{
  "id": "2011.05848",
  "version": "v1",
  "published": "2020-11-10T17:04:34.000Z",
  "updated": "2020-11-10T17:04:34.000Z",
  "title": "A note on generalized $q$-difference equations for general Al-Salam--Carlitz polynomials",
  "authors": [
    "Jian Cao",
    "Binbin Xu",
    "Sama Arjika"
  ],
  "comment": "14 pages",
  "journal": "Advances in Difference Equations (2020)",
  "categories": [
    "math.CO",
    "math.CA",
    "math.FA",
    "math.NT"
  ],
  "abstract": "In this paper, we deduce the generalized $q$-difference equations for general Al-Salam--Carlitz polynomials and generalize Arjika's recently results [$q$-difference equation for homogeneous $q$-difference operators and their applications, J. Differ. Equ. Appl. {\\bf 26}, 987--999 (2020)]. In addition, we obtain transformational identities by the method of $q$-difference equation. Moreover, we deduce $U(n+1)$ type generating functions and Ramanujan's integrals involving general Al-Salam--Carlitz polynomials by $q$-difference equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-10T17:04:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "11B65",
      "33D15",
      "33D45",
      "33D60",
      "39A13",
      "39B32"
    ],
    "keywords": [
      "general al-salam-carlitz polynomials",
      "difference equation",
      "difference operators",
      "ramanujans integrals",
      "transformational identities"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}