New Proofs of the Basel Problem using Stochastic Processes

Abstract

The number $\frac{{\pi }^2}{6}$ is involved in the variance of several distributions in statistics. At the same time it holds ${\sum }_{k=1}^{\infty }{k}^{-2}=\frac{{\pi }^2}{6}$, which solves the famous Basel problem. We first provide a historical perspective on the Basel problem, and second show how to generate further proofs building on stochastic processes.