{
  "id": "2008.01601",
  "version": "v1",
  "published": "2020-08-04T14:38:54.000Z",
  "updated": "2020-08-04T14:38:54.000Z",
  "title": "Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters",
  "authors": [
    "Nico M. Temme",
    "Raffaello Seri"
  ],
  "comment": "14 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We derive asymptotic expansions of the Kummer functions $M(a,b,z)$ and $U(a,b+1,z)$ for large positive values of $a$ and $b$, with $z$ fixed. For both functions we consider $b/a\\le 1$ and $b/a\\ge 1$, with special attention for the case $a\\sim b$. We use a uniform method to handle all cases of these parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-04T14:38:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C15",
      "41A60"
    ],
    "keywords": [
      "kummer hypergeometric functions",
      "large values",
      "parameters",
      "derive asymptotic expansions",
      "kummer functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}