Definition:Inverse Hyperbolic Cosecant/Complex/Principal Branch

Definition
The principal branch of the complex inverse hyperbolic cosecant function is defined as:
 * $\forall z \in \C_{\ne 0}: \operatorname{Csch}^{-1} \left({z}\right) := \operatorname{Ln} \left({\dfrac {1 + \sqrt{z^2 + 1} } z}\right)$

where:
 * $\operatorname{Ln}$ denotes the principal branch of the complex natural logarithm
 * $\sqrt{z^2 + 1}$ denotes the principal square root of $z^2 + 1$.

Also see

 * Derivation of Hyperbolic Arccosecant from Inverse Hyperbolic Cosecant Multifunction