Algorithm 926: Incomplete Gamma Functions with Negative Arguments

An algorithm for accurately computing the lower incomplete gamma function gamma (alpha, t) in the case where alpha = n + 1/2, n is an element of Z and t < 0 is described. Series expansions and analytic continuation are employed to compute the function for certain critical values of n, and these results are used to initiate stable recurrence. The algorithm has been implemented in Fortran 2003, with precompuations carried out in Maple.