A uniform asymptotic expansion for the incomplete gamma function

Authors:
R. B. Paris
Affiliations:
Division of Mathematical Sciences, University of Abertay Dundee, Dundee DD1 1HG, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 1
Cited 1

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A simplification of Laplace's method: Applications to the Gamma function and Gauss hypergeometric function

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Abstract

We describe a new uniform asymptotic expansion for the incomplete gamma function Γ(a,z) valid for large values of z. This expansion contains a complementary error function of an argument measuring transition across the point z = a (which is different from that in the well-known uniform expansion for large a of Temme), with easily computable coefficients that do not involve a removable singularity at z = a. Our expansion is, however, valid in a smaller domain of the parameters than that of Temme. Numerical examples are given to illustrate the accuracy of the expansion.