{
  "id": "1411.1371",
  "version": "v1",
  "published": "2014-11-05T19:38:14.000Z",
  "updated": "2014-11-05T19:38:14.000Z",
  "title": "Generalizations of generating functions for basic hypergeometric orthogonal polynomials",
  "authors": [
    "Howard S. Cohl",
    "Roberto S. Costas-Santos",
    "Philbert R. Hwang"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for Askey-Wilson, Rogers/continuous $q$-ultrapherical, little $q$-Laguerre/Wall, and $q$-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and $q$-integrals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-05T19:38:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "05A15",
      "33C20",
      "34L10",
      "30E20"
    ],
    "keywords": [
      "basic hypergeometric orthogonal polynomials",
      "generating functions",
      "generalizations",
      "bilateral infinite series",
      "derive corresponding definite integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}