Using [formula omitted]-operators to construct orthogonal polynomials satisfying higher order q-difference equations

Abstract

Let (pn)n be either the q-Meixner or the q-Laguerre polynomials. We form a new sequence of polynomials (qn)n by considering a linear combination of two consecutive pn: qn=pn+βnpn−1, βn∈R. Using the concept of D-operator, we generate sequences (βn)n for which the polynomials (qn)n are orthogonal with respect to a measure and common eigenfunctions of a higher order q-difference operator.