Evaluations for zeta(2),zeta(4),...,zeta(2k)based on the WZ method

TL;DR

This paper introduces a new evaluation method for specific zeta function values at even integers using the WZ theory, providing explicit formulas and a recurrence relation.

Contribution

It presents a novel approach based on WZ theory to evaluate zeta(2k) and derive a recurrence formula, advancing computational techniques for these constants.

Findings

New explicit evaluations for zeta(2) and zeta(4) using WZ theory

A recurrence formula for zeta(2k) derived from the framework

Enhanced understanding of zeta function values at even integers

Abstract

Based on the framework of the WZ theory, a new evaluation for $\varsigma (2) = \frac{\pi ^2}{6}$ and $\varsigma (4) = \frac{\pi ^4}{90}$ was given respectively, finally, a new recurrence formula for $\varsigma (2k)$ was given.