{
  "id": "2009.06563",
  "version": "v1",
  "published": "2020-09-14T16:46:55.000Z",
  "updated": "2020-09-14T16:46:55.000Z",
  "title": "Generating Functions for Some Families of the Generalized Al-Salam-Carlitz $q$-Polynomials",
  "authors": [
    "Hari Mohan Srivastava",
    "Sama Arjika"
  ],
  "comment": "16 pages",
  "journal": "Advances in Difference Equations (2020)",
  "doi": "10.1186/s13662-020-02963-9",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, by making use of the familiar $q$-difference operators $D_q$ and $D_{q^{-1}}$, we first introduce two homogeneous $q$-difference operators $\\mathbb{T}({\\bf a},{\\bf b},cD_q)$ and $\\mathbb{E}({\\bf a},{\\bf b}, cD_{q^{-1}})$, which turn out to be suitable for dealing with the families of the generalized Al-Salam-Carlitz $q$-polynomials $\\phi_n^{({\\bf a},{\\bf b})}(x,y|q)$ and $\\psi_n^{({\\bf a},{\\bf b})}(x,y|q)$. We then apply each of these two homogeneous $q$-difference operators in order to derive generating functions, Rogers type formulas, the extended Rogers type formulas and the Srivastava-Agarwal type linear as well as bilinear generating functions involving each of these families of the generalized Al-Salam-Carlitz $q$-polynomials. We also show how the various results presented here are related to those in many earlier works on the topics which we study in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-14T16:46:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "33D15",
      "33D45",
      "05A40",
      "11B65"
    ],
    "keywords": [
      "generalized al-salam-carlitz",
      "polynomials",
      "difference operators",
      "srivastava-agarwal type linear",
      "extended rogers type formulas"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}