A counterexample to a conjecture of M. Ismail-Reference-Cited by-同舟云学术

A counterexample to a conjecture of M. Ismail

Published:2024-03-01 Issue:3 Volume:65 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Castillo K.¹^ORCID,Mbouna D.²^ORCID

Affiliation:

1. CMUC, Department of Mathematics, University of Coimbra 1 , 3000-143 Coimbra, Portugal

2. Institute of Mathematics of the University of Seville (IMUS) 2 , Edificio Celestino Mutis-CITUS II, Av. de la Reina Mercedes, s/n, 41012 Seville, Spain

Abstract

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.

Funder

Centro de Matemática, Universidade de Coimbra

ERDF and Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía

Campus of International Excellence CEIMAR

Publisher

AIP Publishing

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0174053/19844960/033507_1_5.0174053.pdf

Reference3 articles.

1. A characterization of continuous q-Jacobi, Chebyshev of the first kind and Al-Salam Chihara polynomials;J. Math. Anal. Appl.,2022

2. On the functional equation for classical orthogonal polynomials on lattices;J. Math. Anal. Appl.,2022

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