  The purpose of this paper is to find the characterization of the Sheffer
polynomial sets satisfying the d-orthogonality conditions. The generating
function form of these polynomial sets is given in Theorem 2.2. As applications
of the Theorem 2.2, we revisit the d-orthogonal polynomial sets exist in the
literature and discover new d-orthogonal polynomial sets. Moreover, we obtain
the d-dimensional functional vector ensuring the d-orthogonality of these new
polynomial sets.
