{
  "id": "2004.01945",
  "version": "v1",
  "published": "2020-04-04T14:32:36.000Z",
  "updated": "2020-04-04T14:32:36.000Z",
  "title": "Uniform asymptotics of a Gauss hypergeometric function with two large parameters, V",
  "authors": [
    "R. B. Paris"
  ],
  "comment": "13 pages, 0 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider the uniform asymptotic expansion for the Gauss hypergeometric function \\[{}_2F_1(a+\\epsilon\\lambda,b;c+\\lambda;x),\\qquad 0<x<1\\] as $\\lambda\\to+\\infty$ in the neigbourhood of $\\epsilon x=1$ when the parameter $\\epsilon>1$ and the constants $a$, $b$ and $c$ are supposed finite. Use of a standard integral representation shows that the problem reduces to consideration of a simple saddle point near an endpoint of the integration path. A uniform asymptotic expansion is first obtained by employing Bleistein's method. An alternative form of uniform expansion is derived following the approach described in Olver's book [{\\it Asymptotics and Special Functions}, p.~346]. This second form has several advantages over the Bleistein form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-04T14:32:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C05",
      "34E05",
      "41A60"
    ],
    "keywords": [
      "gauss hypergeometric function",
      "large parameters",
      "uniform asymptotic expansion",
      "standard integral representation",
      "simple saddle point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}