asin

Function: asin
Section: transcendental
C-Name: gasin
Prototype: Gp
Help: asin(x): arc sine of x.
Doc: principal branch of $\sin^{-1}(x) = -i \log(ix + \sqrt{1 - x^2})$.
 In particular, $\Re(\text{asin}(x))\in [-\pi/2,\pi/2]$ and if $x\in \R$ and
 $|x|>1$ then $\text{asin}(x)$ is complex. The branch cut is in two pieces:
 $]-\infty,-1]$, continuous with quadrant II, and $[1,+\infty[$ continuous
 with quadrant IV. The function satisfies $i \text{asin}(x) =
 \text{asinh}(ix)$.