d-Orthogonality of Hermite type polynomials

In this paper, we state a characterization theorem for d-orthogonal polynomials of Hermite type. As application, we solve two characterization problems related to Gould-Hopper polynomials and Charlier type polynomials. Various properties of the resulting generalized hypergeometric polynomials are singled out. In particularly, we derive the d-dimensional functional vectors ensuring the d-orthogonality of these polynomials. The obtained weight functions are reduced to the well-known weight functions of Charlier and Hermite polynomials for d=1. We also explicitly express the d-dimensional functional vector associated with polynomials of Laguerre type, which are related to the obtained Hermite type polynomials.