On a solution to the Basel problem based on the fundamental theorem of calculus

TL;DR

This paper presents a novel proof of the Basel problem's solution, demonstrating that the sum of the reciprocals of the squares equals pi squared over six, using fundamental calculus techniques.

Contribution

It introduces a new proof of the Basel problem leveraging the fundamental theorem of calculus and differentiation under the integral sign, differing from traditional methods.

Findings

Confirmed the value of ζ(2) as π^2/6

Provided a new proof technique for the Basel problem

Enhanced understanding of integral calculus applications

Abstract

We give a proof of the identity $\zeta(2)=\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}6$ using the fundamental theorem of calculus and differentiation under the integral sign.