{
  "id": "1408.0674",
  "version": "v2",
  "published": "2014-08-04T13:12:31.000Z",
  "updated": "2015-02-07T09:50:38.000Z",
  "title": "The resurgence properties of the incomplete gamma function I",
  "authors": [
    "Gergő Nemes"
  ],
  "comment": "36 pages, 4 figures. arXiv admin note: text overlap with arXiv:1311.2522, arXiv:1309.2209, arXiv:1312.2765",
  "categories": [
    "math.CA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-04T13:12:31.000Z",
      "title": "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.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-07T09:50:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A60",
      "33B20",
      "34M40"
    ],
    "keywords": [
      "incomplete gamma function",
      "resurgence properties",
      "asymptotic expansions",
      "realistic error bounds",
      "large arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.0674N"
    }
  }
}