{
  "id": "1411.1645",
  "version": "v1",
  "published": "2014-11-06T16:00:39.000Z",
  "updated": "2014-11-06T16:00:39.000Z",
  "title": "The resurgence properties of the Incomplete gamma function II",
  "authors": [
    "Gergő Nemes"
  ],
  "comment": "22 pages, 3 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we derive a new representation 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 this representation, we obtain numerically computable bounds for the remainder term of the asymptotic expansion of the incomplete gamma function $\\Gamma \\left( { - a,\\lambda a} \\right)$ with large $a$ and fixed positive $\\lambda$, and an asymptotic expansion for its late coefficients. We also give a rigorous proof of Dingle's formal result regarding the exponentially improved version of the asymptotic series of $\\Gamma \\left( { - a,\\lambda a} \\right)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-06T16:00:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A60",
      "33B20",
      "34M40"
    ],
    "keywords": [
      "incomplete gamma function",
      "resurgence properties",
      "asymptotic expansion",
      "late coefficients",
      "representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}