Definition:Inverse Hyperbolic Cosecant/Complex/Definition 1

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The inverse hyperbolic cosecant is a multifunction defined as:

$\forall z \in \C_{\ne 0}: \map {\csch^{-1} } z := \set {w \in \C: z = \map \csch w}$

where $\map \csch w$ is the hyperbolic cosecant function.

Also known as

The principal branch of the inverse hyperbolic cosecant is also known as the area hyperbolic cosecant, as it can be used, among other things, for evaluating areas of regions bounded by hyperbolas.

Some sources refer to it as hyperbolic arccosecant, but this is strictly a misnomer, as there is nothing arc related about an inverse hyperbolic cosecant.

Also see