{
  "id": "1410.3241",
  "version": "v1",
  "published": "2014-10-13T09:50:15.000Z",
  "updated": "2014-10-13T09:50:15.000Z",
  "title": "Extensions of the classical theorems for very well-poised hypergeometric functions",
  "authors": [
    "Yashoverdhan Vyas",
    "Kalpana Fatawat"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "The classical summation and transformation theorems for very well-poised hypergeometric functions, namely, $_{5}F_4(1)$ summation, Dougall's $_{7}F_6(1)$ summation, Whipple's $_{7}F_6(1)$ to $_{4}F_3(1)$ transformation and Bailey's $_{9}F_8(1)$ to $_{9}F_8(1)$ transformation are extended. These extensions are derived by applying the well-known Bailey's transform method along with the classical very well-poised summation and transformation theorems for very well-poised hypergeometric functions and the Rakha and Rathie's extension of the Saalsch\\\"{u}tz's theorem. To show importance and applications of the discovered extensions, a number of special cases are pointed out, which leads not only to the extensions of other classical theorems for very well-poised and well-poised hypergeometric functions but also generate new hypergeometric summations and transformations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-13T09:50:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C20"
    ],
    "keywords": [
      "well-poised hypergeometric functions",
      "classical theorems",
      "well-known baileys transform method",
      "transformation theorems",
      "special cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.3241V"
    }
  }
}