Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T00:48:36.041Z Has data issue: false hasContentIssue false

A Set of Algorithms for the Incomplete Gamma Functions

Published online by Cambridge University Press:  27 July 2009

N. M. Temme
Affiliation:
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands

Abstract

This paper gives fast and reliable algorithms for the numerical evaluation of the incomplete gamma functions and for auxiliary functions, such as functions related with the gamma function and error function. All these functions are of basic importance in applied probability problems.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Cody, W.J. (1969). Rational Chebyshev approximations for the error function. Mathematics of Computation 23: 631637.CrossRefGoogle Scholar
2.Cody, W.J. & Hillstrom, K.E. (1967). Chebyshev approximations for the natural logarithm of the gamma function. Mathematics of Computation 21: 198203.CrossRefGoogle Scholar
3.DiDonato, A.R. & Morris, A.H. Jr., (1986). Computation of the incomplete gamma functions. ACM Transactions on Mathematical Software 12: 377393.CrossRefGoogle Scholar
4.Gautschi, W. (1979). A computational procedure for incomplete gamma functions. ACM Transactions on Mathematical Software 5: 466481.CrossRefGoogle Scholar
5.Macleod, A.J. (1989). A robust and reliable algorithm for the logarithm of the gamma function; algorithm AS 245. Applied Statistics 38: 397423.CrossRefGoogle Scholar
6.Shea, B.L. (1988). Chi-squared and incomplete gamma integral. Applied Statistics 37: 466473.CrossRefGoogle Scholar
7.Temme, N.M. (1979). The asymptotic expansions of the incomplete gamma functions. SIAM Journal on Mathematical Analysis 10: 239253.CrossRefGoogle Scholar
8.Temme, N.M. (1987). On the computation of the incomplete gamma functions for large values of the parameters. In Mason, E.J.C. & Cox, M.G. (eds.), Algorithms for approximation. Proceedings of the IMA-Conference, Shrivenham, July 15–19, 1985, Oxford, Clarendon, pp. 479489.Google Scholar