{
  "id": "1908.03207",
  "version": "v1",
  "published": "2019-08-08T14:13:31.000Z",
  "updated": "2019-08-08T14:13:31.000Z",
  "title": "Some homogeneous $q$-difference operators and the associated generalized Hahn polynomials",
  "authors": [
    "Hari M. Srivastava",
    "Sama Arjika",
    "Abey Sherif Kelil"
  ],
  "comment": "15 pages",
  "journal": "Appl. Set-Valued Anal. Optim. 1 (2019) No. 2, pp. 187-201",
  "doi": "10.23952/asvao.1.2019.2.07",
  "categories": [
    "math.CA",
    "math-ph",
    "math.CO",
    "math.FA",
    "math.MP"
  ],
  "abstract": "In this paper, we first construct the homogeneous $q$-shift operator $\\widetilde{E}(a,b;D_{q})$ and the homogeneous $q$-difference operator $\\widetilde{L}(a,b; \\theta_{xy})$. We then apply these operators in order to represent and investigate generalized Cauchy and a general form of Hahn polynomials. We derive some $q$-identities such as: generating functions, extended generating functions, Mehler's formula and Roger's formula for these $q$-polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-08T14:13:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "33D15",
      "33D45"
    ],
    "keywords": [
      "associated generalized hahn polynomials",
      "difference operator",
      "homogeneous",
      "generating functions",
      "general form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}