d-orthogonality of discrete q-Hermite type polynomials

In this paper, we solve a characterization problem involving a suitable basic-hypergeometric form of a polynomial set. That allows us to introduce new examples of L-q-classical d-orthogonal polynomials, generalizing the discrete q-Hermite polynomials in the context of d-orthogonality, and a q-analogous for the d-orthogonal polynomials of Gould-Hopper. For the resulting polynomials, we derive miscellaneous properties. Those turn out to be limit relations, recurrence relations of order (d + 1), difference formulas, generating functions, inversion formulas, and d-dimensional functional vectors. (C) 2012 Elsevier Inc. All rights reserved.