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Sbornik: Mathematics, 2002, Volume 193, Issue 7, Pages 1071–1089
DOI: https://doi.org/10.1070/SM2002v193n07ABEH000670
(Mi sm670)
 

This article is cited in 16 scientific papers (total in 16 papers)

Beta-integrals and finite orthogonal systems of Wilson polynomials

Yu. A. Neretin

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
References:
Abstract: The integral
$$ \frac1{2\pi}\int_{-\infty}^\infty\biggl|\frac{\prod_{k=1}^3\Gamma(a_k+is)} {\Gamma(2is)\Gamma(b+is)}\biggr|^2\,ds =\frac{\Gamma(b-a_1-a_2-a_3)\prod_{1\leqslant k<l\leqslant 3}\Gamma(a_k+a_l)} {\prod_{k=1}^3\Gamma(b-a_k)} $$
is calculated and the system of orthogonal polynomials with weight equal to the corresponding integrand is constructed. This weight decreases polynomially, therefore only finitely many of its moments converge. As a result the system of orthogonal polynomials is finite.
Systems of orthogonal polynomials related to ${}_5H_5$-Dougall's formula and the Askey integral is also constructed. All the three systems consist of Wilson polynomials outside the domain of positiveness of the usual weight.
Received: 20.11.2001
Bibliographic databases:
UDC: 517.444+517.588+517.587
MSC: 33D45, 33D60, 33D05
Language: English
Original paper language: Russian
Citation: Yu. A. Neretin, “Beta-integrals and finite orthogonal systems of Wilson polynomials”, Sb. Math., 193:7 (2002), 1071–1089
Citation in format AMSBIB
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\by Yu.~A.~Neretin
\paper Beta-integrals and finite orthogonal systems of Wilson polynomials
\jour Sb. Math.
\yr 2002
\vol 193
\issue 7
\pages 1071--1089
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Linking options:
  • https://www.mathnet.ru/eng/sm670
  • https://doi.org/10.1070/SM2002v193n07ABEH000670
  • https://www.mathnet.ru/eng/sm/v193/i7/p131
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:651
    Russian version PDF:263
    English version PDF:20
    References:129
    First page:3
     
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