{
  "id": "1711.07780",
  "version": "v1",
  "published": "2017-11-21T13:41:47.000Z",
  "updated": "2017-11-21T13:41:47.000Z",
  "title": "A $(p,ν)$-extension of the Appell function $F_1(\\cdot)$ and its properties",
  "authors": [
    "S A Dar",
    "R B Paris"
  ],
  "comment": "11 pages, 0 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we obtain a $(p,v)$-extension of the Appell hypergeometric function $ F_{1}(\\cdot)$, together with its integral representation, by using the extended Beta function $B_{p,v}(x,y)$ introduced in arXiv:1502.06200. Also, we give some of its main properties, namely the Mellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, some new integral representations of the extended Appell function$ F_{1,p,v}(\\cdot)$ involving Meijer's $G$-function are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-21T13:41:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C60",
      "33C65",
      "33B15",
      "33C45",
      "33C10"
    ],
    "keywords": [
      "integral representation",
      "appell hypergeometric function",
      "recursion formulas",
      "extended appell function",
      "extended beta function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}