On d-symmetric classical d-orthogonal polynomials

摘要

The d-symmetric classical d-orthogonal polynomials are an extension of the standard symmetric classical polynomials according to the Hahn property. In this work, we give some characteristic properties for these polynomials related to generating functions and recurrence-differential equations. As applications, we characterize the d-symmetric classical d-orthogonal polynomials of Boas-Buck type, we construct a (d+1)-order linear differential equation with polynomial coefficients satisfied by each polynomial of a d-symmetric classical d-orthogonal set and we show that the d-symmetric classical d-orthogonal property is preserved by the derivative operator. Some of the obtained properties appear to be new, even for the case d=1.