D-Orthogonality of Hermite type polynomials

Abstract

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.