Apostol-Euler polynomials arising from umbral calculus

TL;DR

This paper uses umbral calculus to derive explicit formulas expressing various well-known polynomials as linear combinations of Apostol-Euler polynomials, highlighting their interconnectedness.

Contribution

It introduces a method to represent classical polynomials in terms of Apostol-Euler polynomials using umbral calculus techniques.

Findings

Explicit formulas for classical polynomials as linear combinations of Apostol-Euler polynomials.

Demonstrates the applicability of umbral calculus in polynomial transformations.

Provides a unified framework for polynomial representations.

Abstract

In this paper, by using the orthogonality type as defined in the umbral calculus, we derive explicit formula for several well known polynomials as a linear combination of the Apostol-Euler polynomials.