{
  "id": "1203.6857",
  "version": "v1",
  "published": "2012-03-30T16:53:39.000Z",
  "updated": "2012-03-30T16:53:39.000Z",
  "title": "A conjecture on Exceptional Orthogonal Polynomials",
  "authors": [
    "David Gomez-Ullate",
    "Niky Kamran",
    "Robert Milson"
  ],
  "journal": "Found. Comput. Math. 13:615-656 (2013)",
  "doi": "10.1007/s10208-012-9128-6",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical system by a Darboux-Crum transformation. We give a proof of this conjecture for codimension 2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The classification includes all cases known to date plus some new examples of X2-Laguerre and X2-Jacobi polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-30T16:53:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "33C47"
    ],
    "keywords": [
      "exceptional orthogonal polynomial system",
      "conjecture",
      "cprs orthogonal polynomials",
      "x2-jacobi polynomials",
      "darboux-crum transformation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.6857G"
    }
  }
}