Beta-integrals and finite orthogonal systems of Wilson polynomials

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 $w(s)=\mathrm{\mid }p(s)\mathrm{/}q(s){\mathrm{\mid }}^2$, where $p(s)=\mathrm{\Gamma }(a+is)\mathrm{\Gamma }(b+is)\mathrm{\Gamma }(c+is)$ and $q(s)=\mathrm{\Gamma }(d+is)\mathrm{\Gamma }(2is)$. 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.