A unified matrix approach to the representation of Appell polynomials

Abstract

In this paper we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix - a special matrix which has only the natural numbers as entries and is closely related to the well known Pascal matrix. By this means we stress the arithmetical origins of Appell polynomials. The approach also allows to derive, in a simplified way, the properties of Appell polynomials by using only matrix operations.