of a function may be generated, on the average, in less than $ p + 1 $ iterations.

entry:
@Article{Baker:1975:PMA,
  author =       "P. W. Baker",
  title =        "Parallel Multiplicative Algorithms for Some Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "322--325",
  month =        mar,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224215",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:51 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/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672808",
  abstract =     "This correspondence presents generalized higher radix
                 algorithms for some elementary functions which use fast
                 parallel $m$-bit multipliers where $ \mathrm {radix} =
                 2^m $. These algorithms are extensions of those
                 iterative schemes which are based on multiplications by
                 $ (1 + 2^{-i}) $ and the use of prestored values of $
                 \ln (1 + 2^{-i}) $ and $ \tan^{-1}(2^{-i}) $. The
                 particular functions under consideration are $ y / x $,
                 $ y / x^{1 / 2} $, $ y \exp (x) $, $ y + \ln (x) $, $
                 \sin (x) $ and $ \cos (x) $ [and hence $ \tan (x) $ ].
                 The extended algorithms rely on multiplication by $ (1
                 + \mathrm {dir}^{-k}) $ where $ \mathrm {dir} $, $ 0
                 \leq \mathrm {dir} $, is an $m$-bit integer. Using a
                 simple selection procedure for $ \mathrm {dir} $,
                 simulations show that $p$ (radix $r$) digits of a
                 function may be generated, on the average, in less than
                 $ p + 1 $ iterations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  received =     "27 March 1973",
  remark =       "The final paragraph says: ``In order to obtain an
                 answer with $p$ correct digits in radix $ 2^m$, an
                 extra $ \log_2 ((p + 1) m)$ guard digits ought to be
                 used and $k$ should be taken to $ p + 2$ with the final
                 result rounded to $p$ digits.'' That corresponds to 5
                 to 7 extra bits in the four IEEE 754 binary formats.",
  revised =      "7 October 1974",
}


bibtype: article
filename: elefunt.bib
label: Boris:1975:NEO
author: Jay P. Boris and Elaine S. Oran
title: Numerical evaluation of oscillatory integrals such as the modified Bessel function $ K_i zeta (x) $
journal: j-J-COMPUT-PHYS
volume: 17
number: 4
pages: 425--433
month: apr
monthnumber: 4
year: 1975
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(75)90045-5
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 09:15:17 MST 2012
bibtimestamp: 2012.01.01 09:15:17 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999175900455
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Jay P. Boris and Elaine S. Oran
rawtitle:
Numerical evaluation of oscillatory integrals such as the modified {Bessel} function {$ K_{i \zeta }(x) $}

entry:
@Article{Boris:1975:NEO,
  author =       "Jay P. Boris and Elaine S. Oran",
  title =        "Numerical evaluation of oscillatory integrals such as
                 the modified {Bessel} function {$ K_{i \zeta }(x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "17",
  number =       "4",
  pages =        "425--433",
  month =        apr,
  year =         "1975",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(75)90045-5",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:17 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999175900455",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: techreport
filename: elefunt.bib
label: Brent:1975:FMP
author: R. P. Brent
title: Fast Multiple-precision Evaluation of Elementary Functions
type: Technical Report
number: STAN-CS-75-515
institution: inst-STAN-CS
address: inst-STAN-CS:adr
pages: i + 22
month: aug
monthnumber: 8
year: 1975
bibdate: Thu Jan 11 16:47:21 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.01.11 16:47:21 ???
acknowledgement: ack-nhfb
rawauthor: R. P. Brent
rawtitle: Fast Multiple-precision Evaluation of Elementary Functions
URL:
https://bitsavers.org/pdf/stanford/cs_techReports/STAN-CS-75_515_Brent_Fast_Multiple-Precision_Evaluation_Of_Elementary_Functions_Aug75.pdf

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

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

entry:
@TechReport{Brent:1975:FMP,
  author =       "R. P. Brent",
  title =        "Fast Multiple-precision Evaluation of Elementary
                 Functions",
  type =         "Technical Report",
  number =       "STAN-CS-75-515",
  institution =  inst-STAN-CS,
  address =      inst-STAN-CS:adr,
  pages =        "i + 22",
  month =        aug,
  year =         "1975",
  bibdate =      "Thu Jan 11 16:47:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://bitsavers.org/pdf/stanford/cs_techReports/STAN-CS-75_515_Brent_Fast_Multiple-Precision_Evaluation_Of_Elementary_Functions_Aug75.pdf",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \arctan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply n-bit
                 integers. We show that f(x) can be evaluated, with
                 relative error $ O(2^{-n}) $, in $ O(M(n) \log (n)) $
                 operations as $ n \to \infty $, for any floating-point
                 number $x$ (with an $n$-bit fraction) in a suitable
                 finite interval. From the Sch{\"o}nhage--Strassen bound
                 on $ M(n)$, it follows that an $n$-bit approximation to
                 $ f(x)$ may be evaluated in $ O(n \log^2 (n) \log \log
                 (n))$ operations. Special cases include the evaluation
                 of constants such as $ \pi $, $e$, and $ e^p i$. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic--geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: elefunt.bib
label: Brent:1975:MZM
author: R. P. (Richard P.) Brent
title: Multiple-precision zero-finding methods and the complexity of elementary function evaluation
institution: Department of Computer Science, Carnegie-Mellon University
address: Pittsburgh, PA, USA
pages: 26
year: 1975
bibdate: Sat Jan 11 10:14:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 10:14:06 MST
keywords: Iterative methods (Mathematics)
acknowledgement: ack-nhfb
rawauthor: R. P. (Richard P.) Brent
rawtitle: Multiple-precision zero-finding methods and the complexity of elementary function evaluation
entry:
@TechReport{Brent:1975:MZM,
  author =       "R. P. (Richard P.) Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "26",
  year =         "1975",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Iterative methods (Mathematics)",
  searchkey =    "ti:elementary n1 function",
}


bibtype: article
filename: elefunt.bib
label: Carta:1975:LOA
author: David G. Carta
title: Low-Order Approximations for the Normal Probability Integral and the Error Function
journal: j-MATH-COMPUT
volume: 29
number: 131
pages: 856--862
month: jul
monthnumber: 7
year: 1975
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: David G. Carta
rawtitle: Low-Order Approximations for the Normal Probability Integral and the Error Function
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database

keywords:
error function; fraction; integral equations; linear minimax problems; linear programming; low; normal probability integral; order approximations; polynomials; rational

classcodes:
B0260 (Optimisation techniques); B0290R (Integral equations); C1180 (Optimisation techniques); C4180 (Integral equations)

entry:
@Article{Carta:1975:LOA,
  author =       "David G. Carta",
  title =        "Low-Order Approximations for the Normal Probability
                 Integral and the Error Function",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "856--862",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0260 (Optimisation techniques); B0290R (Integral
                 equations); C1180 (Optimisation techniques); C4180
                 (Integral equations)",
  corpsource =   "Jet Propulsion Lab., California Inst. of Technol.,
                 Pasadena, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "error function; fraction; integral equations; linear
                 minimax problems; linear programming; low; normal
                 probability integral; order approximations;
                 polynomials; rational",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Cody:1975:FPS
author: W. J. Cody
title: The FUNPACK Package of Special Function Subroutines
journal: j-TOMS
volume: 1
number: 1
pages: 13--25
month: mar
monthnumber: 3
year: 1975
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355626.355631
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Aug 26 23:44:16 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.26 23:44:16 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. J. Cody
rawtitle: The {FUNPACK} Package of Special Function Subroutines
entry:
@Article{Cody:1975:FPS,
  author =       "W. J. Cody",
  title =        "The {FUNPACK} Package of Special Function
                 Subroutines",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "13--25",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355631",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: phdthesis
filename: elefunt.bib
label: Epstein:1975:AET
author: Harvey Irwin Epstein
title: Algorithms for elementary transcendental function arithmetic
school: University of Wisconsin
address: Madison, WI, USA
pages: 409
year: 1975
bibdate: Sat Jan 11 10:14:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 10:14:06 MST
keywords: Algorithms.; Functions -- Data processing.; Functions, Transcendental.
acknowledgement: ack-nhfb
annote: Typescript. Vita. Thesis (Ph. D.)--University of Wisconsin--Madison, 1975.
rawauthor: Harvey Irwin Epstein
rawtitle: Algorithms for elementary transcendental function arithmetic
entry:
@PhdThesis{Epstein:1975:AET,
  author =       "Harvey Irwin Epstein",
  title =        "Algorithms for elementary transcendental function
                 arithmetic",
  school =       "University of Wisconsin",
  address =      "Madison, WI, USA",
  pages =        "409",
  year =         "1975",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "Typescript. Vita. Thesis (Ph. D.)--University of
                 Wisconsin--Madison, 1975.",
  keywords =     "Algorithms.; Functions -- Data processing.; Functions,
                 Transcendental.",
  searchkey =    "ti:elementary n1 function",
}


bibtype: phdthesis
filename: elefunt.bib
label: Ercegovac:1975:GMEa
author: Milos Dragutin Ercegovac
title: A General Method for Evaluation of Functions and Computations in a Digital Computer
type: Ph.D. Thesis
school: Department of Computer Science, University of Illinois at Urbana-Champaign
address: Urbana-Champaign, IL, USA
pages: viii + 109
month: jul
monthnumber: 7
year: 1975
bibdate: Mon Feb 10 07:18:12 2020
bibtimestamp: 2020.02.10 07:18:12 ???
URL: https://search.proquest.com/pqdtglobal/docview/302756306
acknowledgement: ack-nhfb
advisor: James E. Robertson
rawauthor: Milo{\v{s}} Dragutin Ercegovac
rawtitle: A General Method for Evaluation of Functions and Computations in a Digital Computer
entry:
@PhdThesis{Ercegovac:1975:GMEa,
  author =       "Milo{\v{s}} Dragutin Ercegovac",
  title =        "A General Method for Evaluation of Functions and
                 Computations in a Digital Computer",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana-Champaign, IL, USA",
  pages =        "viii + 109",
  month =        jul,
  year =         "1975",
  bibdate =      "Mon Feb 10 07:18:12 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://search.proquest.com/pqdtglobal/docview/302756306",
  acknowledgement = ack-nhfb,
  advisor =      "James E. Robertson",
}


bibtype: article
filename: elefunt.bib
label: Ferguson:1975:PFI
author: Helaman Rolfe Pratt Ferguson and Dale E. Nielsen and Grant Cook
title: A partition formula for the integer coefficients of the theta function nome
journal: j-MATH-COMPUT
volume: 29
number: 131
pages: 851--855
month: jul
monthnumber: 7
year: 1975
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: Incomplete elliptic integrals can be expressed as a series of theta functions.
acknowledgement: ack-nhfb
classcodes: B0290R (Integral equations); C4180 (Integral equations)
corpsource: Dept. of Math., Brigham Young Univ., Provo, UT, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Helaman Rolfe Pratt Ferguson and Dale E. Nielsen and Grant Cook
rawtitle: A partition formula for the integer coefficients of the theta function nome
keywords:
coefficients; complete elliptic integrals; elliptic function theory; elliptic integrals; incomplete; integral equations; partition formula; theta function nome integer

