{
  "id": "1104.3773",
  "version": "v2",
  "published": "2011-04-19T15:20:47.000Z",
  "updated": "2011-07-13T05:10:53.000Z",
  "title": "Recurrence Coefficients of a New Generalization of the Meixner Polynomials",
  "authors": [
    "Galina Filipuk",
    "Walter Van Assche"
  ],
  "journal": "SIGMA 7 (2011), 068, 11 pages",
  "doi": "10.3842/SIGMA.2011.068",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate new generalizations of the Meixner polynomials on the lattice $\\mathbb{N}$, on the shifted lattice $\\mathbb{N}+1-\\beta$ and on the bi-lattice $\\mathbb{N}\\cup (\\mathbb{N}+1-\\beta)$. We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlev\\'e equation P$_{\\textup V}$. Initial conditions for different lattices can be transformed to the classical solutions of P$_{\\textup V}$ with special values of the parameters. We also study one property of the B\\\"acklund transformation of P$_{\\textup V}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-13T05:10:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M55",
      "33E17",
      "33C47",
      "42C05",
      "64Q30"
    ],
    "keywords": [
      "meixner polynomials",
      "recurrence coefficients",
      "generalization",
      "three-term recurrence relation",
      "fifth painleve equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2011,
      "month": "Jul",
      "volume": 7,
      "pages": "068"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011SIGMA...7..068F"
    }
  }
}