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

Details Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

1996-03-22

arxiv.org/abs/math/9603218v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We consider the asymptotic behavior of the incomplete gamma functions gamma(-a,-z) and Gamma(-a,-z) as a goes to infinity. Uniform expansions are needed to describe the transition area z~a in which case error functions are used as main approximants. We use integral representations of the incomplete gamma functions and derive a uniform equation by applying techniques used for the existing uniform expansions for gamma(a,z) and Gamma(a,z). The result is compared with Olver's uniform expansion for the generalized exponential integral. A numerical verification of the expansion is given in a final section.

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