K. Castillo, D. Mbouna
Published 2022-06-16Version 1
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.
On a conjecture on sparse binomial-type polynomials by Brown, Dilcher and Manna
Probabilistic aspects of Al-Salam-Chihara polynomials
On a conjecture of Widom
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