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

Qi Chen; Xinrong Ma; Jin Wang

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arXiv · 2207.13563

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

Qi Chen·Xinrong Ma·Jin Wang

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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 $\,_8\phi_7$ series is just a dual form of the orthogonality relation of the Askey-Wilson polynomials.

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Qi Chen, Xinrong Ma, Jin Wang. 2022-07-27. Dual forms of the orthogonality relations of some classical q-orthogonal polynomials. https://arxiv.org/abs/2207.13563

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