entry:
@Article{Ferguson:1975:PFI,
  author =       "Helaman Rolfe Pratt Ferguson and Dale E. Nielsen and
                 Grant Cook",
  title =        "A partition formula for the integer coefficients of
                 the theta function nome",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "851--855",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290R (Integral equations); C4180 (Integral
                 equations)",
  corpsource =   "Dept. of Math., Brigham Young Univ., Provo, UT, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "coefficients; complete elliptic integrals; elliptic
                 function theory; elliptic integrals; incomplete;
                 integral equations; partition formula; theta function
                 nome integer",
  remark =       "Fullerton: Incomplete elliptic integrals can be
                 expressed as a series of theta functions.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Fornberg:1975:CZJ
author: B. Fornberg and K. S. Kolbig
title: Complex zeros of the Jonquiere or polylogarithm function
journal: j-MATH-COMPUT
volume: 29
number: 130
pages: 582--599
month: apr
monthnumber: 4
year: 1975
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: CERN, Geneva, Switzerland
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: B. Fornberg and K. S. Kolbig
rawtitle: Complex zeros of the {Jonquiere} or polylogarithm function
keywords:
asymptotic; behaviour; complex zero trajectories; Jonquiere function; poles and zeros; polylogarithm function; polynomials; Riemann zeta function

entry:
@Article{Fornberg:1975:CZJ,
  author =       "B. Fornberg and K. S. Kolbig",
  title =        "Complex zeros of the {Jonquiere} or polylogarithm
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "130",
  pages =        "582--599",
  month =        apr,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "CERN, Geneva, Switzerland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic; behaviour; complex zero trajectories;
                 Jonquiere function; poles and zeros; polylogarithm
                 function; polynomials; Riemann zeta function",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gargantini:1975:PSR
author: I. Gargantini
editor: K. Nickel
booktitle: Interval Mathematics
title: Parallel Square Root Iterations
volume: 29
publisher: pub-SV
address: pub-SV:adr
pages: 196--204
year: 1975
bibdate: Fri Jan 12 11:37:56 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.01.12 11:37:56 ???
series: Lecture Notes In Computer Science
acknowledgement: ack-jr
rawauthor: I. Gargantini
rawbooktitle: Interval Mathematics
raweditor: K. Nickel
rawtitle: Parallel Square Root Iterations
entry:
@InProceedings{Gargantini:1975:PSR,
  author =       "I. Gargantini",
  editor =       "K. Nickel",
  booktitle =    "Interval Mathematics",
  title =        "Parallel Square Root Iterations",
  volume =       "29",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "196--204",
  year =         "1975",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes In Computer Science",
  acknowledgement = ack-jr,
}


bibtype: inproceedings
filename: elefunt.bib
label: Gautschi:1975:CMS
author: W. Gautschi
title: Computational Methods in Special Functions --- a Survey
crossref: Askey:1975:TAS
pages: 1--98
year: 1975
bibdate: Sat Oct 30 07:42:41 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 07:42:41 ???
remark: Fullerton: Extensive list of references.
acknowledgement: ack-nhfb
rawauthor: W. Gautschi
rawtitle: Computational Methods in Special Functions --- a Survey
entry:
@InProceedings{Gautschi:1975:CMS,
  author =       "W. Gautschi",
  title =        "Computational Methods in Special Functions --- a
                 Survey",
  crossref =     "Askey:1975:TAS",
  pages =        "1--98",
  year =         "1975",
  bibdate =      "Sat Oct 30 07:42:41 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: Extensive list of references.",
}


bibtype: article
filename: elefunt.bib
label: Ginsberg:1975:AAD
author: E. S. Ginsberg and Dorothy Zaborowski
title: ACM Algorithm 490: The Dilogarithm Function of a Real Argument [S22]
journal: j-CACM
volume: 18
number: 4
pages: 200--202
month: apr
monthnumber: 4
year: 1975
CODEN: CACMA2
DOI: https://doi.org/10.1145/360715.360722
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:44:28 MST 2001
bibtimestamp: 2001.01.22 06:44:28 MST
note: See also cite Morris:1976:RDF.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
classcodes: B0290D (Functional analysis); C4120 (Functional analysis); C7310 (Mathematics computing)
corpsource: Dept. of Phys., Univ. of Massachusetts, Boston, MA, USA
journalURL: https://dl.acm.org/loi/cacm
treatment: A Application; T Theoretical or Mathematical
rawauthor: E. S. Ginsberg and Dorothy Zaborowski
rawnote: See also \cite{Morris:1976:RDF}.
rawtitle: {ACM Algorithm 490}: The Dilogarithm Function of a Real Argument [{S22}]
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#GinsbergZ75; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
dilogarithm function; electrodynamics; ferromagnets; function evaluation; function subroutine; ideal; library; network analysis; polymers; quantum; real argument; subprograms; subroutines; thermodynamics

remark:
Fullerton: FORTRAN routine accurate to 15 digits for evaluating $ operatorname Li_2 (x) = - int _0^infty frac ln (1 z)z d z $.

entry:
@Article{Ginsberg:1975:AAD,
  author =       "E. S. Ginsberg and Dorothy Zaborowski",
  title =        "{ACM Algorithm 490}: The Dilogarithm Function of a
                 Real Argument [{S22}]",
  journal =      j-CACM,
  volume =       "18",
  number =       "4",
  pages =        "200--202",
  month =        apr,
  year =         "1975",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/360715.360722",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:44:28 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#GinsbergZ75;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Morris:1976:RDF}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis); C7310 (Mathematics computing)",
  corpsource =   "Dept. of Phys., Univ. of Massachusetts, Boston, MA,
                 USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "dilogarithm function; electrodynamics; ferromagnets;
                 function evaluation; function subroutine; ideal;
                 library; network analysis; polymers; quantum; real
                 argument; subprograms; subroutines; thermodynamics",
  oldlabel =     "GinsbergZ75",
  remark =       "Fullerton: FORTRAN routine accurate to 15 digits for
                 evaluating $ \operatorname {Li}_2 (x) = - \int_0^\infty
                 \frac {\ln (1 z)z} \, d z $.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GinsbergZ75",
}


bibtype: article
filename: elefunt.bib
label: Headley:1975:DZG
author: V. B. Headley and V. K. Barwell
title: On the distribution of the zeros of generalized Airy functions
journal: j-MATH-COMPUT
volume: 29
number: 131
pages: 863--877
month: jul
monthnumber: 7
year: 1975
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290P (Differential equations); C4170 (Differential equations)
corpsource: Dept. of Math., Brock Univ., St. Catherines, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: V. B. Headley and V. K. Barwell
rawtitle: On the distribution of the zeros of generalized {Airy} functions
keywords:
Bessel functions; boundary rays; differential equations; generalized Airy functions; nonreal zeros; zeros distribution

entry:
@Article{Headley:1975:DZG,
  author =       "V. B. Headley and V. K. Barwell",
  title =        "On the distribution of the zeros of generalized {Airy}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "863--877",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290P (Differential equations); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Math., Brock Univ., St. Catherines, Ont.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; boundary rays; differential
                 equations; generalized Airy functions; nonreal zeros;
                 zeros distribution",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hitotumatu:1975:SRU
author: Sin Hitotumatu
title: Some remarks on the unified treatment of elementary functions by microprogramming
crossref: Miller:1975:TNA
pages: 51--56 (vol. 2)
year: 1975
MRclass: 65D15
MRnumber: 54 \#11733
MRreviewer: Luciano Biasini
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Sin Hitotumatu
rawtitle: Some remarks on the unified treatment of elementary functions by microprogramming
entry:
@InProceedings{Hitotumatu:1975:SRU,
  author =       "Sin Hitotumatu",
  title =        "Some remarks on the unified treatment of elementary
                 functions by microprogramming",
  crossref =     "Miller:1975:TNA",
  pages =        "51--56 (vol. 2)",
  year =         "1975",
  MRclass =      "65D15",
  MRnumber =     "54 \#11733",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Ikebe:1975:ZRC
author: Yasuhiko Ikebe
title: The Zeros of Regular Coulomb Wave Functions and of Their Derivatives
journal: j-MATH-COMPUT
volume: 29
number: 131
pages: 878--887
month: jul
monthnumber: 7
year: 1975
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290H (Linear algebra); C4140 (Linear algebra)
corpsource: Centre Numerical Analysis, Univ. of Texas, Austin, TX, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Yasuhiko Ikebe
rawtitle: The Zeros of Regular {Coulomb} Wave Functions and of Their Derivatives
keywords:
Bessel function; compact matrix; eigenvalues; eigenvalues and eigenfunctions; function zeros characterisation; matrix algebra; methods; numerical; operators; regular Coulomb wave functions; wave functions; zeros

entry:
@Article{Ikebe:1975:ZRC,
  author =       "Yasuhiko Ikebe",
  title =        "The Zeros of Regular {Coulomb} Wave Functions and of
                 Their Derivatives",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "878--887",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290H (Linear algebra); C4140 (Linear algebra)",
  corpsource =   "Centre Numerical Analysis, Univ. of Texas, Austin, TX,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; compact matrix; eigenvalues;
                 eigenvalues and eigenfunctions; function zeros
                 characterisation; matrix algebra; methods; numerical;
                 operators; regular Coulomb wave functions; wave
                 functions; zeros",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Kaufman:1975:URA
author: E. H. Kaufman and G. D. Taylor
title: Uniform rational approximation of functions of several variables
journal: j-INT-J-NUMER-METHODS-ENG
volume: 9
number: 2
pages: 297--323
month: jan
monthnumber: 1
year: 1975
CODEN: IJNMBH
DOI: https://doi.org/10.1002/nme.1620090204
ISSN: 0029-5981 (print), 1097-0207 (electronic) OR 00295981 (print), 10970207 (electronic)
ISSNL: 0029-5981 OR 00295981
bibdate: Mon Nov 10 09:55:39 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.11.10 09:55:39 ???
fjournal: International Journal for Numerical Methods in Engineering
acknowledgement: ack-nhfb
ajournal: Int. J. Numer. Methods Eng.
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207
rawauthor: E. H. Kaufman and G. D. Taylor
rawtitle: Uniform rational approximation of functions of several variables
entry:
@Article{Kaufman:1975:URA,
  author =       "E. H. Kaufman and G. D. Taylor",
  title =        "Uniform rational approximation of functions of several
                 variables",
  journal =      j-INT-J-NUMER-METHODS-ENG,
  volume =       "9",
  number =       "2",
  pages =        "297--323",
  month =        jan,
  year =         "1975",
  CODEN =        "IJNMBH",
  DOI =          "https://doi.org/10.1002/nme.1620090204",
  ISSN =         "0029-5981 (print), 1097-0207 (electronic)",
  ISSN-L =       "0029-5981",
  bibdate =      "Mon Nov 10 09:55:39 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Numer. Methods Eng.",
  fjournal =     "International Journal for Numerical Methods in
                 Engineering",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
}


bibtype: article
filename: elefunt.bib
label: Kioustelidis:1975:PLA
author: J. B. Kioustelidis and J. K. Petrou
title: A Piecewise Linear Approximation of $ log _2 x $ with Equal Maximum Errors in All Intervals
journal: j-IEEE-TRANS-COMPUT
volume: C-24
number: 9
pages: 858--861
month: sep
monthnumber: 9
year: 1975
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1975.224330
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 07:57:56 MDT 2011
bibtimestamp: 2011.07.12 07:57:56 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672923
fjournal: IEEE Transactions on Computers
keywords: $log _2(x)$; elementary function
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. B. Kioustelidis and J. K. Petrou
rawtitle: A Piecewise Linear Approximation of $ \log_2 x $ with Equal Maximum Errors in All Intervals
abstract:
In this paper it is shown how to divide the interval $ [1, 2] $ into $n$ parts so that the uniform linear approximation of $ log _2 x $ in each subinterval has the same maximum error. This error is, in the case $ n = 4 $, smaller by a factor of $ 2.3 $ than the error of the linear mean-square approximation given by Hall et al. [1]. The final products of the mathematical analysis are explicit formulas which allow the direct determination of all parameters and the maximum error for any desired number $n$ of subdivisions of $ [1, 2] $.

