{
  "id": "math/0005095",
  "version": "v3",
  "published": "2000-05-10T11:41:38.000Z",
  "updated": "2000-10-31T14:23:27.000Z",
  "title": "A generalization of Kummer's identity",
  "authors": [
    "Raimundas Vidunas"
  ],
  "comment": "13 pages; classical proofs simplified, possible transformations reviewed; in the algoritmic part similar evaluations of other series added",
  "categories": [
    "math.CA"
  ],
  "abstract": "The well-known Kummer's formula evaluates the hypergeometric series 2F1(A,B;C;-1) when the relation B-A+C=1 holds. This paper deals with evaluation of 2F1(-1) series in the case when C-A+B is an integer. Such a series is expressed as a sum of two \\Gamma-terms multiplied by terminating 3F2(1) series. A few such formulas were essentially known to Whipple in 1920's. Here we give a simpler and more complete overview of this type of evaluations. Additionally, algorithmic aspects of evaluating hypergeometric series are considered. We illustrate Zeilberger's method and discuss its applicability to non-terminating series, and present a couple of similar generalizations of other known formulas.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-10-31T14:23:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C05",
      "33F10",
      "39A10"
    ],
    "keywords": [
      "kummers identity",
      "well-known kummers formula evaluates",
      "illustrate zeilbergers method",
      "hypergeometric series 2f1",
      "similar generalizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......5095V"
    }
  }
}