{
  "id": "1510.02579",
  "version": "v1",
  "published": "2015-10-09T07:09:38.000Z",
  "updated": "2015-10-09T07:09:38.000Z",
  "title": "Exceptional Hahn and Jacobi orthogonal polynomials",
  "authors": [
    "Antonio J. Durán"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1310.4658, arXiv:1309.1175",
  "categories": [
    "math.CA"
  ],
  "abstract": "Using Casorati determinants of Hahn polynomials $(h_n^{\\alpha,\\beta,N})_n$, we construct for each pair $\\F=(F_1,F_2)$ of finite sets of positive integers polynomials $h_n^{\\alpha,\\beta,N;\\F}$, $n\\in \\sigma _\\F$, which are eigenfunctions of a second order difference operator, where $\\sigma _\\F$ is certain set of nonnegative integers, $\\sigma _\\F \\varsubsetneq \\NN$. When $N\\in \\NN$ and $\\alpha$, $\\beta$, $N$ and $\\F$ satisfy a suitable admissibility condition, we prove that the polynomials $h_n^{\\alpha,\\beta,N;\\F}$ are also orthogonal and complete with respect to a positive measure (exceptional Hahn polynomials). By passing to the limit, we transform the Casorati determinant of Hahn polynomials into a Wronskian type determinant of Jacobi polynomials $(P_n^{\\alpha,\\beta})_n$. Under suitable conditions for $\\alpha$, $\\beta$ and $\\F$, these Wronskian type determinants turn out to be exceptional Jacobi polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-09T07:09:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45",
      "33E30"
    ],
    "keywords": [
      "jacobi orthogonal polynomials",
      "second order difference operator",
      "casorati determinant",
      "wronskian type determinants turn",
      "exceptional hahn polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}