{
  "id": "math/0206199",
  "version": "v1",
  "published": "2002-06-19T16:18:59.000Z",
  "updated": "2002-06-19T16:18:59.000Z",
  "title": "Beta-integrals and finite orthogonal systems of Wilson polynomials",
  "authors": [
    "Neretin Yurii"
  ],
  "comment": "18 pages",
  "journal": "Sbornik: Mathematics, 2002, 193:7, 1071-1089",
  "doi": "10.4213/sm670 10.1070/SM2002v193n07ABEH000670",
  "categories": [
    "math.CA"
  ],
  "abstract": "We construct 3 finite systems of $4-F-3$ hypergeometric orthogonal polynomials. The weights are 1) the weight defined by the $5-H-5$ Dougall summation formula; 2) the integrand in the Askey beta-integral; 3) the weight $w(s)=|p(s)/q(s)|^2$, where $p(s)=\\Gamma(a+is)\\Gamma(b+is)\\Gamma(c+is)$ and $q(s)=\\Gamma(d+is)\\Gamma(2is)$. We also evaluate the integral of the function $w(s)$ using the Jacobi transform (the Olevsky transform); this integral also can be reduced to the Nassrallah--Rahman integral.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-06-19T16:18:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C05",
      "33C20",
      "33C45",
      "44A15"
    ],
    "keywords": [
      "finite orthogonal systems",
      "wilson polynomials",
      "dougall summation formula",
      "hypergeometric orthogonal polynomials",
      "finite systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Sbornik: Mathematics",
      "year": 2002,
      "month": "Aug",
      "volume": 193,
      "number": 7,
      "pages": 1071
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002SbMat.193.1071N"
    }
  }
}