The d-symmetric classical polynomials

An extension of symmetric classical orthogonal polynomials is d-symmetric classical d-orthogonal polynomials, d being a positive number. These polynomials and their derivatives satisfy particular (d+1)-order recurrence relations. Many works deals with these families. Our purpose is to derive some more results for this class of polynomials. In fact, in terms of hypergeometric functions, we express their generating functions, the explicit representation, and the corresponding component sets. Moreover, we state the inversion formula, which is used to obtain the moments of the corresponding d-dimensional vector of the linear functionals and the corresponding vectors of weights, providing of integral representations for these moments.