{
  "id": "2202.12857",
  "version": "v1",
  "published": "2022-02-25T18:06:54.000Z",
  "updated": "2022-02-25T18:06:54.000Z",
  "title": "Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters $a$, $b$ and $z$",
  "authors": [
    "N. M. Temme",
    "E. J. M. Veling"
  ],
  "comment": "16 pages, 2 tables, 1 figure",
  "categories": [
    "math.CA"
  ],
  "abstract": "In a recent paper \\cite{Temme:2021:AKH} new asymptotic expansions are given for the Kummer functions $M(a,b,z)$ and $U(a,b+1,z)$ for large positive values of $a$ and $b$, with $z$ fixed and special attention for the case $a\\sim b$. In this paper we extend the approach and also accept large values of $z$. The new expansions are valid when at least one of the parameters $a$, $b$, or $z$ is large. We provide numerical tables to show the performance of the expansions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-25T18:06:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A60",
      "33C15",
      "G.0",
      "G.1"
    ],
    "keywords": [
      "kummer hypergeometric functions",
      "asymptotic expansions",
      "asymptotic parameters",
      "accept large values",
      "large positive values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}