Dual forms of the orthogonality relations of some classical q-orthogonal polynomials

2022/07/27 by Chen, Qi, Ma, Xinrong, Wang, Jin
#05A30 #33D15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.13563

Abstract

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 ₈ϕ₇ series is just a dual form of the orthogonality relation of the Askey-Wilson polynomials.

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