Beta-integrals and finite orthogonal systems of Wilson polynomials

©, 2002 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd
, , Citation Yu A Neretin 2002 Sb. Math. 193 1071 DOI 10.1070/SM2002v193n07ABEH000670

1064-5616/193/7/1071

Abstract

The integral

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 -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.

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10.1070/SM2002v193n07ABEH000670