Another proof of $\displaystyle\boldsymbol{\zeta(2)=\frac{\pi^2}{6}}$ using double integrals

TL;DR

This paper presents a novel proof of the Basel Problem's solution, demonstrating that al{zeta}(2) equals rac{76}{6} using a double integral approach.

Contribution

It introduces a new double integral method to prove the Basel Problem's famous result, offering an alternative to existing proofs.

Findings

Confirmed al{zeta}(2) = rac{76}{6} using double integrals

Provides a different perspective on the Basel Problem

Enhances understanding of integral techniques in number theory

Abstract

Using a double integral we give another solution to the Basel Problem