Solution of the Basel problem in the framework of distribution theory

TL;DR

This paper presents a straightforward proof of Euler's Basel problem formula using distribution theory, offering new identities as byproducts, thus bridging classical analysis with distribution theory.

Contribution

It introduces a novel proof of Euler's formula for the Basel problem within the framework of distribution theory, expanding the theoretical tools available.

Findings

Proof of Euler's formula using distribution theory

Derivation of additional mathematical identities

Bridging classical analysis with distribution theory

Abstract

A simple proof of Euler's formula which states that the sum of the reciprocals of all natural numbers squared equals $\pi^2/6$ is presented based on the distribution theory introduced by Laurent Schwartz. Additional identities are obtained as a byproduct of the derivation.