{
  "id": "2103.05742",
  "version": "v1",
  "published": "2021-03-09T22:33:05.000Z",
  "updated": "2021-03-09T22:33:05.000Z",
  "title": "Remarks on Askey-Wilson polynomials and Meixner polynomials of the second kind",
  "authors": [
    "K. Castillo",
    "D. Mbouna",
    "J. Petronilho"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The purpose of this note is twofold: firstly to characterize all the sequences of orthogonal polynomials $(P_n)_{n\\geq 0}$ such that $$ \\frac{\\triangle}{{\\bf \\triangle} x(s-1/2)}P_{n+1}(x(s-1/2))=c_n(\\triangle +2\\,\\mathrm{I})P_n(x(s-1/2)), $$ where $\\mathrm{I}$ is the identity operator, $x$ defines a class of lattices with, generally, nonuniform step-size, and $\\triangle f(s)=f(s+1)-f(s)$; and secondly to present, in a friendly way, a method to deal with these kind of problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-09T22:33:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45"
    ],
    "keywords": [
      "meixner polynomials",
      "askey-wilson polynomials",
      "second kind",
      "orthogonal polynomials",
      "identity operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}