{
  "id": "math/0307250",
  "version": "v3",
  "published": "2003-07-17T18:50:12.000Z",
  "updated": "2003-10-06T18:37:16.000Z",
  "title": "On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials",
  "authors": [
    "N. M. Atakishiyev",
    "A. U. Klimyk"
  ],
  "comment": "26 pages, LaTeX, the exposition is slightly improved and some additional references have been added",
  "categories": [
    "math.CA",
    "math.QA"
  ],
  "abstract": "This paper studies properties of q-Jacobi polynomials and their duals by means of operators of the discrete series representations for the quantum algebra U_q(su_{1,1}). Spectrum and eigenfunctions of these operators are found explicitly. These eigenfunctions, when normalized, form an orthogonal basis in the representation space. The initial U_q(su_{1,1})-basis and the bases of these eigenfunctions are interconnected by matrices, whose entries are expressed in terms of little and big q-Jacobi polynomials. The orthogonality by rows in these unitary connection matrices leads to the orthogonality relations for little and big q-Jacobi polynomials. The orthogonality by columns in the connection matrices leads to an explicit form of orthogonality relations on the countable set of points for {}_3\\phi_2 and {}_3\\phi_1 polynomials, which are dual to big and little q-Jacobi polynomials, respectively. The orthogonality measure for the dual little q-Jacobi polynomials proves to be extremal, whereas the measure for the dual big q-Jacobi polynomials is not extremal.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-10-06T18:37:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D80",
      "33D45",
      "17B37"
    ],
    "keywords": [
      "q-orthogonal polynomials",
      "orthogonality relations",
      "dual little q-jacobi polynomials",
      "dual big q-jacobi polynomials",
      "discrete series representations"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7250A"
    }
  }
}