Euler Numbers and polynomials associated with zeta functions

TL;DR

This paper explores identities linking Euler numbers with zeta functions and provides new values of Euler zeta function at positive even integers, enhancing understanding of their mathematical relationships.

Contribution

It introduces novel identities between Euler numbers and zeta functions and computes new values of Euler zeta function at positive even integers.

Findings

New identities between Euler numbers and zeta functions

Explicit values of Euler zeta function at positive even integers

Enhanced understanding of Euler numbers in relation to zeta functions

Abstract

In this paper we give some interesting identities between Euler numbers and zeta functions. Finally we will give the new values of Euler zeta function at positive even integers.