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Computation of the incomplete gamma function ratios and their inverse. (English) Zbl 0623.65016
Authors’ summary: An algorithm is given for computing the incomplete gamma function ratios P(a,x) and Q(a,x) for a0, x0, a+x0. 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.
Reviewer: K.S.Kölbig

65D20Computation of special functions, construction of tables
33B15Gamma, beta and polygamma functions
Algorithm 524