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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)
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
Citation:
Yu. A. Neretin, “Beta-integrals and finite orthogonal systems of Wilson polynomials”, Sb. Math., 193:7 (2002), 1071–1089
Linking options:
https://www.mathnet.ru/eng/sm670https://doi.org/10.1070/SM2002v193n07ABEH000670 https://www.mathnet.ru/eng/sm/v193/i7/p131
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Abstract page: | 651 | Russian version PDF: | 263 | English version PDF: | 20 | References: | 129 | First page: | 3 |
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