The asymptotic expansion of a generalised 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:
2003

Citing 3
Cited 1

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Asymptotics and closed form of a generalized incomplete gamma function

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Exponentially small expansions in the asymptotics of the Wright function

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Abstract

We define a generalised incomplete gamma function Lp(a,z), which coincides with the familiar normalised function Q(a,z) = Γ(a,z)/Γ(a) when the integer parameter p = 1. It is shown that the large-z asymptotics of Lp(a,z) in the sector |argz| p consists of p exponential expansions. In Re(z) 0, all these expansions are recessive at infinity and form a sequence of increasingly subdominant exponential contributions.