English

The resurgence properties of the incomplete gamma function I

Classical Analysis and ODEs 2016-07-29 v3

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.

Keywords

Cite

@article{arxiv.1408.0674,
  title  = {The resurgence properties of the incomplete gamma function I},
  author = {Gergő Nemes},
  journal= {arXiv preprint arXiv:1408.0674},
  year   = {2016}
}

Comments

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