Beta-integrals and finite orthogonal systems of Wilson polynomials

Details Beta-integrals and finite orthogonal systems of Wilson polynomials Beta-integrals and finite orthogonal systems of Wilson polynomials

2002-06-19

arxiv.org/abs/math/0206199v1

Mathematics

Classical Analysis and ODEs

18 pages

Scientific paper

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.

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