Integral and discrete representations of certain Brenke type orthogonal q-polynomials

Abstract

We investigate the Hq-semiclassical character, duality, and the standard perturbation to characterize a well known non-symmetric MOPS {Zn(⋅;b,q)}n≥0 of Brenke type related to the Wall’s one. We prove that its corresponding regular linear form \(\mathcal{Z}(b,q)\) is a perturbation of a Brenke type symmetric regular linear form \(\mathcal{Y}(b,q)\), and so \(\mathcal{Z}(b,q)\) is \(H_{\sqrt{q}}\)-semiclassical of class two. Consequently, moments, integral, and discrete representations of \(\mathcal{Z}(b,q)\) are given.