L-classical d-orthogonal polynomial sets of Sheffer type.

Abstract

In this paper, we characterize L-classical d-orthogonal polynomial sets of Sheffer type where L being a lowering operator commutating with the derivative operator D and belonging to {D, e^D −1, sin(D)}. For the first case we state a (d + 1)-order differential equation satisfied by the corresponding polynomials. We, also, show that, with these three lowering operators, all the orthogonal polynomial sets are classified as L-classical orthogonal polynomial sets.