Arcus Tangens

definiendum	$\arctan: \{z\in\mathbb C\mid \|z\|\le 1, z\neq \pm i\}\to\mathbb C$
definiendum	$\arctan(z):=\sum_{n=0}^\infty (-1)^n\frac{1}{2n+1} z^{2n+1}$

$\frac{{\mathrm d}}{{\mathrm d}z}\arctan(z)=\frac{1}{1+z^2}$