### Only for the elite of Mathematics

Inviato:

**23 giu 2017, 19:44**How do you prove this $\displaystyle z\cot \left(z\right)=1-2\sum _{k=1}^{\infty}\frac{z^2}{k^2\pi ^2-z^2}$ ?

i’ve seen this formula on a document about Bernoulli’s numbers and their relations with Riemann’s zeta function (http://www.luciocadeddu.com/tesi/Aru_magistrale.pdf corollario 2.5.2) but i really don’t understand why this is true…

i’ve seen this formula on a document about Bernoulli’s numbers and their relations with Riemann’s zeta function (http://www.luciocadeddu.com/tesi/Aru_magistrale.pdf corollario 2.5.2) but i really don’t understand why this is true…