Е. К. Склянин "New linearization formula for q-ultraspherical polynomials"

Mathematical and Theoretical Physics, dedicated to Ludwig Faddeev
28-31 мая 2024 года
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.