Computation of the incomplete gamma function ratios and their inverse

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 .