Arcsinh
From specialfunctionswiki
The inverse hyperbolic sine function $\mathrm{arcsinh}$ is function is the inverse function of the hyperbolic sine function. It may be defined by $$\mathrm{arcsinh}(z)=\log \left(z + \sqrt{1+z^2} \right).$$
Plot of $\mathrm{arcsinh}$ on $[-10,10]$.
Domain coloring of analytic continuation of $\mathrm{arcsinh}$.
