{
  "id": "1611.00548",
  "version": "v1",
  "published": "2016-11-02T11:18:30.000Z",
  "updated": "2016-11-02T11:18:30.000Z",
  "title": "A uniform asymptotic expansion for the incomplete gamma functions revisited",
  "authors": [
    "R B Paris"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "A new uniform asymptotic expansion for the incomplete gamma function $\\Gamma(a,z)$ valid for large values of $z$ was given by the author in {\\it J. Comput. Appl. Math.} {\\bf 148} (2002) 323--339. This expansion contains a complementary error function of an argument measuring transition across the point $z=a$, with easily computable coefficients that do not involve a removable singularity in the neighbourhood of this point. In this note we correct a misprint in the listing of certain coefficients in this expansion and discuss in more detail the situation corresponding to $\\Gamma(a,a)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-02T11:18:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30E15",
      "33B20",
      "34E05",
      "41A30",
      "41A60"
    ],
    "keywords": [
      "incomplete gamma function",
      "uniform asymptotic expansion",
      "complementary error function",
      "large values",
      "argument measuring transition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}