Partial Fractions Expansion of Cotangent

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

Then:


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