Dual forms of the orthogonality relations of q-orthogonal polynomials

Xinrong Ma, Jin Wang

Published 2022-07-27Version 1

In this paper, by introducing new matrix operations and using a specific inverse relation, we establish the dual forms of the orthogonality relations for some well-known discrete and continuous q-orthogonal polynomials from the Askey-scheme such as the little and big q-Jacobi, q-Racah, (generalized) q-Laguerre, as well as the Askey-Wilson polynomials. As one of the most interesting results, we show that the Askey-Wilson q-beta integral represented in terms of the VWP-balanced 8{\phi}7 series is just a dual form of the orthogonality relation of the Askey-Wilson polynomials.