Explicit matrix inverses for lower triangular matrices with entries involving continuous qq-ultraspherical polynomials

For a one-parameter family of lower triangular matrices with entries involving continuous qq-ultraspherical polynomials we give an explicit lower triangular inverse matrix, with entries involving again continuous qq-ultraspherical functions. The matrices are qq-analogues of results given by Cagliero and Koornwinder recently. The proofs are not qq-analogues of the Cagliero–Koornwinder case, but are of a different nature involving qq-Racah polynomials. Some applications of these new formulas are given. Also the limit β→0β→0 is studied and gives rise to continuous qq-Hermite polynomials for 01q>1.