Partial Fractions Expansion of Cotangent

Theorem
Let $x \in \R - \Z$, that is such that $x$ is a real number that is not an integer.

Then:


 * $\pi \cot \pi x = \dfrac 1 2 + 2 x \displaystyle \sum_{n \mathop = 1}^\infty \frac 1 {x^2 - n^2}$