{
  "id": "math/0505042",
  "version": "v3",
  "published": "2005-05-03T04:33:48.000Z",
  "updated": "2005-06-21T15:00:19.000Z",
  "title": "The $(f,g)$-inversion formula and its applications: the $(f,g)$-summation formula",
  "authors": [
    "Xinrong Ma"
  ],
  "comment": "33 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A complete characterization of two functions $f(x,y)$ and $g(x,y)$ in the $(f,g)$-inversion is presented. As an application to the theory of hypergeometric series, a general bibasic summation formula determined by $f(x,y)$ and $g(x,y)$ as well as four arbitrary sequences is obtained which unifies Gasper and Rahman's, Chu's and Macdonald's bibasic summation formula. Furthermore, an alternative proof of the $(f,g)$-inversion derived from the $(f,g)$-summation formula is presented. A bilateral $(f,g)$-inversion containing Schlosser's bilateral matrix inversion as a special case is also obtained.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-06-21T15:00:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A10",
      "33C20"
    ],
    "keywords": [
      "inversion formula",
      "application",
      "macdonalds bibasic summation formula",
      "inversion containing schlossers bilateral matrix",
      "containing schlossers bilateral matrix inversion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5042M"
    }
  }
}