Recurrence relation approach for expansion and connection coefficients in series of q-Laguerre polynomials

Abstract

In this manuscript, we expand some functions of a q-discrete variable as linear combination of the q-Laguerre polynomials. The recurrence relations satisfied by the expansion coefficients are derived and in many cases, explicit solutions of these recurrence relations are computed. We show how our results can be used to solve some q-difference equations and to illustrate this, we solve the connection problem between classical q-orthogonal polynomials and the q-Laguerre polynomials. Mathematics Subject Classification (2010). 33D45, 42C10, 65Q30.