Computation of the incomplete gamma function for negative values of the argument

08/14/2016

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by   A. Gil, et al.

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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.