A unified matrix approach to the representation of Appell polynomials

TL;DR

This paper introduces a unified matrix framework for representing Appell polynomials, leveraging the creation matrix related to Pascal matrices to simplify derivations of their properties.

Contribution

It presents a novel matrix-based approach that unifies various types of Appell polynomials and highlights their arithmetic foundations.

Findings

Matrix representation simplifies derivation of polynomial properties

Creation matrix closely related to Pascal matrix

Unified approach applies to different Appell polynomial types

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.