Algorithm 969: Computation of the Incomplete Gamma Function for Negative Values of the Argument

摘要

An algorithm for computing the incomplete gamma function. gamma*(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, Poincare-type expansions, uniform asymptotic expansions, and recurrence relations, depending on the parameter region. A relative accuracy similar to 10(-13) in the parameter region ( a, z) epsilon [- 500, 500] x [- 500, 0) can be obtained when computing the function. gamma*( a, z) with the Fortran 90 module IncgamNEG implementing the algorithm.