In this paper, we compute explicitly the reproducing kernel of the space of homogeneous polynomials of degree and Dunkl polyharmonic of degree , i.e. , , where is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.
The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials...