On m-symmetric d-orthogonal polynomials

In this paper, we give two characterizations of m-symmetric d-orthogonal polynomial sequences in terms of their dual sequences and a specific lacunary (d + 1)-order recurrence relation when d + 1 is a multiple of m + 1. Then we derive some properties of the components extending for this purpose some results already obtained by Douak and Maroni for the case m = d. That concerns the d-orthogonality, the ”classical” property and the dual sequence. As illustration, we discuss a new symmetric classical 3-orthogonal polynomial set.