rawabstract:
In this paper it is shown how to divide the interval $ [1, 2] $ into $n$ parts so that the uniform linear approximation of $ \log_2 x $ in each subinterval has the same maximum error. This error is, in the case $ n = 4 $, smaller by a factor of $ 2.3 $ than the error of the linear mean-square approximation given by Hall et al. [1]. The final products of the mathematical analysis are explicit formulas which allow the direct determination of all parameters and the maximum error for any desired number $n$ of subdivisions of $ [1, 2] $.

entry:
@Article{Kioustelidis:1975:PLA,
  author =       "J. B. Kioustelidis and J. K. Petrou",
  title =        "A Piecewise Linear Approximation of $ \log_2 x $ with
                 Equal Maximum Errors in All Intervals",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "9",
  pages =        "858--861",
  month =        sep,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224330",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672923",
  abstract =     "In this paper it is shown how to divide the interval $
                 [1, 2] $ into $n$ parts so that the uniform linear
                 approximation of $ \log_2 x $ in each subinterval has
                 the same maximum error. This error is, in the case $ n
                 = 4 $, smaller by a factor of $ 2.3 $ than the error of
                 the linear mean-square approximation given by Hall et
                 al. [1]. The final products of the mathematical
                 analysis are explicit formulas which allow the direct
                 determination of all parameters and the maximum error
                 for any desired number $n$ of subdivisions of $ [1, 2]
                 $.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "$\log_2(x)$; elementary function",
}


bibtype: article
filename: elefunt.bib
label: Lewis:1975:CPF
author: John Gregg Lewis
title: Certification of ``Algorithm 349: Polygamma Functions with Arbitrary Precision''
journal: j-TOMS
volume: 1
number: 4
pages: 380--382
month: dec
monthnumber: 12
year: 1975
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Jun 16 10:31:40 2000
bibtimestamp: 2000.06.16 10:31:40 ???
note: See cite TadeudeMedeiros:1969:APF.
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: polygamma functions; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: John Gregg Lewis
rawnote: See \cite{TadeudeMedeiros:1969:APF}.
rawtitle: Certification of ``{Algorithm} 349: Polygamma Functions with Arbitrary Precision''
entry:
@Article{Lewis:1975:CPF,
  author =       "John Gregg Lewis",
  title =        "Certification of ``{Algorithm} 349: Polygamma
                 Functions with Arbitrary Precision''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "380--382",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 16 10:31:40 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{TadeudeMedeiros:1969:APF}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "polygamma functions; special functions",
}


bibtype: book
filename: elefunt.bib
label: Luke:1975:MFT
author: Yudell L. Luke
title: Mathematical Functions and Their Approximations
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xvii + 568
year: 1975
ISBN: 0-12-459950-8, 1-4832-6245-6 (e-book) OR 0124599508, 1483262456 (ebook)
ISBN13: 978-0-12-459950-5, 978-1-4832-6245-1 (e-book) OR 9780124599505, 9781483262451 (ebook)
LCCN: QA55 .L96 1975
bibdate: Fri Jun 30 05:58:16 MDT 2023
bibtimestamp: 2023.06.30 05:58:16 MDT
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawtitle: Mathematical Functions and Their Approximations
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/master.bib

URL:
https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5

remark:
An updated version of part of Handbook of mathematical functions with formulas, graphs, and mathematical tables, edited by M. Abramowitz and I.A. Stegun. Includes indexes.

subject:
Mathematics; Tables; Fonctions (Matheematiques); Matheematiques; Calculus; Mathematical Analysis; Mathematics; Approximation; Funktion; Mathematik; Spezielle Funktion

TOC:
Preface / xv I. The Gamma Function and Related Functions 1.1 Definitions and Elementary Properties / 1 1.2 Power Series and Other Series Expansions / 1 1.3 Asymptotic Expansions / 7 1.4 Rational Approximations for y (z) / 13 1.5 Inequalities / 17 1.6 Bibliographic and Numerical Data / 20 1.6.1 General References / 20 1.6.2 Description of and References to Tables / 21 1.6.3 Description of and References to Other Approximations and Expansions / 22 II. The Binomial Function 2.1 Power Series / 24 2.2 Expansions in Series of Jacobi and Chebyshev Polynomials / 24 2.3 Expansions in Series of Bessel Functions / 26 2.4 Pade Approximations / 27 24.1 $(1 + 1 / z)^-c$ / 27 2.4.2 The Square Root / 28 2.4.3 Pade Coefficients / 30 2.4.4 The Function $e^-w$ / 31 2.5 Inequalities / 34 III. Elementary Functions 3.1 Logarithmic Functions / 36 3.1.1 Power Series / 36 3.1.2 Expansion in Series of Chebyshev Polynomials / 38 3.1.3 Pade Approximations / 39 3.1.4 Inequalities / 41 3.2 Exponential Function / 42 3.2.1 Series Expansions / 42 3.2.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions / 42 3.2.3 Pade Approximations / 46 3.2.4 Inequalities / 51 3.3 Circular and Hyperbolic Functions / 52 3.3.1 Power Series / 52 3.3.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions / 52 3.3.3 Rational and Pade Approximations / 57 3.3.4 Inequalities / 60 3.4 Inverse Circular and Hyperbolic Functions / 61 3.4.1 Power Series / 61 3.4.2 Expansions in Series of Chebyshev Polynomials / 63 3.4.3 Pade Approximations / 68 3.4.4 Inequalities / 72 3.5 Bibliographic and Numerical Data / 74 3.5.1 Description of and References to Tables / 74 3.5.2 Description of and References to Other Approximations and Expansions / 74 IV. Incomplete Gamma Functions 4.1 Definitions and Series Expansions / 77 4.2 Differential Equations and Difference Equations / 78 4.3 Pade Approximations / 79 4.3.1 $_1F_1(1; nu + 1; -z)$ / 79 4.3.2 $z^1 - nu e^z Gamma (nu , z)$ / 82 4.3.3 The Error $T_n(nu , z)$ for $|rm arg z/k| leq pi $ / 84 4.3.4 The Negative Real Axis and the Zeros of $F_n(nu , z)$ / 89 4.4 Inequalities / 95 4.4.1 $H(nu , z)$ / 95 4.4.2 $Gamma (nu , z)$ / 96 4.5 Notes on the Computation of the Incomplete Gamma Function / 97 4.6 Exponential Integrals / 103 4.6.1 Relation to Incomplete Gamma Function and Other Properties / 103 4.6.2 Expansions in Series of Chebyshev Polynomials / 104 4.6.3 Rational and Pad Approximations / 106 4.7 Cosine and Sine Integrals / 115 4.7.1 Relation to Exponential Integral and Other Properties / 115 4.7.2 Expansions in Series of Chebyshev Polynomials / 116 4.8 Error Functions / 119 4.8.1 Relation to Incomplete Gamma Function and Other Properties / 119 4.8.2 Expansions in Series of Chebyshev Polynomials and Bessel Functions / 122 4.8.3 Pade Approximations / 124 4.8.4 Trapezoidal Rule Approximations / 134 4.8.5 Inequalities / 137 4.9 Fresnel Integrals / 139 4.9.1 Relation to Error Functions and Other Properties / 139 4.9.2 Expansions in Series of Chebyshev Polynomials / 140 4.10 Bibliographic and Numerical Data / 143 4.10.1 References / 143 4.10.2 Description of and References to Tables / 143 4.10.3 Description of and References to Other Approximations and Expansions / 149 V. The Generalized Hypergeometric Function $_pF_g$ and the $G$-Function 5.1 Introduction / 154 5.2 The $_pF_q$ / 155 5.2.1 Power Series / 155 5.2.2 Derivatives and Contiguous Relations / 159 5.2.3 Integral Representations and Integrals Involving the $_pF_q$ / 160 5.2.4 Evaluation for Special Values of the Variable and Parameters / 163 5.3 The $G$-Function / 170 5.3.1 Definition and Relation to the $_pF_q$ / 170 5.3.2 Elementary Properties / 176 5.3.3 Analytic Continuation of $G_p, p^m, n(z)$ / 178 5.4 The Confluence Principle / 179 5.5 Multiplication Theorems / 184 5.6 Integrals Involving $G$-Functions / 186 5.7 Differential Equations / 190 5.7.1 The $_pF_q$ / 190 5.7.2 The $G$-Function / 192 5.8 Series of $G$-Functions / 194 5.8.1 Introduction / 194 5.8.2 Notation / 194 5.8.3 Expansion Theorems / 197 5.9 Asymptotic Expansions / 199 5.9.1 $G_p, q^q, n(z)$, $n = 0, 1$ / 199 5.9.2 $G_p, q^m, n(z)$ / 201 5.9.3 $_pF_q(z)$ / 206 5.10 Expansions in Series of Generalized Jacobi, Generalized Laguerre and Chebyshev Polynomials / 213 5.10.1 Expansions for $G$-Functions / 213 5.10.2 Expansions for $_pF_q$ / 220 5.11 Expansions in Series of Bessel Functions / 223 5.12 Polynomial and Rational Approximations / 224 5.13 Recurrence Formulas for Polynomials and Functions Occurring in Approximations to Generalized Hypergeometric Functions / 234 5.13.1 Introduction / 234 5.13.2 Recursion Formulas for Extended Jacobi and Laguerre Functions / 235 5.13.3 Recursion Formulas for the Numerator and Denominator Polynomials in the Rational Approximations for the Generalized Hypergeometric Function / 244 5.13.4 Recursion Formula for Coefficients in the Expansion of the $G$-Function in Series of Extended Jacobi Polynomials / 247 5.14 Inequalities / 252 VI. The Gaussian Hypergeometric Function $_2F_1$ 6.1 Introduction / 257 6.2 Elementary Properties / 257 6.2.1 Derivatives / 257 6.2.2 Contiguous Relations / 258 6.2.3 Integral Representations / 259 6.3 Differential Equations / 260 6.4 Kummer Solutions and Transformation Formulae / 262 6.5 Analytic Continuation / 263 6.6 The Complete Solution and Wronskians / 265 6.7 Quadratic Transformations / 270 6.8 The $_2F_1$ for Special Values of the Argument / 271 6.9 Expansion in Series of Chebyshev Polynomials / 274 6.10 Pade Approximations for $_2F_1(1, sigma ;rho + 1;-1/z)$ / 274 6.11 Inequalities / 278 6.12 Bibliographic and Numerical Data / 279 6.12.1 References / 279 6.12.2 Description of and References to Tables / 279 VII. The Confluent Hypergeometric Function 7.1 Introduction / 284 7.2 Integral Representations / 284 7.3 Elementary Relations / 285 7.3.1 Derivatives / 285 7.3.2 Contiguous Relations / 285 7.3.3 Products of Confluent Functions / 286 7.4 Differential Equations / 287 7.5 The Complete Solution and Wronskians / 288 7.6 Asymptotic Expansions / 291 7.7 Expansions in Series of Chebyshev Polynomials / 293 7.8 Expansions in Series of Besse! Functions / 294 7.9 Inequalities / 295 7.10 Other Notations and Related Functions / 295 7.11 Bibliographic and Numerical Data / 296 7.11.1 References / 296 7.11.2 Description of and References to Tables and Other Approximations / 296 VIII. Identification of the $_pF_q$, and $G$-Functions with the Special Functions 8.1 Introduction / 298 8.2 Named Special Functions Expressed as $_pF_q$'s / 298 8.2.1 Elementary Functions / 298 8.2.2 The Incomplete Gamma Function and Related Functions / 298 8.2.3 The Gaussian Hypergeometric Function / 298 8.2.4 Legendre Functions / 299 8.2.5 Orthogonal Polynomials / 299 8.2.6 Complete Elliptic Integrals / 299 8.2.7 Confluent Hypergeometric Functions, Whittaker Functions and Bessel Functions / 300 8.3 Named Functions Expressed in Terms of the $G$-Function / 300 8.4 The $G$-Function Expressed as a Named Function / 306 IX. Bessel Functions and Their Integrals 9.1 Introduction / 311 9.2 Definitions, Connecting Relations and Power Series / 311 9.3 Difference--Differential Formulas / 313 9.4 Products of Bessel Functions / 314 9.5 Asymptotic Expansions for Large Variable / 315 9.6 Integrals of Bessel Functions / 315 9.7 Expansions in Series of Chebyshev Polynomials / 316 9.8 Expansions in Series of Bessel Functions / 360 9.9 Rational Approximations / 361 9.9.1 Introduction / 361 9.9.2 $I_nu (z)$, $z$ Small / 361 9.9.3 $K_nu (z)$, $z$ Large / 366 9.10 Computation of Bessel Functions by Use of Recurrence Formulas / 380 9.10.1 Introduction / 380 9.10.2 Backward Recurrence Schemata for Generating $I_nu (z)$ / 380 9.10.3 Closed Form Expressions / 382 9.10.4 Expressions for $J_nu (z)$ / 389 9.10.5 Numerical Examples / 392 9.11 Evaluation of Bessel Functions by Application of Trapezoidal Type Integration Formulas / 395 9.12 Inequalities / 399 9.13 Bibliographic and Numerical Data / 403 9.13.1 References / 403 9.13.2 Description of and References to Tables / 404 9.13.3 Description of and References to Other Approximations and Expansions / 410 X. Lommel Functions, Struve Functions, and Associated Bessel Functions 10.1 Definitions, Connecting Relations and Power Series / 413 10.2 Asymptotic Expansions / 415 10.3 Expansions in Series of Chebyshev Polynomials and Bessel Functions / 415 10.4 Rational Approximations for $H_nu (z) - Y_nu (z)$ and the Errors in These Approximations / 422 10.5 Bibliographic and Numerical Data / 426 10.5.1 References / 426 10.5.2 Description of and References to Tables / 426 XI. Orthogonal Polynomials 11.1 Introduction / 428 11.2 Orthogonal Properties / 428 11.3 Jacobi Polynomials / 436 11.3.1 Expansion Formulae / 436 11.3.2 Difference--Differential Formulae / 439 11.3.3 Integrals / 439 11.3.4 Expansion of $x^rho $ in Series of Jacobi Polynomials / 440 11.3.5 Convergence Theorems for the Expansion of Arbitrary Functions in Series of Jacobi Polynomials / 442 11.3.6 Evaluation and Estimation of the Coefficients in the Expansion of a Given Function $f(x)$ in Series of Jacobi Polynomials / 443 11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ / 453 11.5 The Chebyshev Polynomials $T_n^*(x)$ and $U_n^*(x)$ / 459 11.6 Coefficients for Expansion of Integrals of Functions in Series of Chebyshev Polynomials of the First Kind / 464 11.6.1 Introduction / 464 11.6.2 Series of Shifted Chebyshev Polynomials / 464 11.6.3 Series of Chebyshev Polynomials of Even Order / 468 11.6.4 Series of Chebyshev Polynomials of Odd Order / 468 11.7 Orthogonality Properties of Chebyshev Polynomials with Respect to Summation / 469 11.8 A Nesting Procedure for the Computation of Expansions in Series of Functions Where the Functions Satisfy a Linear Finite Difference Equation / 475 XII. Computation by Use of Recurrence Formulas 12.1 Introduction / 483 12.2 Homogeneous Difference Equations / 483 12.3 Inhomogeneous Difference Equations / 487 XIII. Some Aspects of Rational and Polynomial Approximations 13.1 Introduction / 490 13.2 Approximations in Series of Chebyshev Polynomials of the First Kind / 490 13.3 The Pade Table / 493 13.4 Approximation of Functions Defined by a Differential Equation --- The $tau $-Method / 495 13.5 Approximations of Functions Defined by a Series / 499 13.6 Solution of Differential Equations in Series of Chebyshev Polynomials of the First Kind / 500 XIV. Miscellaneous Topics 14.1 Introduction / 505 14.2 Bernoulli Polynomials and Numbers / 505 14.3 $D$ and $delta $ Operators / 507 14.4 Computation and Check of the Tables / 509 14.5 Mathematical Constants / 512 14.6 Late Bibliography / 516 Bibliography / 517 Notation Index / 545 Subject Index / 551

