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

2016/08/14 by Amparo Gil, Diego Ruiz‐Antolín, Gil, A. +5
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Mathematical and Theoretical Analysis #Numerical Methods and Algorithms #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1608.04152

openalex publication_date 2016/08/14 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Uniform asymptotics for the incomplete gamma functions starting from\n negative values of the parameters

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