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

摘要

Let (p(n))(n) be either the q-Meixner or the q-Laguerre polynomials. We form a new sequence of polynomials (q(n))(n) by considering a linear combination of two consecutive p(n): q(n) = p(n) + beta(n)p(n-1), beta(n) is an element of R. Using the concept of D-operator, we generate sequences (beta(n))(n) for which the polynomials (q(n))(n) are orthogonal with respect to a measure and common eigenfunctions of a higher order q-difference operator. (C) 2014 Elsevier Inc. All rights reserved.