{
  "id": "2207.13563",
  "version": "v1",
  "published": "2022-07-27T14:56:52.000Z",
  "updated": "2022-07-27T14:56:52.000Z",
  "title": "Dual forms of the orthogonality relations of q-orthogonal polynomials",
  "authors": [
    "Xinrong Ma",
    "Jin Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, by introducing new matrix operations and using a specific inverse relation, we establish the dual forms of the orthogonality relations for some well-known discrete and continuous q-orthogonal polynomials from the Askey-scheme such as the little and big q-Jacobi, q-Racah, (generalized) q-Laguerre, as well as the Askey-Wilson polynomials. As one of the most interesting results, we show that the Askey-Wilson q-beta integral represented in terms of the VWP-balanced 8{\\phi}7 series is just a dual form of the orthogonality relation of the Askey-Wilson polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-27T14:56:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "05A30"
    ],
    "keywords": [
      "orthogonality relation",
      "dual form",
      "askey-wilson polynomials",
      "specific inverse relation",
      "askey-wilson q-beta integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}