q-Coherent pairs and q-orthogonal polynomials

Abstract

In this paper we introduce the concept of q-coherent pair of linear functionals. We prove that if (u0,u1) is a q-coherent pair of linear functionals, then at least one of them has to be a q-classical linear functional. Moreover, we present the classification of all q-coherent pairs of positive-definite linear functionals when u0 or u1 is either the little q-Jacobi linear functional or the little q-Laguerre/Wall linear functional. Finally, by using limit processes, we recover the classification of coherent pairs of linear functionals stated by Meijer.