rawTOC:
Preface / xv \\ \\ I. The Gamma Function and Related Functions \\ \\ 1.1 Definitions and Elementary Properties / 1 \\ 1.2 Power Series and Other Series Expansions / 1 \\ 1.3 Asymptotic Expansions / 7 \\ 1.4 Rational Approximations for y (z) / 13 \\ 1.5 Inequalities / 17 \\ 1.6 Bibliographic and Numerical Data / 20 \\ 1.6.1 General References / 20 \\ 1.6.2 Description of and References to Tables / 21 \\ 1.6.3 Description of and References to Other Approximations and Expansions / 22 \\ \\ II. The Binomial Function \\ \\ 2.1 Power Series / 24 \\ 2.2 Expansions in Series of Jacobi and Chebyshev Polynomials / 24 \\ 2.3 Expansions in Series of Bessel Functions / 26 \\ 2.4 Pad{\'e} Approximations / 27 \\ 24.1 $(1 + 1 / z)^{-c}$ / 27 \\ 2.4.2 The Square Root / 28 \\ 2.4.3 Pad{\'e} Coefficients / 30 \\ 2.4.4 The Function $e^{-w}$ / 31 \\ 2.5 Inequalities / 34 \\ \\ III. Elementary Functions \\ \\ 3.1 Logarithmic Functions / 36 \\ 3.1.1 Power Series / 36 \\ 3.1.2 Expansion in Series of Chebyshev Polynomials / 38 \\ 3.1.3 Pad{\'e} Approximations / 39 \\ 3.1.4 Inequalities / 41 \\ 3.2 Exponential Function / 42 \\ 3.2.1 Series Expansions / 42 \\ 3.2.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions / 42 \\ 3.2.3 Pad{\'e} Approximations / 46 \\ 3.2.4 Inequalities / 51 \\ 3.3 Circular and Hyperbolic Functions / 52 \\ 3.3.1 Power Series / 52 \\ 3.3.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions / 52 \\ 3.3.3 Rational and Pad{\'e} Approximations / 57 \\ 3.3.4 Inequalities / 60 \\ 3.4 Inverse Circular and Hyperbolic Functions / 61 \\ 3.4.1 Power Series / 61 \\ 3.4.2 Expansions in Series of Chebyshev Polynomials / 63 \\ 3.4.3 Pad{\'e} Approximations / 68 \\ 3.4.4 Inequalities / 72 \\ 3.5 Bibliographic and Numerical Data / 74 \\ 3.5.1 Description of and References to Tables / 74 \\ 3.5.2 Description of and References to Other Approximations and Expansions / 74 \\ \\ IV. Incomplete Gamma Functions \\ \\ 4.1 Definitions and Series Expansions / 77 \\ 4.2 Differential Equations and Difference Equations / 78 \\ 4.3 Pad{\'e} Approximations / 79 \\ 4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\ 4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\ 4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq \pi$ / 84 \\ 4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu, z)$ / 89 \\ 4.4 Inequalities / 95 \\ 4.4.1 $H(\nu, z)$ / 95 \\ 4.4.2 $\Gamma(\nu, z)$ / 96 \\ 4.5 Notes on the Computation of the Incomplete Gamma Function / 97 \\ 4.6 Exponential Integrals / 103 \\ 4.6.1 Relation to Incomplete Gamma Function and Other Properties / 103 \\ 4.6.2 Expansions in Series of Chebyshev Polynomials / 104 \\ 4.6.3 Rational and Pad Approximations / 106 \\ 4.7 Cosine and Sine Integrals / 115 \\ 4.7.1 Relation to Exponential Integral and Other Properties / 115 \\ 4.7.2 Expansions in Series of Chebyshev Polynomials / 116 \\ 4.8 Error Functions / 119 \\ 4.8.1 Relation to Incomplete Gamma Function and Other Properties / 119 \\ 4.8.2 Expansions in Series of Chebyshev Polynomials and Bessel Functions / 122 \\ 4.8.3 Pad{\'e} Approximations / 124 \\ 4.8.4 Trapezoidal Rule Approximations / 134 \\ 4.8.5 Inequalities / 137 \\ 4.9 Fresnel Integrals / 139 \\ 4.9.1 Relation to Error Functions and Other Properties / 139 \\ 4.9.2 Expansions in Series of Chebyshev Polynomials / 140 \\ 4.10 Bibliographic and Numerical Data / 143 \\ 4.10.1 References / 143 \\ 4.10.2 Description of and References to Tables / 143 \\ 4.10.3 Description of and References to Other Approximations and Expansions / 149 \\ \\ V. The Generalized Hypergeometric Function $_pF_g$ and the $G$-Function \\ \\ 5.1 Introduction / 154 \\ 5.2 The $_pF_q$ / 155 \\ 5.2.1 Power Series / 155 \\ 5.2.2 Derivatives and Contiguous Relations / 159 \\ 5.2.3 Integral Representations and Integrals Involving the $_pF_q$ / 160 \\ 5.2.4 Evaluation for Special Values of the Variable and Parameters / 163 \\ 5.3 The $G$-Function / 170 \\ 5.3.1 Definition and Relation to the $_pF_q$ / 170 \\ 5.3.2 Elementary Properties / 176 \\ 5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ / 178 \\ 5.4 The Confluence Principle / 179 \\ 5.5 Multiplication Theorems / 184 \\ 5.6 Integrals Involving $G$-Functions / 186 \\ 5.7 Differential Equations / 190 \\ 5.7.1 The $_pF_q$ / 190 \\ 5.7.2 The $G$-Function / 192 \\ 5.8 Series of $G$-Functions / 194 \\ 5.8.1 Introduction / 194 \\ 5.8.2 Notation / 194 \\ 5.8.3 Expansion Theorems / 197 \\ 5.9 Asymptotic Expansions / 199 \\ 5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\ 5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\ 5.9.3 $_pF_q(z)$ / 206 \\ 5.10 Expansions in Series of Generalized Jacobi, Generalized Laguerre and Chebyshev Polynomials / 213 \\ 5.10.1 Expansions for $G$-Functions / 213 \\ 5.10.2 Expansions for $_pF_q$ / 220 \\ 5.11 Expansions in Series of Bessel Functions / 223 \\ 5.12 Polynomial and Rational Approximations / 224 \\ 5.13 Recurrence Formulas for Polynomials and Functions Occurring in Approximations to Generalized Hypergeometric Functions / 234 \\ 5.13.1 Introduction / 234 \\ 5.13.2 Recursion Formulas for Extended Jacobi and Laguerre Functions / 235 \\ 5.13.3 Recursion Formulas for the Numerator and Denominator Polynomials in the Rational Approximations for the Generalized Hypergeometric Function / 244 \\ 5.13.4 Recursion Formula for Coefficients in the Expansion of the $G$-Function in Series of Extended Jacobi Polynomials / 247 \\ 5.14 Inequalities / 252 \\ \\ VI. The Gaussian Hypergeometric Function $_2F_1$ \\ \\ 6.1 Introduction / 257 \\ 6.2 Elementary Properties / 257 \\ 6.2.1 Derivatives / 257 \\ 6.2.2 Contiguous Relations / 258 \\ 6.2.3 Integral Representations / 259 \\ 6.3 Differential Equations / 260 \\ 6.4 Kummer Solutions and Transformation Formulae / 262 \\ 6.5 Analytic Continuation / 263 \\ 6.6 The Complete Solution and Wronskians / 265 \\ 6.7 Quadratic Transformations / 270 \\ 6.8 The $_2F_1$ for Special Values of the Argument / 271 \\ 6.9 Expansion in Series of Chebyshev Polynomials / 274 \\ 6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho + 1;-1/z)$ / 274 \\ 6.11 Inequalities / 278 \\ 6.12 Bibliographic and Numerical Data / 279 \\ 6.12.1 References / 279 \\ 6.12.2 Description of and References to Tables / 279 \\ \\ VII. The Confluent Hypergeometric Function \\ \\ 7.1 Introduction / 284 \\ 7.2 Integral Representations / 284 \\ 7.3 Elementary Relations / 285 \\ 7.3.1 Derivatives / 285 \\ 7.3.2 Contiguous Relations / 285 \\ 7.3.3 Products of Confluent Functions / 286 \\ 7.4 Differential Equations / 287 \\ 7.5 The Complete Solution and Wronskians / 288 \\ 7.6 Asymptotic Expansions / 291 \\ 7.7 Expansions in Series of Chebyshev Polynomials / 293 \\ 7.8 Expansions in Series of Besse! Functions / 294 \\ 7.9 Inequalities / 295 \\ 7.10 Other Notations and Related Functions / 295 \\ 7.11 Bibliographic and Numerical Data / 296 \\ 7.11.1 References / 296 \\ 7.11.2 Description of and References to Tables and Other Approximations / 296 \\ \\ VIII. Identification of the $_pF_q$, and $G$-Functions with the Special Functions \\ \\ 8.1 Introduction / 298 \\ 8.2 Named Special Functions Expressed as $_pF_q$'s / 298 \\ 8.2.1 Elementary Functions / 298 \\ 8.2.2 The Incomplete Gamma Function and Related Functions / 298 \\ 8.2.3 The Gaussian Hypergeometric Function / 298 \\ 8.2.4 Legendre Functions / 299 \\ 8.2.5 Orthogonal Polynomials / 299 \\ 8.2.6 Complete Elliptic Integrals / 299 \\ 8.2.7 Confluent Hypergeometric Functions, Whittaker Functions and Bessel Functions / 300 \\ 8.3 Named Functions Expressed in Terms of the $G$-Function / 300 \\ 8.4 The $G$-Function Expressed as a Named Function / 306 \\ \\ IX. Bessel Functions and Their Integrals \\ \\ 9.1 Introduction / 311 \\ 9.2 Definitions, Connecting Relations and Power Series / 311 \\ 9.3 Difference--Differential Formulas / 313 \\ 9.4 Products of Bessel Functions / 314 \\ 9.5 Asymptotic Expansions for Large Variable / 315 \\ 9.6 Integrals of Bessel Functions / 315 \\ 9.7 Expansions in Series of Chebyshev Polynomials / 316 \\ 9.8 Expansions in Series of Bessel Functions / 360 \\ 9.9 Rational Approximations / 361 \\ 9.9.1 Introduction / 361 \\ 9.9.2 $I_\nu(z)$, $z$ Small / 361 \\ 9.9.3 $K_\nu(z)$, $z$ Large / 366 \\ 9.10 Computation of Bessel Functions by Use of Recurrence Formulas / 380 \\ 9.10.1 Introduction / 380 \\ 9.10.2 Backward Recurrence Schemata for Generating $I_\nu(z)$ / 380 \\ 9.10.3 Closed Form Expressions / 382 \\ 9.10.4 Expressions for $J_\nu(z)$ / 389 \\ 9.10.5 Numerical Examples / 392 \\ 9.11 Evaluation of Bessel Functions by Application of Trapezoidal Type Integration Formulas / 395 \\ 9.12 Inequalities / 399 \\ 9.13 Bibliographic and Numerical Data / 403 \\ 9.13.1 References / 403 \\ 9.13.2 Description of and References to Tables / 404 \\ 9.13.3 Description of and References to Other Approximations and Expansions / 410 \\ \\ X. Lommel Functions, Struve Functions, and Associated Bessel Functions \\ \\ 10.1 Definitions, Connecting Relations and Power Series / 413 \\ 10.2 Asymptotic Expansions / 415 \\ 10.3 Expansions in Series of Chebyshev Polynomials and Bessel Functions / 415 \\ 10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$ and the Errors in These Approximations / 422 \\ 10.5 Bibliographic and Numerical Data / 426 \\ 10.5.1 References / 426 \\ 10.5.2 Description of and References to Tables / 426 \\ \\ XI. Orthogonal Polynomials \\ \\ 11.1 Introduction / 428 \\ 11.2 Orthogonal Properties / 428 \\ 11.3 Jacobi Polynomials / 436 \\ 11.3.1 Expansion Formulae / 436 \\ 11.3.2 Difference--Differential Formulae / 439 \\ 11.3.3 Integrals / 439 \\ 11.3.4 Expansion of $x^\rho$ in Series of Jacobi Polynomials / 440 \\ 11.3.5 Convergence Theorems for the Expansion of Arbitrary Functions in Series of Jacobi Polynomials / 442 \\ 11.3.6 Evaluation and Estimation of the Coefficients in the Expansion of a Given Function $f(x)$ in Series of Jacobi Polynomials / 443 \\ 11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ / 453 \\ 11.5 The Chebyshev Polynomials $T_n^*(x)$ and $U_n^*(x)$ / 459 \\ 11.6 Coefficients for Expansion of Integrals of Functions in Series of Chebyshev Polynomials of the First Kind / 464 \\ 11.6.1 Introduction / 464 \\ 11.6.2 Series of Shifted Chebyshev Polynomials / 464 \\ 11.6.3 Series of Chebyshev Polynomials of Even Order / 468 \\ 11.6.4 Series of Chebyshev Polynomials of Odd Order / 468 \\ 11.7 Orthogonality Properties of Chebyshev Polynomials with Respect to Summation / 469 \\ 11.8 A Nesting Procedure for the Computation of Expansions in Series of Functions Where the Functions Satisfy a Linear Finite Difference Equation / 475 \\ \\ XII. Computation by Use of Recurrence Formulas \\ \\ 12.1 Introduction / 483 \\ 12.2 Homogeneous Difference Equations / 483 \\ 12.3 Inhomogeneous Difference Equations / 487 \\ \\ XIII. Some Aspects of Rational and Polynomial Approximations \\ \\ 13.1 Introduction / 490 \\ 13.2 Approximations in Series of Chebyshev Polynomials of the First Kind / 490 \\ 13.3 The Pad{\'e} Table / 493 \\ 13.4 Approximation of Functions Defined by a Differential Equation --- The $\tau$-Method / 495 \\ 13.5 Approximations of Functions Defined by a Series / 499 \\ 13.6 Solution of Differential Equations in Series of Chebyshev Polynomials of the First Kind / 500 \\ \\ XIV. Miscellaneous Topics \\ \\ 14.1 Introduction / 505 \\ 14.2 Bernoulli Polynomials and Numbers / 505 \\ 14.3 $D$ and $\delta$ Operators / 507 \\ 14.4 Computation and Check of the Tables / 509 \\ 14.5 Mathematical Constants / 512 \\ 14.6 Late Bibliography / 516 \\ \\ Bibliography / 517 \\ \\ Notation Index / 545 \\ \\ Subject Index / 551

