{
  "id": "2107.02177",
  "version": "v1",
  "published": "2021-07-04T23:19:00.000Z",
  "updated": "2021-07-04T23:19:00.000Z",
  "title": "Pearson Equations for Discrete Orthogonal Polynomials: II. Generalized Charlier, Meixner and Hahn of type I cases",
  "authors": [
    "Itsaso Fernández-Irisarri",
    "Manuel Mañas"
  ],
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "The Cholesky factorization of the moment matrix is considered for the generalized Charlier, generalized Meixner and generalized Hahn of type I discrete orthogonal polynomials. For the generalized Charlier we present an alternative derivation of the Laguerre-Freud relations found by Smet and Van Assche. Third order and second order order nonlinear ordinary differential equations are found for the recursion coefficient $\\gamma_n$. Laguerre-Freud relations are also found for the generalized Meixner case, which are compared with those of Smet and Van Assche. Finally, the generalized Hahn of type I discrete orthogonal polynomials are studied as well, and Laguerre-Freud equations are found and the differences with the equations found by Dominici and by Filipuk and Van Assche are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-04T23:19:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45",
      "33C47"
    ],
    "keywords": [
      "discrete orthogonal polynomials",
      "generalized charlier",
      "nonlinear ordinary differential equations",
      "pearson equations",
      "order nonlinear ordinary differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}