Formula omitted]-orthogonality of discrete [formula omitted]-Hermite type polynomials

Abstract

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 Lq-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.