d-orthogonality of Little q-Laguerre type polynomials

In this paper, we solve a characterization problem in the context of the d-orthogonality. That allows us, on one hand, to provide a q-analog for the d-orthogonal polynomials of Laguerre type introduced by the first author and Douak, and on the other hand, to derive new L-q-classical d-orthogonal polynomials generalizing the Little q-Laguerre polynomials. Various properties of the resulting basic hypergeometric polynomials are singled out. For d = 1, we obtain a characterization theorem involving, as far as we know, new L-q-classical orthogonal polynomials, for which we give the recurrence relation and the difference equation. (C) 2011 Elsevier B.V. All rights reserved.