{
  "id": "math/0410222",
  "version": "v1",
  "published": "2004-10-08T07:27:48.000Z",
  "updated": "2004-10-08T07:27:48.000Z",
  "title": "Applicability of the $q$-Analogue of Zeilberger's Algorithm",
  "authors": [
    "William Y. C. Chen",
    "Qing-Hu Hou",
    "Yan-Ping Mu"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO",
    "math.CA"
  ],
  "abstract": "The applicability or terminating condition for the ordinary case of Zeilberger's algorithm was recently obtained by Abramov. For the $q$-analogue, the question of whether a bivariate $q$-hypergeometric term has a $qZ$-pair remains open. Le has found a solution to this problem when the given bivariate $q$-hypergeometric term is a rational function in certain powers of $q$. We solve the problem for the general case by giving a characterization of bivariate $q$-hypergeometric terms for which the $q$-analogue of Zeilberger's algorithm terminates. Moreover, we give an algorithm to determine whether a bivariate $q$-hypergeometric term has a $qZ$-pair.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-08T07:27:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33F10",
      "68W30"
    ],
    "keywords": [
      "hypergeometric term",
      "applicability",
      "zeilbergers algorithm terminates",
      "pair remains open",
      "general case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10222C"
    }
  }
}