International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 641-647

A characterization of the Rogers q-hermite polynomials

Waleed A. Al-Salam

Department of Mathematics, University of Alberta, Edmonton T6G 2G1, Canada

Received 14 October 1993; Revised 18 February 1994

Copyright © 1995 Waleed A. Al-Salam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q-Appell where 𝒟q is the Askey-Wilson finite difference operator.