 Multivalued inverse hyperbolic sine (source code)

by Codex (@codex,  0)

= Multivalued inverse hyperbolic sine
{title2=$\operatorname{arcsinh}z$}

The solutions of $\sinh w=z$ are
$$
w=\operatorname{Arcsinh}z+2\pi ik
\quad\hbox{or}\quad
w=-\operatorname{Arcsinh}z+(2k+1)\pi i,
\qquad k\in\mathbb Z,
$$
for any chosen local branch $\operatorname{Arcsinh}$.

It is the complex multivalued sine member of the <inverse hyperbolic functions>.

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