q-SOBOLEV ORTHOGONALITY OF THE q-LAGUERRE POLYNOMIALS {L_n^(-N)(·q)}_n=0^∞FOR POSITIVE INTEGERS N

Abstract

Abstract. The family of q-Laguerre polynomials {L (α) n (·; q)} ∞ n=0 is usually defined for 0 < q < 1 and α > −1. We extend this family to a new one in which arbitrary complex values of the parameter α are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter α is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials {L, for positive integers N , become orthogonal.