{
  "id": "math/0603408",
  "version": "v1",
  "published": "2006-03-16T20:26:41.000Z",
  "updated": "2006-03-16T20:26:41.000Z",
  "title": "On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials",
  "authors": [
    "Valentyna A. Groza",
    "Ivan I. Kachuryk"
  ],
  "comment": "Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/",
  "journal": "SIGMA 2 (2006), 034, 8 pages",
  "doi": "10.3842/SIGMA.2006.034",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The dual discrete $q$-ultraspherical polynomials $D_n^{(s)}(\\mu (x;s)|q)$ correspond to indeterminate moment problem and, therefore, have one-parameter family of extremal orthogonality relations. It is shown that special cases of dual discrete $q$-ultraspherical polynomials $D_n^{(s)}(\\mu (x;s)|q)$, when $s=q^{-1}$ and $s=q$, are directly connected with $q^{-1}$-Hermite polynomials. These connections are given in an explicit form. Using these relations, all extremal orthogonality relations for these special cases of polynomials $D_n^{(s)}(\\mu (x;s)|q)$ are found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-16T20:26:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dual discrete q-ultraspherical polynomials",
      "extremal orthogonality relations",
      "special cases",
      "indeterminate moment problem",
      "hermite polynomials"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2006,
      "month": "Mar",
      "volume": 2,
      "pages": "034"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006SIGMA...2..034G"
    }
  }
}