Find the Taylor series of $\tanh(z)$ around $z_0=0$.
$z$ is a complex variable.
I can use all the basic series as facts like the $\cosh$ and $\sinh$ series. I know how to calculate the series with the derivatives but I want a closed form like the others have. Wikipedia says something about Bernoulli numbers; I don't know a thing about that and there was no mention of those numbers. So I kinda need to find a formula using only the series of the other basic functions. I am not good using properties of series so don't make big steps as to what you might think it is trivial.