Algorithm 969

Abstract

An algorithm for computing the incomplete gamma function γ * ( a , z ) for real values of the parameter a and negative real values of the argument z is presented. The algorithm combines the use of series expansions, Poincaré-type expansions, uniform asymptotic expansions, and recurrence relations, depending on the parameter region. A relative accuracy ∼10 −13 in the parameter region ( a , z ) ∈ [− 500, 500] × [− 500, 0) can be obtained when computing the function γ * ( a , z ) with the Fortran 90 module IncgamNEG implementing the algorithm.