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 $\sum\nolimits_{k=1}^{\infty }k^{-2}= \frac{\pi ^{2}}{6}$, 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.