Definition:Inverse Hyperbolic Sine/Complex/Principal Branch

Definition
The principal branch of the complex inverse hyperbolic sine function is defined as:
 * $\forall z \in \C: \operatorname{Sinh}^{-1} \left({z}\right) := \operatorname{Ln} \left({z + \sqrt{z^2 + 1} }\right)$

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 Arcsine from Inverse Hyperbolic Sine Multifunction