The resurgence properties of the incomplete gamma function I

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 (Howls, Proc. R. Soc. Lond. A 439 (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.

36 pages, 4 figures. arXiv admin note: text overlap with arXiv:1311.2522, arXiv:1309.2209, arXiv:1312.2765

References in corpus (2)

• An explicit formula for the coefficients in Laplace's method
• Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal

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