entry:
@Book{Luke:1975:MFT,
  author =       "Yudell L. Luke",
  title =        "Mathematical Functions and Their Approximations",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 568",
  year =         "1975",
  ISBN =         "0-12-459950-8, 1-4832-6245-6 (e-book)",
  ISBN-13 =      "978-0-12-459950-5, 978-1-4832-6245-1 (e-book)",
  LCCN =         "QA55 .L96 1975",
  bibdate =      "Fri Jun 30 05:58:16 MDT 2023",
  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/master.bib",
  URL =          "https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5",
  acknowledgement = ack-nhfb,
  libnote =      "Not in my library.",
  remark =       "An updated version of part of Handbook of mathematical
                 functions with formulas, graphs, and mathematical
                 tables, edited by M. Abramowitz and I.A. Stegun.
                 Includes indexes.",
  subject =      "Mathematics; Tables; Fonctions (Math{\'e}ematiques);
                 Math{\'e}ematiques; Calculus; Mathematical Analysis;
                 Mathematics; Approximation; Funktion; Mathematik;
                 Spezielle Funktion",
  tableofcontents = "Preface / xv \\
                 \\
                 I. The Gamma Function and Related Functions \\
                 \\
                 1.1 Definitions and Elementary Properties / 1 \\
                 1.2 Power Series and Other Series Expansions / 1 \\
                 1.3 Asymptotic Expansions / 7 \\
                 1.4 Rational Approximations for y (z) / 13 \\
                 1.5 Inequalities / 17 \\
                 1.6 Bibliographic and Numerical Data / 20 \\
                 1.6.1 General References / 20 \\
                 1.6.2 Description of and References to Tables / 21 \\
                 1.6.3 Description of and References to Other
                 Approximations and Expansions / 22 \\
                 \\
                 II. The Binomial Function \\
                 \\
                 2.1 Power Series / 24 \\
                 2.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials / 24 \\
                 2.3 Expansions in Series of Bessel Functions / 26 \\
                 2.4 Pad{\'e} Approximations / 27 \\
                 24.1 $(1 + 1 / z)^{-c}$ / 27 \\
                 2.4.2 The Square Root / 28 \\
                 2.4.3 Pad{\'e} Coefficients / 30 \\
                 2.4.4 The Function $e^{-w}$ / 31 \\
                 2.5 Inequalities / 34 \\
                 \\
                 III. Elementary Functions \\
                 \\
                 3.1 Logarithmic Functions / 36 \\
                 3.1.1 Power Series / 36 \\
                 3.1.2 Expansion in Series of Chebyshev Polynomials / 38
                 \\
                 3.1.3 Pad{\'e} Approximations / 39 \\
                 3.1.4 Inequalities / 41 \\
                 3.2 Exponential Function / 42 \\
                 3.2.1 Series Expansions / 42 \\
                 3.2.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials and Bessel Functions / 42 \\
                 3.2.3 Pad{\'e} Approximations / 46 \\
                 3.2.4 Inequalities / 51 \\
                 3.3 Circular and Hyperbolic Functions / 52 \\
                 3.3.1 Power Series / 52 \\
                 3.3.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials and Bessel Functions / 52 \\
                 3.3.3 Rational and Pad{\'e} Approximations / 57 \\
                 3.3.4 Inequalities / 60 \\
                 3.4 Inverse Circular and Hyperbolic Functions / 61 \\
                 3.4.1 Power Series / 61 \\
                 3.4.2 Expansions in Series of Chebyshev Polynomials /
                 63 \\
                 3.4.3 Pad{\'e} Approximations / 68 \\
                 3.4.4 Inequalities / 72 \\
                 3.5 Bibliographic and Numerical Data / 74 \\
                 3.5.1 Description of and References to Tables / 74 \\
                 3.5.2 Description of and References to Other
                 Approximations and Expansions / 74 \\
                 \\
                 IV. Incomplete Gamma Functions \\
                 \\
                 4.1 Definitions and Series Expansions / 77 \\
                 4.2 Differential Equations and Difference Equations /
                 78 \\
                 4.3 Pad{\'e} Approximations / 79 \\
                 4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\
                 4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\
                 4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq
                 \pi$ / 84 \\
                 4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu,
                 z)$ / 89 \\
                 4.4 Inequalities / 95 \\
                 4.4.1 $H(\nu, z)$ / 95 \\
                 4.4.2 $\Gamma(\nu, z)$ / 96 \\
                 4.5 Notes on the Computation of the Incomplete Gamma
                 Function / 97 \\
                 4.6 Exponential Integrals / 103 \\
                 4.6.1 Relation to Incomplete Gamma Function and Other
                 Properties / 103 \\
                 4.6.2 Expansions in Series of Chebyshev Polynomials /
                 104 \\
                 4.6.3 Rational and Pad Approximations / 106 \\
                 4.7 Cosine and Sine Integrals / 115 \\
                 4.7.1 Relation to Exponential Integral and Other
                 Properties / 115 \\
                 4.7.2 Expansions in Series of Chebyshev Polynomials /
                 116 \\
                 4.8 Error Functions / 119 \\
                 4.8.1 Relation to Incomplete Gamma Function and Other
                 Properties / 119 \\
                 4.8.2 Expansions in Series of Chebyshev Polynomials and
                 Bessel Functions / 122 \\
                 4.8.3 Pad{\'e} Approximations / 124 \\
                 4.8.4 Trapezoidal Rule Approximations / 134 \\
                 4.8.5 Inequalities / 137 \\
                 4.9 Fresnel Integrals / 139 \\
                 4.9.1 Relation to Error Functions and Other Properties
                 / 139 \\
                 4.9.2 Expansions in Series of Chebyshev Polynomials /
                 140 \\
                 4.10 Bibliographic and Numerical Data / 143 \\
                 4.10.1 References / 143 \\
                 4.10.2 Description of and References to Tables / 143
                 \\
                 4.10.3 Description of and References to Other
                 Approximations and Expansions / 149 \\
                 \\
                 V. The Generalized Hypergeometric Function $_pF_g$ and
                 the $G$-Function \\
                 \\
                 5.1 Introduction / 154 \\
                 5.2 The $_pF_q$ / 155 \\
                 5.2.1 Power Series / 155 \\
                 5.2.2 Derivatives and Contiguous Relations / 159 \\
                 5.2.3 Integral Representations and Integrals Involving
                 the $_pF_q$ / 160 \\
                 5.2.4 Evaluation for Special Values of the Variable and
                 Parameters / 163 \\
                 5.3 The $G$-Function / 170 \\
                 5.3.1 Definition and Relation to the $_pF_q$ / 170 \\
                 5.3.2 Elementary Properties / 176 \\
                 5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ /
                 178 \\
                 5.4 The Confluence Principle / 179 \\
                 5.5 Multiplication Theorems / 184 \\
                 5.6 Integrals Involving $G$-Functions / 186 \\
                 5.7 Differential Equations / 190 \\
                 5.7.1 The $_pF_q$ / 190 \\
                 5.7.2 The $G$-Function / 192 \\
                 5.8 Series of $G$-Functions / 194 \\
                 5.8.1 Introduction / 194 \\
                 5.8.2 Notation / 194 \\
                 5.8.3 Expansion Theorems / 197 \\
                 5.9 Asymptotic Expansions / 199 \\
                 5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\
                 5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\
                 5.9.3 $_pF_q(z)$ / 206 \\
                 5.10 Expansions in Series of Generalized Jacobi,
                 Generalized Laguerre and Chebyshev Polynomials / 213
                 \\
                 5.10.1 Expansions for $G$-Functions / 213 \\
                 5.10.2 Expansions for $_pF_q$ / 220 \\
                 5.11 Expansions in Series of Bessel Functions / 223 \\
                 5.12 Polynomial and Rational Approximations / 224 \\
                 5.13 Recurrence Formulas for Polynomials and Functions
                 Occurring in Approximations to Generalized
                 Hypergeometric Functions / 234 \\
                 5.13.1 Introduction / 234 \\
                 5.13.2 Recursion Formulas for Extended Jacobi and
                 Laguerre Functions / 235 \\
                 5.13.3 Recursion Formulas for the Numerator and
                 Denominator Polynomials in the Rational Approximations
                 for the Generalized Hypergeometric Function / 244 \\
                 5.13.4 Recursion Formula for Coefficients in the
                 Expansion of the $G$-Function in Series of Extended
                 Jacobi Polynomials / 247 \\
                 5.14 Inequalities / 252 \\
                 \\
                 VI. The Gaussian Hypergeometric Function $_2F_1$ \\
                 \\
                 6.1 Introduction / 257 \\
                 6.2 Elementary Properties / 257 \\
                 6.2.1 Derivatives / 257 \\
                 6.2.2 Contiguous Relations / 258 \\
                 6.2.3 Integral Representations / 259 \\
                 6.3 Differential Equations / 260 \\
                 6.4 Kummer Solutions and Transformation Formulae / 262
                 \\
                 6.5 Analytic Continuation / 263 \\
                 6.6 The Complete Solution and Wronskians / 265 \\
                 6.7 Quadratic Transformations / 270 \\
                 6.8 The $_2F_1$ for Special Values of the Argument /
                 271 \\
                 6.9 Expansion in Series of Chebyshev Polynomials / 274
                 \\
                 6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho
                 + 1;-1/z)$ / 274 \\
                 6.11 Inequalities / 278 \\
                 6.12 Bibliographic and Numerical Data / 279 \\
                 6.12.1 References / 279 \\
                 6.12.2 Description of and References to Tables / 279
                 \\
                 \\
                 VII. The Confluent Hypergeometric Function \\
                 \\
                 7.1 Introduction / 284 \\
                 7.2 Integral Representations / 284 \\
                 7.3 Elementary Relations / 285 \\
                 7.3.1 Derivatives / 285 \\
                 7.3.2 Contiguous Relations / 285 \\
                 7.3.3 Products of Confluent Functions / 286 \\
                 7.4 Differential Equations / 287 \\
                 7.5 The Complete Solution and Wronskians / 288 \\
                 7.6 Asymptotic Expansions / 291 \\
                 7.7 Expansions in Series of Chebyshev Polynomials / 293
                 \\
                 7.8 Expansions in Series of Besse! Functions / 294 \\
                 7.9 Inequalities / 295 \\
                 7.10 Other Notations and Related Functions / 295 \\
                 7.11 Bibliographic and Numerical Data / 296 \\
                 7.11.1 References / 296 \\
                 7.11.2 Description of and References to Tables and
                 Other Approximations / 296 \\
                 \\
                 VIII. Identification of the $_pF_q$, and $G$-Functions
                 with the Special Functions \\
                 \\
                 8.1 Introduction / 298 \\
                 8.2 Named Special Functions Expressed as $_pF_q$'s /
                 298 \\
                 8.2.1 Elementary Functions / 298 \\
                 8.2.2 The Incomplete Gamma Function and Related
                 Functions / 298 \\
                 8.2.3 The Gaussian Hypergeometric Function / 298 \\
                 8.2.4 Legendre Functions / 299 \\
                 8.2.5 Orthogonal Polynomials / 299 \\
                 8.2.6 Complete Elliptic Integrals / 299 \\
                 8.2.7 Confluent Hypergeometric Functions, Whittaker
                 Functions and Bessel Functions / 300 \\
                 8.3 Named Functions Expressed in Terms of the
                 $G$-Function / 300 \\
                 8.4 The $G$-Function Expressed as a Named Function /
                 306 \\
                 \\
                 IX. Bessel Functions and Their Integrals \\
                 \\
                 9.1 Introduction / 311 \\
                 9.2 Definitions, Connecting Relations and Power Series
                 / 311 \\
                 9.3 Difference--Differential Formulas / 313 \\
                 9.4 Products of Bessel Functions / 314 \\
                 9.5 Asymptotic Expansions for Large Variable / 315 \\
                 9.6 Integrals of Bessel Functions / 315 \\
                 9.7 Expansions in Series of Chebyshev Polynomials / 316
                 \\
                 9.8 Expansions in Series of Bessel Functions / 360 \\
                 9.9 Rational Approximations / 361 \\
                 9.9.1 Introduction / 361 \\
                 9.9.2 $I_\nu(z)$, $z$ Small / 361 \\
                 9.9.3 $K_\nu(z)$, $z$ Large / 366 \\
                 9.10 Computation of Bessel Functions by Use of
                 Recurrence Formulas / 380 \\
                 9.10.1 Introduction / 380 \\
                 9.10.2 Backward Recurrence Schemata for Generating
                 $I_\nu(z)$ / 380 \\
                 9.10.3 Closed Form Expressions / 382 \\
                 9.10.4 Expressions for $J_\nu(z)$ / 389 \\
                 9.10.5 Numerical Examples / 392 \\
                 9.11 Evaluation of Bessel Functions by Application of
                 Trapezoidal Type Integration Formulas / 395 \\
                 9.12 Inequalities / 399 \\
                 9.13 Bibliographic and Numerical Data / 403 \\
                 9.13.1 References / 403 \\
                 9.13.2 Description of and References to Tables / 404
                 \\
                 9.13.3 Description of and References to Other
                 Approximations and Expansions / 410 \\
                 \\
                 X. Lommel Functions, Struve Functions, and Associated
                 Bessel Functions \\
                 \\
                 10.1 Definitions, Connecting Relations and Power Series
                 / 413 \\
                 10.2 Asymptotic Expansions / 415 \\
                 10.3 Expansions in Series of Chebyshev Polynomials and
                 Bessel Functions / 415 \\
                 10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$
                 and the Errors in These Approximations / 422 \\
                 10.5 Bibliographic and Numerical Data / 426 \\
                 10.5.1 References / 426 \\
                 10.5.2 Description of and References to Tables / 426
                 \\
                 \\
                 XI. Orthogonal Polynomials \\
                 \\
                 11.1 Introduction / 428 \\
                 11.2 Orthogonal Properties / 428 \\
                 11.3 Jacobi Polynomials / 436 \\
                 11.3.1 Expansion Formulae / 436 \\
                 11.3.2 Difference--Differential Formulae / 439 \\
                 11.3.3 Integrals / 439 \\
                 11.3.4 Expansion of $x^\rho$ in Series of Jacobi
                 Polynomials / 440 \\
                 11.3.5 Convergence Theorems for the Expansion of
                 Arbitrary Functions in Series of Jacobi Polynomials /
                 442 \\
                 11.3.6 Evaluation and Estimation of the Coefficients in
                 the Expansion of a Given Function $f(x)$ in Series of
                 Jacobi Polynomials / 443 \\
                 11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
                 453 \\
                 11.5 The Chebyshev Polynomials $T_n^*(x)$ and
                 $U_n^*(x)$ / 459 \\
                 11.6 Coefficients for Expansion of Integrals of
                 Functions in Series of Chebyshev Polynomials of the
                 First Kind / 464 \\
                 11.6.1 Introduction / 464 \\
                 11.6.2 Series of Shifted Chebyshev Polynomials / 464
                 \\
                 11.6.3 Series of Chebyshev Polynomials of Even Order /
                 468 \\
                 11.6.4 Series of Chebyshev Polynomials of Odd Order /
                 468 \\
                 11.7 Orthogonality Properties of Chebyshev Polynomials
                 with Respect to Summation / 469 \\
                 11.8 A Nesting Procedure for the Computation of
                 Expansions in Series of Functions Where the Functions
                 Satisfy a Linear Finite Difference Equation / 475 \\
                 \\
                 XII. Computation by Use of Recurrence Formulas \\
                 \\
                 12.1 Introduction / 483 \\
                 12.2 Homogeneous Difference Equations / 483 \\
                 12.3 Inhomogeneous Difference Equations / 487 \\
                 \\
                 XIII. Some Aspects of Rational and Polynomial
                 Approximations \\
                 \\
                 13.1 Introduction / 490 \\
                 13.2 Approximations in Series of Chebyshev Polynomials
                 of the First Kind / 490 \\
                 13.3 The Pad{\'e} Table / 493 \\
                 13.4 Approximation of Functions Defined by a
                 Differential Equation --- The $\tau$-Method / 495 \\
                 13.5 Approximations of Functions Defined by a Series /
                 499 \\
                 13.6 Solution of Differential Equations in Series of
                 Chebyshev Polynomials of the First Kind / 500 \\
                 \\
                 XIV. Miscellaneous Topics \\
                 \\
                 14.1 Introduction / 505 \\
                 14.2 Bernoulli Polynomials and Numbers / 505 \\
                 14.3 $D$ and $\delta$ Operators / 507 \\
                 14.4 Computation and Check of the Tables / 509 \\
                 14.5 Mathematical Constants / 512 \\
                 14.6 Late Bibliography / 516 \\
                 \\
                 Bibliography / 517 \\
                 \\
                 Notation Index / 545 \\
                 \\
                 Subject Index / 551",
}


