{
  "id": "2202.10167",
  "version": "v2",
  "published": "2022-02-21T12:23:33.000Z",
  "updated": "2022-05-31T10:02:37.000Z",
  "title": "On another characterization of Askey-Wilson polynomials",
  "authors": [
    "D. Mbouna",
    "A. Suzuki"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2103.05742",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\\geq 0}$ satisfying \\begin{align*} \\phi(x)\\mathcal{D}_q P_{n}(x)=a_n\\mathcal{S}_q P_{n+1}(x) +b_n\\mathcal{S}_q P_n(x) +c_n\\mathcal{S}_q P_{n-1}(x), \\end{align*} ($c_n\\neq 0$) where $\\phi$ is a well chosen polynomial of degree at most two, $\\mathcal{D}_q$ is the Askey-Wilson operator and $\\mathcal{S}_q$ the averaging operator, are the multiple of Askey-Wilson polynomials, or specific or limiting cases of them.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-05-31T10:02:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "askey-wilson polynomials",
      "characterization",
      "askey-wilson operator",
      "orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}