{
  "id": "math/9611218",
  "version": "v1",
  "published": "1996-11-29T00:00:00.000Z",
  "updated": "1996-11-29T00:00:00.000Z",
  "title": "Preud's equations for orthogonal polynomials as discrete Painlevé equations",
  "authors": [
    "Alphonse P. Magnus"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider orthogonal polynomials p_n with respect to an exponential weight function w(x) = exp(-P(x)). The related equations for the recurrence coefficients have been explored by many people, starting essentially with Laguerre [49], in order to study special continued fractions, recurrence relations, and various asymptotic expansions (G. Freud's contribution [28, 56]). Most striking example is n = 2tw_n + w_n(w_n+1 + w_n + w_n-1) for the recurrence coefficients p_n+1 = xp_n - w_np_n-1 of the orthogonal polynomials related to the weight w(x) = exp(-4(tx^3 + x^4)) (notation of [26, pp. 34-36]). This example appears in practically all the references below. The connection with discrete Painlev\\'e equations is described here.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-11-29T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orthogonal polynomials",
      "preuds equations",
      "recurrence coefficients",
      "study special continued fractions",
      "discrete painleve equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}