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In an earlier work K. Castillo et al., J. Math. Anal. Appl. 514, 126358 (2022), 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.
Castillo et al. (Fri,) studied this question.
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