bibtype: article
filename: elefunt.bib
label: Luke:1975:SRU
author: Y. L. Luke
title: Some remarks on uniform asymptotic expansions for Bessel functions
journal: j-COMPUT-MATH-APPL
volume: 1
number: 3--4
pages: 285--290
year: 1975
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 18:51:12 MST 2017
bibtimestamp: 2017.03.01 18:51:12 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122175900279
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: Y. L. Luke
rawtitle: Some remarks on uniform asymptotic expansions for {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Luke:1975:SRU,
  author =       "Y. L. Luke",
  title =        "Some remarks on uniform asymptotic expansions for
                 {Bessel} functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "1",
  number =       "3--4",
  pages =        "285--290",
  month =        "????",
  year =         "1975",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:12 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122175900279",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: book
filename: elefunt.bib
label: Masser:1975:EFT
author: D. W. Masser
title: Elliptic Functions and Transcendence
volume: 437
publisher: pub-SV
address: pub-SV:adr
pages: 112 (est.)
year: 1975
CODEN: LNMAA2
DOI: https://doi.org/10.1007/BFb0069432
ISBN: 3-540-07136-9 (print), 3-540-37410-8 (e-book) OR 3540071369 (print), 3540374108 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
LCCN: QA3 .L28 no. 437
MRclass: 11J81 (14K22; 33E05; 11G15; 11J17; 11-02)
bibdate: Tue May 6 14:52:13 MDT 2014
bibtimestamp: 2014.05.06 14:52:13 MDT
series: ser-LECT-NOTES-MATH
ZMnumber: 0312.10023
acknowledgement: ack-nhfb
rawauthor: D. W. Masser
rawtitle: Elliptic Functions and Transcendence
ISBN13:
978-3-540-07136-5 (print), 978-3-540-37410-7 (e-book) OR 9783540071365 (print), 9783540374107 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lnm1975.bib

