{
  "id": "math/0012259",
  "version": "v2",
  "published": "2000-12-29T05:10:19.000Z",
  "updated": "2001-08-01T07:21:31.000Z",
  "title": "Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle",
  "authors": [
    "Mourad E. H. Ismail",
    "Nicholas S. Witte"
  ],
  "comment": "27 pages, Latex2e plus AMS packages Fix to Eqs. (2.72) and (2.74)",
  "journal": "J. Approx. Theory 110 (2001), 200-228",
  "categories": [
    "math.CA"
  ],
  "abstract": "We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-08-01T07:21:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "33C45"
    ],
    "keywords": [
      "unit circle",
      "polynomials orthogonal",
      "discriminants",
      "orthogonal polynomial coefficients",
      "general functional equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....12259I"
    }
  }
}