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The resurgence properties of the incomplete gamma function, I

Gergő Nemes

Department of Mathematics and its Applications, Central European University, H-1051 Budapest, Nádor utca 9, Hungary

https://doi.org/10.1142/S0219530515500128Cited by:6 (Source: Crossref)

Abstract

In this paper, we derive new representations for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls [Hyperasymptotics for integrals with finite endpoints, Proc. Roy. Soc. London Ser. A439 (1992) 373–396]. Using these representations, we obtain a number of properties of the asymptotic expansions of the incomplete gamma function with large arguments, including explicit and realistic error bounds, asymptotics for the late coefficients, exponentially improved asymptotic expansions, and the smooth transition of the Stokes discontinuities.

Keywords:

AMSC: 41A60, 33B20, 34M40

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