atan

Function: atan
Section: transcendental
C-Name: gatan
Prototype: Gp
Help: atan(x): arc tangent of x.
Doc: principal branch of $\text{tan}^{-1}(x) = \log ((1+ix)/(1-ix)) /
 2i$. In particular the real part of $\text{atan}(x)$ belongs to
 $]-\pi/2,\pi/2[$.
 The branch cut is in two pieces:
 $]-i\infty,-i[$, continuous with quadrant IV, and $]i,+i \infty[$ continuous
 with quadrant II. The function satisfies $\text{atan}(x) =
 -i\text{atanh}(ix)$ for all $x\neq \pm i$.