{
  "id": "1309.1175",
  "version": "v3",
  "published": "2013-09-04T20:09:13.000Z",
  "updated": "2014-09-16T18:46:55.000Z",
  "title": "Exceptional Charlier and Hermite orthogonal polynomials",
  "authors": [
    "Antonio J. Duran"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Using Casorati determinants of Charlier polynomials, we construct for each finite set $F$ of positive integers a sequence of polynomials $r_n^F$, $n\\in \\sigma_F$, which are eigenfunction of a second order difference operator, where $\\sigma_F$ is an infinite set of nonnegative integers, $\\sigma_F \\varsubsetneq \\NN$. For certain finite sets $F$ (we call them admissible sets), we prove that the polynomials $r_n^F$, $n\\in \\sigma_F$, are actually exceptional Charlier 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 Charlier polynomials into a Wronskian determinant of Hermite polynomials. For admissible sets, these Wronskian determinants turn out to be exceptional Hermite polynomials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-17T11:21:27.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-16T18:46:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45",
      "33E30"
    ],
    "keywords": [
      "hermite orthogonal polynomials",
      "finite set",
      "casorati determinant",
      "second order difference operator",
      "exceptional charlier polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1175D"
    }
  }
}