English

A counterexample to a conjecture of M. Ismail

Classical Analysis and ODEs 2022-06-20 v1

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 qq-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.

Keywords

Cite

@article{arxiv.2206.08375,
  title  = {A counterexample to a conjecture of M. Ismail},
  author = {K. Castillo and D. Mbouna},
  journal= {arXiv preprint arXiv:2206.08375},
  year   = {2022}
}