Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 1996
 DOI:
 10.48550/arXiv.math/9603218
 arXiv:
 arXiv:math/9603218
 Bibcode:
 1996math......3218T
 Keywords:

 Mathematics  Classical Analysis and ODEs