Bourlet's Theorem for the product of differential operators, an application of the operator method and a proof for $\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$, that Euler missed, derived from difference equations

Abstract

We give another proof for \[ \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6} \] that basically follows from the theory of difference equations.