Authors’ summary: An algorithm is given for computing the incomplete gamma function ratios P(a,x) and Q(a,x) for
. 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.