dd-orthogonality of discrete qq-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 LqLq-classical dd-orthogonal polynomials, generalizing the discrete qq-Hermite polynomials in the context of dd-orthogonality, and a qq-analogous for the dd-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)(d+1), difference formulas, generating functions, inversion formulas, and dd-dimensional functional vectors.