Computation of the Incomplete Gamma Function Ratios and Their Inverse

Abstract

An algorithm is given for computing the incomplete gamma function ratios P(a, x) and Q>(a, x) for a ≩ 0, x ≩ 0, a + x ≠ 0. Temme's uniform asymptotic expansions 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. © 1986, ACM. All rights reserved.