On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials

Abstract

The dual discrete q-ultraspherical polynomials D(s) n (μ(x; s)|q) correspond to indeterminate moment problem and, therefore, have one-parameter family of extremal orthogonality relations. It is shown that special cases of dual discrete q-ultraspherical polynomials D(s) n (μ(x; s)|q), when s = q−1 and s = q, are directly connected with q−1-Hermite polynomials. These connections are given in an explicit form. Using these relations, all extremal orthogonality relations for these special cases of polynomials D(s) n (μ(x; s)|q) are found.