{
  "id": "1309.7569",
  "version": "v1",
  "published": "2013-09-29T10:26:59.000Z",
  "updated": "2013-09-29T10:26:59.000Z",
  "title": "Orthogonality relations for Al-Salam--Carlitz polynomials of type II",
  "authors": [
    "Wolter Groenevelt"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Using a special case of Askey's $q$-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam--Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of $\\mathbb R$. From spectral analysis of the corresponding second-order $q$-difference operator we obtain an infinite set of functions that complement the Al-Salam--Carlitz II polynomials to an orthogonal basis of the associated $L^2$-space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-29T10:26:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "al-salam-carlitz polynomials",
      "beta integral evaluation formula",
      "determine orthogonality relations",
      "discrete subset",
      "orthogonal basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7569G"
    }
  }
}