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arXiv · 2206.08375

A counterexample to a conjecture of M. Ismail

K. Castillo·D. Mbouna
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Abstract

In an earlier work [K. Castillo et al., J. Math. Anal. Appl., 514 (2022) 126358], we give positive answer to the first, and apparently more easy, part of a conjecture of M. Ismail concerning the characterization of the continuous $q$-Jacobi polynomials, Al-Salam-Chihara polynomials or special or limiting cases of them. In this note we present an example that disproves the second part of such a conjecture, and so this issue is definitively closed.

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K. Castillo, D. Mbouna. 2022-06-16. A counterexample to a conjecture of M. Ismail. https://arxiv.org/abs/2206.08375

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