{
  "id": "1101.1817",
  "version": "v1",
  "published": "2011-01-10T13:55:27.000Z",
  "updated": "2011-01-10T13:55:27.000Z",
  "title": "Orthogonal polynomials on a bi-lattice",
  "authors": [
    "Christophe Smet",
    "Walter Van Assche"
  ],
  "comment": "25 pages, 2 figures",
  "journal": "Constr. Approx. 36 (2012), 215-242",
  "doi": "10.1007/s00365-011-9145-8",
  "categories": [
    "math.CA"
  ],
  "abstract": "We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N+1-\\beta. We combine both lattices to obtain the bi-lattice N \\cup (N+1-\\beta) and show that the orthogonal polynomials on this bi-lattice have recurrence coefficients which satisfy a non-linear system of recurrence equations, which we can identify as a limiting case of an (asymmetric) discrete Painlev\\'e equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-10T13:55:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C47",
      "42C05",
      "34M55",
      "65Q30"
    ],
    "keywords": [
      "orthogonal polynomials",
      "bi-lattice",
      "discrete painleve equation",
      "meixner polynomials",
      "recurrence equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1817S"
    }
  }
}