{
  "id": "1805.05893",
  "version": "v1",
  "published": "2018-05-12T06:21:13.000Z",
  "updated": "2018-05-12T06:21:13.000Z",
  "title": "A $q$-summation and the orthogonality relations for the $q$-Hahn polynomials and the big $q$-Jacobi polynomials",
  "authors": [
    "Zhi-Guo Liu"
  ],
  "comment": "22 pages",
  "journal": "Journal of Mathematical Analysis and Applications 419 (2014)1045--1064",
  "categories": [
    "math.CO",
    "math.CV",
    "math.NT"
  ],
  "abstract": "Using a general $q$-summation formula, we derive a generating function for the $q$-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the $q$-Hahn polynomials. A new proof of the orthogonality relation for the big $q$-Jacobi polynomials is also given. A simple evaluation of the Nassrallah-Rahman integral is derived by using this summation formula. A new $q$-beta integral formula is established, which includes the Nassrallah-Rahman integral as a special case. The $q$-summation formula also allows us to recover several strange $q$-series identities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-12T06:21:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "33D15",
      "33D45",
      "11E25"
    ],
    "keywords": [
      "hahn polynomials",
      "orthogonality relation",
      "jacobi polynomials",
      "summation formula",
      "nassrallah-rahman integral"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}