Some identities of higher-order Euler polynomials arising from Euler basis

TL;DR

This paper systematically studies higher-order Euler numbers and polynomials, deriving new identities using their basis properties, which enhances understanding of their algebraic structure and relationships.

Contribution

It introduces new identities for higher-order Euler polynomials based on their basis properties, expanding the theoretical framework of Euler polynomials.

Findings

Derived new identities for higher-order Euler polynomials.

Established basis properties of higher-order Euler polynomials.

Enhanced the algebraic understanding of Euler polynomial families.

Abstract

The purpose of this paper is to present a syatemic study of some familes of higher-order Euler numbers and polynomials. In particular, by using the basis property of higher-order Euler polynomials for the space of polynomials of degree less than and equal to n, we derive some interesting identities for the higher-order Euler polynomias.