On d-orthogonal polynomials with Brenke type generating functions

Abstract

The polynomial sequences of Brenke type {Pn}n≥0 are defined by the following generating function:∑n=0∞Pn(x)n!tn=A(t)B(xt), where A and B are two formal power series subject to the conditions A(0)B(k)(0)≠0,k=0,1,2….In this work, we characterize all d-orthogonal polynomial sets of Brenke type. That allows us to obtain several new and known results. We give some examples as illustration.