A counterexample to a conjecture of M. Ismail

2022/06/16 by Castillo, K., Mbouna, D.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.08375

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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