Using DD-operators to construct orthogonal polynomials satisfying higher order q-difference equations

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