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arXiv · 1608.04152

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

A. Gil·D. Ruiz-Antolín·J. Segura·N. M. Temme
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Abstract

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, Poincar\'e-type expansions, uniform asymptotic expansions and recurrence relations, depending on the parameter region. A relative accuracy $\sim 10^{-13}$ in the parameter region $(a,z) \in [-500,\,500] \times [-500,\,0)$ can be obtained when computing the function $\gamma^*(a,z)$ with the Fortran 90 module IncgamNEG implementing the algorithm.

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A. Gil, D. Ruiz-Antolín, J. Segura, N. M. Temme. 2016-08-14. Computation of the incomplete gamma function for negative values of the argument. https://arxiv.org/abs/1608.04152

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