A counterexample to a conjecture of M. Ismail

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.