Dual forms of the orthogonality relations of some classical q-orthogonal polynomials
Combinatorics
2024-12-02 v2
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 -orthogonal polynomials from the Askey-scheme such as the little and big -Jacobi, -Racah, (generalized) -Laguerre, as well as the Askey-Wilson polynomials. As one of the most interesting results, we show that the Askey-Wilson -beta integral represented in terms of the VWP-balanced series is just a dual form of the orthogonality relation of the Askey-Wilson polynomials.
Keywords
Cite
@article{arxiv.2207.13563,
title = {Dual forms of the orthogonality relations of some classical q-orthogonal polynomials},
author = {Qi Chen and Xinrong Ma and Jin Wang},
journal= {arXiv preprint arXiv:2207.13563},
year = {2024}
}