Hahn's Problem with Respect to Some Perturbations of the Raising Operator X−C

Abstract

In this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator X−c, where c is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the q-Hermite (resp. Charlier) polynomial is the only Hα,q-classical (resp. Sλ-classical) orthogonal polynomial, where Hα,q:=X+αHq and Sλ:=(X+1)−λτ−1.