{
  "id": "1011.1669",
  "version": "v3",
  "published": "2010-11-07T18:33:17.000Z",
  "updated": "2011-11-20T05:55:49.000Z",
  "title": "A \"missing\" family of classical orthogonal polynomials",
  "authors": [
    "Luc Vinet",
    "Alexei Zhedanov"
  ],
  "comment": "20 pages",
  "journal": "J. Phys. A: Math. Theor. v.44 (2011), 085201",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study a family of \"classical\" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi polynomials in the limit $q=-1$. We also show that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for $q=-1$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-20T05:55:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "33C47",
      "42C05"
    ],
    "keywords": [
      "classical orthogonal polynomials",
      "eigenvalue problem",
      "askey-wilson algebra",
      "nontrivial realization",
      "jacobi polynomials"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/44/8/085201",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2011,
      "month": "Feb",
      "volume": 44,
      "number": 8,
      "pages": "085201"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JPhA...44h5201V"
    }
  }
}