URL:
http://link.springer.com/book/10.1007/BFb0069432; http://www.springerlink.com/content/978-3-540-37410-7

entry:
@Book{Masser:1975:EFT,
  author =       "D. W. Masser",
  title =        "Elliptic Functions and Transcendence",
  volume =       "437",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "112 (est.)",
  year =         "1975",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0069432",
  ISBN =         "3-540-07136-9 (print), 3-540-37410-8 (e-book)",
  ISBN-13 =      "978-3-540-07136-5 (print), 978-3-540-37410-7
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  LCCN =         "QA3 .L28 no. 437",
  MRclass =      "11J81 (14K22; 33E05; 11G15; 11J17; 11-02)",
  bibdate =      "Tue May 6 14:52:13 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1975.bib",
  series =       ser-LECT-NOTES-MATH,
  URL =          "http://link.springer.com/book/10.1007/BFb0069432;
                 http://www.springerlink.com/content/978-3-540-37410-7",
  ZMnumber =     "0312.10023",
  acknowledgement = ack-nhfb,
  series-URL =   "http://link.springer.com/bookseries/304",
}


bibtype: article
filename: elefunt.bib
label: Midy:1975:ICG
author: P. Midy
journal: j-NUM-MATH
volume: 25
number: 1
pages: 99--101
month: mar
monthnumber: 3
year: 1975
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 16:12:48 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.17 16:12:48 MDT
fjournal: Numerische Mathematik
keywords: elliptic integral; integration; Landen transformation; second kind
acknowledgement: ack-nhfb
corpsource: Centre de Calcul Paris Sud Informatique, Univ. Paris XI, Orsay, France
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: P. Midy
title:
An improved calculation of the general elliptic integral of the second kind in the neighbourhood of $ x = 0 $

rawtitle:
An improved calculation of the general elliptic integral of the second kind in the neighbourhood of $ x = 0 $

entry:
@Article{Midy:1975:ICG,
  author =       "P. Midy",
  title =        "An improved calculation of the general elliptic
                 integral of the second kind in the neighbourhood of $ x
                 = 0 $",
  journal =      j-NUM-MATH,
  volume =       "25",
  number =       "1",
  pages =        "99--101",
  month =        mar,
  year =         "1975",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Centre de Calcul Paris Sud Informatique, Univ. Paris
                 XI, Orsay, France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "elliptic integral; integration; Landen transformation;
                 second kind",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Miller:1975:CCN
author: Webb Miller
title: Computational Complexity and Numerical Stability
journal: j-SIAM-J-COMPUT
volume: 4
number: 2
pages: 97--107
month: jun
monthnumber: 6
year: 1975
CODEN: SMJCAT
DOI: https://doi.org/10.1137/0204009
ISSN: 0097-5397 (print), 1095-7111 (electronic) OR 00975397 (print), 10957111 (electronic)
ISSNL: 0097-5397 OR 00975397
bibdate: Mon Nov 29 10:58:08 MST 2010
bibtimestamp: 2010.11.29 10:58:08 MST
fjournal: SIAM Journal on Computing
keywords: complexity; number of multiplications to evaluate a polynomial; numerical analysis; rounding error
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicomp
key: Miller
rawauthor: Webb Miller
rawtitle: Computational Complexity and Numerical Stability
bibsource:
http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/4/2; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjcomput.bib; Parallel/Multi.bib; Theory/Matrix.bib

entry:
@Article{Miller:1975:CCN,
  author =       "Webb Miller",
  key =          "Miller",
  title =        "Computational Complexity and Numerical Stability",
  journal =      j-SIAM-J-COMPUT,
  volume =       "4",
  number =       "2",
  pages =        "97--107",
  month =        jun,
  year =         "1975",
  CODEN =        "SMJCAT",
  DOI =          "https://doi.org/10.1137/0204009",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Mon Nov 29 10:58:08 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/4/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjcomput.bib;
                 Parallel/Multi.bib; Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
  keywords =     "complexity; number of multiplications to evaluate a
                 polynomial; numerical analysis; rounding error",
}


bibtype: techreport
filename: elefunt.bib
label: Morris:1975:LRS
author: Robert Morris
title: A Library of Reference Standard Mathematical Subroutines
type: Technical Memorandum
number: 1074 (TM 75-1271-6)
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
day: 1
month: may
monthnumber: 5
year: 1975
bibdate: Tue Jun 06 08:07:45 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib
bibtimestamp: 2023.06.06 08:07:45 ???
acknowledgement: ack-nhfb
authordates: Robert Morris (25 July 1932--26 June 2011)
rawauthor: Robert Morris
rawtitle: A Library of Reference Standard Mathematical Subroutines
abstract:
This memo describes a set of mathematical library functions to use arbitrary accuracy. Relevant error analysis and subroutines listings are given.

rawabstract:
This memo describes a set of mathematical library functions to use arbitrary accuracy. Relevant error analysis and subroutines listings are given.

entry:
@TechReport{Morris:1975:LRS,
  author =       "Robert Morris",
  title =        "A Library of Reference Standard Mathematical
                 Subroutines",
  type =         "Technical Memorandum",
  number =       "1074 (TM 75-1271-6)",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "??",
  day =          "1",
  month =        may,
  year =         "1975",
  bibdate =      "Tue Jun 06 08:07:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "This memo describes a set of mathematical library
                 functions to use arbitrary accuracy. Relevant error
                 analysis and subroutines listings are given.",
  acknowledgement = ack-nhfb,
  author-dates = "Robert Morris (25 July 1932--26 June 2011)",
}


bibtype: article
filename: elefunt.bib
label: Ng:1975:CCM
author: Edward W. Ng
title: A Comparison of Computational Methods and Algorithms for the Complex Gamma Function
journal: j-TOMS
volume: 1
number: 1
pages: 56--70
month: mar
monthnumber: 3
year: 1975
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355626.355635
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20
MRnumber: 52 #2148
bibdate: Fri Aug 26 23:44:16 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.26 23:44:16 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
reviewer: R. H. Bartels
rawauthor: Edward W. Ng
rawtitle: A Comparison of Computational Methods and Algorithms for the Complex Gamma Function
entry:
@Article{Ng:1975:CCM,
  author =       "Edward W. Ng",
  title =        "A Comparison of Computational Methods and Algorithms
                 for the Complex Gamma Function",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "56--70",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355635",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "52 #2148",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. H. Bartels",
}


bibtype: article
filename: elefunt.bib
label: Oliver:1975:SME
author: J. Oliver
title: Stable methods for evaluating the points $ cos (i pi / n) $
journal: j-J-INST-MATH-APPL
volume: 16
number: 2
pages: 247--257
month: oct
monthnumber: 10
year: 1975
CODEN: JMTAA8
DOI: https://doi.org/10.1093/imamat/16.2.247
ISSN: 0020-2932 OR 00202932
ISSNL: 0020-2932 OR 00202932
MRclass: 65D05
MRnumber: 52 #12292 (391471)
MRreviewer: C. W. Clenshaw
bibdate: Mon Nov 13 08:14:42 2023
bibtimestamp: 2023.11.13 08:14:42 ???
fjournal: Journal of the Institute of Mathematics and its Applications
ZMnumber: 0308.65011
acknowledgement: ack-nhfb
journalURL: http://imamat.oxfordjournals.org/content/by/year
rawauthor: J. Oliver
rawtitle: Stable methods for evaluating the points $ \cos (i \pi / n) $
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib

entry:
@Article{Oliver:1975:SME,
  author =       "J. Oliver",
  title =        "Stable methods for evaluating the points $ \cos (i \pi
                 / n) $",
  journal =      j-J-INST-MATH-APPL,
  volume =       "16",
  number =       "2",
  pages =        "247--257",
  month =        oct,
  year =         "1975",
  CODEN =        "JMTAA8",
  DOI =          "https://doi.org/10.1093/imamat/16.2.247",
  ISSN =         "0020-2932",
  ISSN-L =       "0020-2932",
  MRclass =      "65D05",
  MRnumber =     "52 #12292 (391471)",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Mon Nov 13 08:14:42 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
  ZMnumber =     "0308.65011",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
}


bibtype: article
filename: elefunt.bib
label: Prince:1975:AAF
author: P. J. Prince
title: Algorithm 498: Airy Functions Using Chebyshev Series Approximations
journal: j-TOMS
volume: 1
number: 4
pages: 372--379
month: dec
monthnumber: 12
year: 1975
CODEN: ACMSCU
DOI: https://doi.org/10.1145/355656.355663
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 27 00:24:33 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.27 00:24:33 ???
note: See also cite Razaz:1981:RAF.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: P. J. Prince
rawnote: See also \cite{Razaz:1981:RAF}.
rawtitle: {Algorithm 498}: {Airy} Functions Using {Chebyshev} Series Approximations
remark:
Fullerton: FORTRAN routines of fixed 10D precision for the two Airy functions and their derivatives are given.

