Beta-integrals and finite orthogonal systems of Wilson polynomials

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.

18 pages

References in corpus (1)

• Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes

Cited by in corpus (1)

• Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems