New Characterization of Appell polynomials

TL;DR

This paper characterizes Appell polynomials using symmetry, relates them to Bernoulli and Euler polynomials, and derives their Fourier expansions, extending known results to higher-order cases.

Contribution

It provides a new symmetric characterization of Appell polynomials and derives their Fourier expansions, including for higher-order Bernoulli-Euler polynomials.

Findings

Symmetric property characterizes Appell polynomials.

Linear relations with Bernoulli and Euler polynomials established.

Fourier expansions for higher-order Bernoulli-Euler polynomials obtained.

Abstract

We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials. As applications, we give interesting examples. In addition, from our study, we obtain Fourier expansions of Appell polynomials. This result recovers Fourier expansions known for Bernoulli and Euler polynomials and obtains the Fourier expansions for higher order Bernoulli-Euler's one.