{
  "id": "1204.5070",
  "version": "v2",
  "published": "2012-04-23T14:05:54.000Z",
  "updated": "2012-11-30T10:01:50.000Z",
  "title": "The generalized Krawtchouk polynomials and the fifth Painlevé equation",
  "authors": [
    "Lies Boelen",
    "Galina Filipuk",
    "Christophe Smet",
    "Walter Van Assche",
    "Lun Zhang"
  ],
  "comment": "15 pages, 4 figures, references added with more details and explanations, to appear in Journal of Difference Equations and Applications",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study the recurrence coefficients of the orthogonal polynomials with respect to a semi-classical extension of the Krawtchouk weight. We derive a coupled discrete system for these coefficients and show that they satisfy the fifth Painlev\\'e equation when viewed as functions of one of the parameters in the weight.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-30T10:01:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M55",
      "33E17",
      "33C47",
      "42C05",
      "65Q30"
    ],
    "keywords": [
      "generalized krawtchouk polynomials",
      "fifth painleve equation",
      "orthogonal polynomials",
      "recurrence coefficients",
      "krawtchouk weight"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5070B"
    }
  }
}