Computation of the incomplete gamma function for negative values of the argument. 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, Poincare-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.

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