A Substitution to Bernoulli Numbers in easier computation of (\zeta(2k))

TL;DR

This paper introduces a recursive formula that simplifies and accelerates the computation of the Riemann zeta function at even integers, eliminating the need for Bernoulli numbers.

Contribution

It presents a novel recursive method for calculating (2k) that is more efficient than traditional Bernoulli number-based formulas.

Findings

Reduces computational complexity for large (2k) values.

Eliminates dependence on Bernoulli numbers in zeta function evaluation.

Provides a recursive approach that improves calculation speed.

Abstract

An alternative formula is presented for the evaluation of the zeta function values $\zeta(2k)$ without the need for Bernoulli numbers. Our formula is recursive, and improves the efficiency with which we can calculate large values of the zeta function.