Аннотация:
For the product Cm(x;β|q)Cn(x;β′|q) of two continuous q-ultraspherical polynomials with different parameters β and β′, explicit formulae are presented for the coefficients of its expansion in the basis Ck(x;β|q) in the case β′=qβ−1. We also discuss a generalization to multivariate Jack and Macdonald polynomials and its relation to Pieri formulas and Q-operators.