{
  "id": "1310.4658",
  "version": "v1",
  "published": "2013-10-17T11:31:04.000Z",
  "updated": "2013-10-17T11:31:04.000Z",
  "title": "Exceptional Meixner and Laguerre orthogonal polynomials",
  "authors": [
    "Antonio J. Duran"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1309.1175",
  "categories": [
    "math.CA"
  ],
  "abstract": "Using Casorati determinants of Meixner polynomials $(m_n^{a,c})_n$, we construct for each pair $\\F=(F_1,F_2)$ of finite sets of positive integers a sequence of polynomials $m_n^{a,c;\\F}$, $n\\in \\sigma_\\F$, which are eigenfunctions of a second order difference operator, where $\\sigma_\\F$ is certain infinite set of nonnegative integers, $\\sigma_\\F \\varsubsetneq \\NN$. When $c$ and $\\F$ satisfy a suitable admissibility condition, we prove that the polynomials $m_n^{a,c;\\F}$, $n\\in \\sigma_\\F$, are actually exceptional Meixner polynomials; that is, in addition, they are orthogonal and complete with respect to a positive measure. By passing to the limit, we transform the Casorati determinant of Meixner polynomials into a Wronskian type determinant of Laguerre polynomials $(L_n^\\alpha)_n$. Under the admissibility conditions for $\\F$ and $\\alpha$, these Wronskian type determinants turn out to be exceptional Laguerre polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-17T11:31:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45",
      "33E30"
    ],
    "keywords": [
      "laguerre orthogonal polynomials",
      "second order difference operator",
      "casorati determinant",
      "admissibility condition",
      "wronskian type determinants turn"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4658D"
    }
  }
}