Truncated Euler polynomials

TL;DR

This paper introduces truncated Euler polynomials as a new generalization of classical Euler polynomials, explores their properties, and investigates their relations with hypergeometric Bernoulli polynomials.

Contribution

It defines truncated Euler polynomials and studies their properties and connections with hypergeometric Bernoulli polynomials, expanding the understanding of polynomial generalizations.

Findings

Defined truncated Euler polynomials $E_{m,n}(x)$.

Established properties and relations with hypergeometric Bernoulli polynomials.

Enhanced the theoretical framework of polynomial generalizations.

Abstract

We define a truncated Euler polynomial $E_{m,n}(x)$ as a generalization of the classical Euler polynomial $E_n(x)$. In this paper we give its some properties and relations with the hypergeometric Bernoulli polynomial.