{
  "id": "0901.0947",
  "version": "v2",
  "published": "2009-01-07T22:57:33.000Z",
  "updated": "2010-07-04T12:35:55.000Z",
  "title": "Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlevé equations",
  "authors": [
    "Philippe Biane"
  ],
  "comment": "26 pages 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider orthogonal polynomials on the unit circle with respect to a weight which is a quotient of $q$-gamma functions. We show that the Verblunsky coefficients of these polynomials satisfy discrete Painlev\\'e equations, in a Lax form, which correspond to an $A_3^{(1)}$ surface in Sakai's classification.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-04T12:35:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05"
    ],
    "keywords": [
      "orthogonal polynomials",
      "unit circle",
      "gamma weights",
      "polynomials satisfy discrete painleve equations",
      "verblunsky coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.0947B"
    }
  }
}