entry:
@Article{Prince:1975:AAF,
  author =       "P. J. Prince",
  title =        "{Algorithm 498}: {Airy} Functions Using {Chebyshev}
                 Series Approximations",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "372--379",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355663",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:24:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Razaz:1981:RAF}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: FORTRAN routines of fixed 10D precision for
                 the two Airy functions and their derivatives are
                 given.",
}


bibtype: article
filename: elefunt.bib
label: Rudnicki-Bujnowski:1975:EFC
author: Georges Rudnicki-Bujnowski
title: Explicit Formulas for Clebsch--Gordan Coefficients
journal: j-COMP-PHYS-COMM
volume: 10
number: 4
pages: 245--250
month: oct
monthnumber: 10
year: 1975
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(75)90069-7
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sun Feb 12 14:24:38 MST 2012
bibtimestamp: 2012.02.12 14:24:38 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465575900697
fjournal: Computer Physics Communications
remark: Fullerton: A PL/I-FORMAC procedure is discussed.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Georges Rudnicki-Bujnowski
rawtitle: Explicit Formulas for {Clebsch--Gordan} Coefficients
entry:
@Article{Rudnicki-Bujnowski:1975:EFC,
  author =       "Georges Rudnicki-Bujnowski",
  title =        "Explicit Formulas for {Clebsch--Gordan} Coefficients",
  journal =      j-COMP-PHYS-COMM,
  volume =       "10",
  number =       "4",
  pages =        "245--250",
  month =        oct,
  year =         "1975",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(75)90069-7",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sun Feb 12 14:24:38 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465575900697",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: A PL/I-FORMAC procedure is discussed.",
}


bibtype: article
filename: elefunt.bib
label: Skovgaard:1975:RAJ
author: Ove Skovgaard
title: Remark on ``Algorithm 332: Jacobi Polynomials''
journal: j-CACM
volume: 18
number: 2
pages: 116--117
year: 1975
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:22:18 MST 2001
bibtimestamp: 2001.01.22 07:22:18 MST
note: See cite Witte:1968:AAJ.
fjournal: Communications of the ACM
remark: Fullerton: Modifications to an adjustable-precision FORTRAN routine.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Ove Skovgaard
rawnote: See \cite{Witte:1968:AAJ}.
rawtitle: Remark on ``{Algorithm 332}: {Jacobi} Polynomials''
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Skovgaard75; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Skovgaard:1975:RAJ,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 332}: {Jacobi} Polynomials''",
  journal =      j-CACM,
  volume =       "18",
  number =       "2",
  pages =        "116--117",
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:22:18 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Skovgaard75;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Witte:1968:AAJ}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Skovgaard75",
  remark =       "Fullerton: Modifications to an adjustable-precision
                 FORTRAN routine.",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Skovgaard75",
}


bibtype: article
filename: elefunt.bib
label: Skovgaard:1975:RBF
author: Ove Skovgaard
title: Remark on ``Algorithm 236: Bessel Functions of the First Kind [S17]''
journal: j-TOMS
volume: 1
number: 3
pages: 282--284
month: sep
monthnumber: 9
year: 1975
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:26:43 1996
bibtimestamp: 1996.02.06 05:26:43 ???
note: See cite Gautschi:1964:AAB.
fjournal: ACM Transactions on Mathematical Software
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ove Skovgaard
rawnote: See \cite{Gautschi:1964:AAB}.
rawtitle: Remark on ``{Algorithm 236: Bessel Functions of the First Kind [S17]}''
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Skovgaard:1975:RBF,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 236: Bessel Functions of the
                 First Kind [S17]}''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "282--284",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:26:43 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1964:AAB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Temme:1975:NEM
author: N. M. Temme
title: On the Numerical Evaluation of the Modified Bessel Function of the Third Kind
journal: j-J-COMPUT-PHYS
volume: 19
number: 3
pages: 324--337
month: nov
monthnumber: 11
year: 1975
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(75)90082-0
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sat Oct 30 11:20:31 2010
bibtimestamp: 2010.10.30 11:20:31 ???
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: N. M. Temme
rawtitle: On the Numerical Evaluation of the Modified {Bessel} Function of the Third Kind
entry:
@Article{Temme:1975:NEM,
  author =       "N. M. Temme",
  title =        "On the Numerical Evaluation of the Modified {Bessel}
                 Function of the Third Kind",
  journal =      j-J-COMPUT-PHYS,
  volume =       "19",
  number =       "3",
  pages =        "324--337",
  month =        nov,
  year =         "1975",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(75)90082-0",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 11:20:31 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Temme:1975:UAE
author: N. M. Temme
title: Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function
journal: j-MATH-COMPUT
volume: 29
number: 132
pages: 1109--1114
month: oct
monthnumber: 10
year: 1975
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: Dept. of Appl. Math., Amsterdam, Netherlands
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: N. M. Temme
rawtitle: Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function
keywords:
asymptotic expansions; asymptotic series; complementary error function; function approximation; incomplete beta function; incomplete gamma functions; uniform

entry:
@Article{Temme:1975:UAE,
  author =       "N. M. Temme",
  title =        "Uniform asymptotic expansions of the incomplete gamma
                 functions and the incomplete beta function",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "132",
  pages =        "1109--1114",
  month =        oct,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Appl. Math., Amsterdam, Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic expansions; asymptotic series;
                 complementary error function; function approximation;
                 incomplete beta function; incomplete gamma functions;
                 uniform",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: book
filename: elefunt.bib
label: VanBuren:1975:TAS
author: A. L. (Arnie Lee) Van Buren and others
title: Tables of Angular Spheroidal Wave Functions
publisher: Naval Research Laboratory
address: Washington, DC, USA
year: 1975
LCCN: QC174.26.W3 T27
bibdate: Sat Apr 1 14:32:29 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:32:29 MDT
subject: Wave functions; Tables; Spheroidal functions
TOC: v. 1. Prolate, m = O v. 2. Oblate, m = O
acknowledgement: ack-nhfb
rawauthor: A. L. (Arnie Lee) {Van Buren} and others
rawtitle: Tables of Angular Spheroidal Wave Functions
rawTOC: v. 1. Prolate, m = O \\ v. 2. Oblate, m = O
entry:
@Book{VanBuren:1975:TAS,
  author =       "A. L. (Arnie Lee) {Van Buren} and others",
  title =        "Tables of Angular Spheroidal Wave Functions",
  publisher =    "Naval Research Laboratory",
  address =      "Washington, DC, USA",
  pages =        "????",
  year =         "1975",
  LCCN =         "QC174.26.W3 T27",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Wave functions; Tables; Spheroidal functions",
  tableofcontents = "v. 1. Prolate, m = O \\
                 v. 2. Oblate, m = O",
}


bibtype: techreport
filename: elefunt.bib
label: Warner:1975:PDG
author: D. D. Warner
title: A partial derivative generator
type: Computing Science Technical Report
number: 28
institution: inst-ATT-BELL
address: inst-ATT-BELL:adr
year: 1975
bibdate: Mon May 19 13:30:58 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Theory/auto.diff.bib
bibtimestamp: 1997.05.19 13:30:58 ???
keywords: differentiation arithmetic; precompiler.
acknowledgement: ack-nhfb
rawauthor: D. D. Warner
rawtitle: A partial derivative generator
abstract:
A precompiler is described which takes a specification of a function as input and produces a Fortran subroutine which will evaluate the component functions and the corresponding Jacobian. Many of the Fortran elementary functions are provided, as well as a facility which allows the user to specify their own differentiation rules.

rawabstract:
A precompiler is described which takes a specification of a function as input and produces a Fortran subroutine which will evaluate the component functions and the corresponding Jacobian. Many of the Fortran elementary functions are provided, as well as a facility which allows the user to specify their own differentiation rules.

entry:
@TechReport{Warner:1975:PDG,
  author =       "D. D. Warner",
  title =        "A partial derivative generator",
  type =         "Computing Science Technical Report",
  number =       "28",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  year =         "1975",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Theory/auto.diff.bib",
  abstract =     "A precompiler is described which takes a specification
                 of a function as input and produces a Fortran
                 subroutine which will evaluate the component functions
                 and the corresponding Jacobian. Many of the Fortran
                 elementary functions are provided, as well as a
                 facility which allows the user to specify their own
                 differentiation rules.",
  acknowledgement = ack-nhfb,
  keywords =     "differentiation arithmetic; precompiler.",
  referred =     "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].",
}


bibtype: article
filename: elefunt.bib
label: Assmus:1976:NFS
author: E. F. Assmus, Jr. and H. F. Mattson, Jr. and Howard E. Sachar
title: A New Form of the Square Root Bound
journal: j-SIAM-J-APPL-MATH
volume: 30
number: 2
pages: 352--354
month: mar
monthnumber: 3
year: 1976
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Thu Oct 15 18:16:06 MDT 1998
bibtimestamp: 1998.10.15 18:16:06 MDT
fjournal: SIAM Journal on Applied Mathematics
keywords: combinatorial mathematics; linear codes; square root bound; sufficient combinatorial conditions
acknowledgement: ack-nhfb
corpsource: Dept. of Math., Lehigh Univ., Bethlehem, PA, USA
journalURL: http://epubs.siam.org/siap
treatment: T Theoretical or Mathematical
rawauthor: E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and Howard E. Sachar
rawtitle: A New Form of the Square Root Bound
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/siamjapplmath.bib; JSTOR database

entry:
@Article{Assmus:1976:NFS,
  author =       "E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and
                 Howard E. Sachar",
  title =        "A New Form of the Square Root Bound",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "30",
  number =       "2",
  pages =        "352--354",
  month =        mar,
  year =         "1976",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0250 (Combinatorial mathematics); C1160
                 (Combinatorial mathematics)",
  corpsource =   "Dept. of Math., Lehigh Univ., Bethlehem, PA, USA",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  keywords =     "combinatorial mathematics; linear codes; square root
                 bound; sufficient combinatorial conditions",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Badhe:1976:NAN
author: Sahadeo K. Badhe
title: New approximation of the normal distribution function
journal: j-COMMUN-STAT-SIMUL-COMPUT
volume: 5
number: 4
pages: 173--176
year: 1976
CODEN: CSSCDB
DOI: https://doi.org/10.1080/03610917608812017
ISSN: 0361-0918 OR 03610918
ISSNL: 0361-0918 OR 03610918
bibdate: Sat Jan 30 06:32:08 MST 2016
bibtimestamp: 2016.01.30 06:32:08 MST
fjournal: Communications in Statistics: Simulation and Computation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/lssp20
rawauthor: Sahadeo K. Badhe
rawtitle: New approximation of the normal distribution function
bibsource:
https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Badhe:1976:NAN,
  author =       "Sahadeo K. Badhe",
  title =        "New approximation of the normal distribution
                 function",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "5",
  number =       "4",
  pages =        "173--176",
  year =         "1976",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1080/03610917608812017",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  bibdate =      "Sat Jan 30 06:32:08 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
}


bibtype: article
filename: elefunt.bib
label: Baker:1976:SFB
author: P. W. Baker
title: Suggestion for a fast binary sine / cosine generator
journal: j-IEEE-TRANS-COMPUT
volume: C-25
number: 11
pages: 1134--1136
month: nov
monthnumber: 11
year: 1976
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1976.1674566
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Jul 12 06:24:55 MDT 2011
bibtimestamp: 2011.07.12 06:24:55 MDT
URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674566
fjournal: IEEE Transactions on Computers
keywords: $cos (x)$; $sin (x)$; elementary function
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. W. Baker
rawtitle: Suggestion for a fast binary sine\slash cosine generator
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/ieeetranscomput1970.bib

entry:
@Article{Baker:1976:SFB,
  author =       "P. W. Baker",
  title =        "Suggestion for a fast binary sine\slash cosine
                 generator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "11",
  pages =        "1134--1136",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674566",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:55 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/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674566",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "$\cos(x)$; $\sin(x)$; elementary function",
}


