article

Free access

Complex gamma function with error control

Author:

Hirondo KukiAuthors Info & Claims

Communications of the ACM, Volume 15, Issue 4

Pages 262 - 267

https://doi.org/10.1145/361284.361296

Published: 01 April 1972 Publication History

PDF eReader

Abstract

An algorithm to compute the gamma function and the loggamma function of a complex variable is presented. The standard algorithm is modified in several respects to insure the continuity of the function value and to reduce accumulation of round-off errors. In addition to computation of function values, this algorithm includes an object-time estimation of round-off errors. Experimental data with regard to the effectiveness of this error control are presented. A Fortran program for the algorithm appears in the algorithms section of this issue.

References

[1]

Abramowitz, M., and Stegun, I.A. (Eds.) Handbook of Mathematical Functions. National Bureau of Standards, A.M.S. 55, Washington, D.C., 1964, pp. 255-259.

Google Scholar

[2]

Kuki, H. Mathematical function subprograms for basic system libraries: objectives, constraints, and trade-off. Proc. Syrup. on Mathematical Software, Lafayette, Ind., Apr. 1970, Academic Press, New York, 1971.

Google Scholar

[3]

Fan, T., and Kuki, H. Review of SDA 3230, SHARE Secretary Distribution 164, Pt. II, U-67, Apr. 1967.

Google Scholar

[4]

Hart, J. F., et al. Computer Approximations. Wiley, New York, 1968, pp. 42-54.

Digital Library

Google Scholar

[5]

Luke, Y.L. Evaluation of the Gamma function by means of Pad6 approximations. SIAM J. Math. Anal. 1, 2 (May 1970), 266-281.

Crossref

Google Scholar

[6]

Kuki, Hirondo. Algorithm 421, Complex gamma function with error control. Comm. ACM 15, 4 (Apr. 1972), 271-272.

Digital Library

Google Scholar

Cited By

View all

Witte NGreenwood P(2023)On the density arising from the domain of attraction of an operator interpolating between sum and supremum: The α-Sun operatorJournal of Mathematical Analysis and Applications10.1016/j.jmaa.2023.127371527:1(127371)Online publication date: Nov-2023
https://doi.org/10.1016/j.jmaa.2023.127371
Hornyak IKruppa A(2015)An algorithm for the calculation of the partial wave expansion of the Coulomb-distorted plane waveComputer Physics Communications10.1016/j.cpc.2015.08.018197(291-297)Online publication date: Dec-2015
https://doi.org/10.1016/j.cpc.2015.08.018
Rump S(2014)Verified sharp bounds for the real gamma function over the entire floating-point rangeNonlinear Theory and Its Applications, IEICE10.1587/nolta.5.3395:3(339-348)Online publication date: 2014
https://doi.org/10.1587/nolta.5.339
Show More Cited By

Recommendations

Algorithm 421: complex gamma function with error control [S14]

This Fortran program computes either the gamma function or the loggamma function of a complex variable in double precision. In addition, it provides an error estimate of the computed answer. The calling sequences are: CALL CDLGAM (Z, W, E, 0) for the ...
Estimating gamma function by digamma function

The aim of this paper is to refine some recent results stated by Alzer and Grinshpan [H. Alzer, A.Z. Grinshpan, Inequalities for the gamma and q-gamma functions J. Approx. Theory 144 (2007) 67-83] and Batir [N. Batir, An interesting double inequality ...
Two families of approximations for the gamma function

In this paper, we establish two families of approximations for the gamma function: $$ \begin{array}{lll} {\varGamma}(x+1)&=\sqrt{2\pi x}{\left({\frac{x+a}{{\mathrm{e}}}}\right)}^x {\left({\frac{x+a}{x-a}}\right)}^{-\frac{x}{2}+\frac{1}{4}} {\left({\frac{...

Comments

Information & Contributors

Information

Published In

Communications of the ACM Volume 15, Issue 4

April 1972

70 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/361284

Editor:
M. Stuart Lynn
Rice Univ., Houston, TX

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1972

Published in CACM Volume 15, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

18
Total Citations
View Citations
563
Total Downloads

Downloads (Last 12 months)87
Downloads (Last 6 weeks)12

Reflects downloads up to 15 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Witte NGreenwood P(2023)On the density arising from the domain of attraction of an operator interpolating between sum and supremum: The α-Sun operatorJournal of Mathematical Analysis and Applications10.1016/j.jmaa.2023.127371527:1(127371)Online publication date: Nov-2023
https://doi.org/10.1016/j.jmaa.2023.127371
Hornyak IKruppa A(2015)An algorithm for the calculation of the partial wave expansion of the Coulomb-distorted plane waveComputer Physics Communications10.1016/j.cpc.2015.08.018197(291-297)Online publication date: Dec-2015
https://doi.org/10.1016/j.cpc.2015.08.018
Rump S(2014)Verified sharp bounds for the real gamma function over the entire floating-point rangeNonlinear Theory and Its Applications, IEICE10.1587/nolta.5.3395:3(339-348)Online publication date: 2014
https://doi.org/10.1587/nolta.5.339
Brown BEastham MMcCormack DPlum M(2013)On a New Algorithm For The Computation of Enclosures for the Titchmarsh-Weyl m-FunctionResults in Mathematics10.1007/BF0332206933:1-2(50-64)Online publication date: 17-Apr-2013
https://doi.org/10.1007/BF03322069
Kodama M(2008)Algorithm 877ACM Transactions on Mathematical Software10.1145/1377596.137760234:4(1-21)Online publication date: 1-Jul-2008
https://dl.acm.org/doi/10.1145/1377596.1377602
Brown BKirby VEvans WPlum M(2008)Safe numerical bounds for the Titchmarsh–Weyl m(λ)-functionMathematical Proceedings of the Cambridge Philosophical Society10.1017/S0305004100076222113:03(583)Online publication date: 24-Oct-2008
https://doi.org/10.1017/S0305004100076222
(1997)On an inequality of the Kolmogorov type for a second-order differential expressionProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences10.1098/rspa.1993.0121442:1916(555-569)Online publication date: Jan-1997
https://doi.org/10.1098/rspa.1993.0121
(1997) Numerical determination of the Titchmarsh-Weyl m -coefficient and its applications to HELP inequalities Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences10.1098/rspa.1989.0122426:1870(167-188)Online publication date: Jan-1997
https://doi.org/10.1098/rspa.1989.0122
(1996) Computation of the M matrix for fourth-order problems Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences10.1098/rspa.1996.0094452:1951(1765-1788)Online publication date: Jan-1996
https://doi.org/10.1098/rspa.1996.0094
Brown BEvans WEveritt W(1992)HELP integral and series inequalitiesGeneral Inequalities 610.1007/978-3-0348-7565-3_23(269-305)Online publication date: 1992
https://doi.org/10.1007/978-3-0348-7565-3_23
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Recommendations

Algorithm 421: complex gamma function with error control [S14]

Estimating gamma function by digamma function

Two families of approximations for the gamma function

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations