Beta-integrals and finite orthogonal systems of Wilson polynomials

The integral 1/2pi integral(-infinity)(infinity)\Pi(k = 1)(3) Gamma(a(k) + is)/Gamma(2is)Gamma(b + is)\(2) ds = Gamma(b = a(1) - a(2) - a(3))Pi(1 less than or equal to k < l less than or equal to 3)Gamma(a(k) + a(l))/Pi(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 H-5(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.