{
  "id": "0808.0982",
  "version": "v1",
  "published": "2008-08-07T09:00:32.000Z",
  "updated": "2008-08-07T09:00:32.000Z",
  "title": "$q$-Discrete Painlevé equations for recurrence coefficients of modified $q$-Freud orthogonal polynomials",
  "authors": [
    "Lies Boelen",
    "Christophe Smet",
    "Walter Van Assche"
  ],
  "comment": "16 pages, 4 figures. Accepted, to appear in Journal of Difference Equations and Applications",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present an asymmetric $q$-Painlev\\'e equation. We will derive this using $q$-orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this $q$-Painlev\\'e equation (up to a simple transformation). We will show a stable method of computing a special solution which gives the recurrence coefficients. We establish a connection with $\\alpha-q-P_V$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-07T09:00:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M55",
      "65Q05",
      "33D45",
      "39A13"
    ],
    "keywords": [
      "freud orthogonal polynomials",
      "recurrence coefficients",
      "painleve equation",
      "generalized freud weights",
      "simple transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.0982B"
    }
  }
}