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Zbl 0623.65016
Didonato, Armido R.; Morris, Alfred H.jun.
Computation of the incomplete gamma function ratios and their inverse. (English)
[J] ACM Trans. Math. Softw. 12, 377-393 (1986). ISSN 0098-3500

Authors' summary: An algorithm is given for computing the incomplete gamma function ratios P(a,x) and Q(a,x) for $a\ge 0$, $x\ge 0$, $a+x\ne 0$. {\it N. M. Temme}'s uniform asymptotic expansions [Math. Comput. 29, 1109-1114 (1975; Zbl 0313.33002)] are used. The algorithm is robust; results accurate to 14 significant digits can be obtained. An extensive set of coefficients for the Temme expansions is included. An algorithm, employing third-order Schröder iteration supported by Newton-Raphson iteration, is provided for computing x when a, P(a,x), and Q(a,x) are given. Three iterations at most are required to obtain 10 significant digit accuracy for x.
[K.S.Kölbig]

MSC 2000:: *65D20 Computation of special functions
33B15 Gamma-functions, etc.

Keywords: chi-square distribution; minimax approximations; percentile points; incomplete gamma function; third-order Schröder iteration; Newton- Raphson iteration

Citations: Zbl 0313.33002

Cited in: Zbl 0635.65014

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Zentralblatt MATH Berlin [Germany]