{
  "id": "2311.05636",
  "version": "v1",
  "published": "2023-10-26T17:31:05.000Z",
  "updated": "2023-10-26T17:31:05.000Z",
  "title": "On classical orthogonal polynomials on bi-lattices",
  "authors": [
    "K. Castillo",
    "G. Filipuk",
    "D. Mbouna"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2102.00033",
  "categories": [
    "math.CA"
  ],
  "abstract": "In [J. Phys. A: Math. Theor. 45 (2012)], while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomials, that they called para-Krawtchouk polynomials, defined on a bilinear lattice. In this note we present necessary and sufficient conditions for the regularity of solutions of the corresponding functional equation. Moreover, the functional Rodrigues formula and a closed formula for the recurrence coefficients are presented. As a consequence, we characterize all solutions of the functional equation, including as very particular cases the Meixner, Charlier, Krawtchouk, Hahn, and para-Krawtchouk polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-26T17:31:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45"
    ],
    "keywords": [
      "classical orthogonal polynomials",
      "para-krawtchouk polynomials",
      "bi-lattices",
      "admit perfect state transfer",
      "functional rodrigues formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}