Definition:Inverse Hyperbolic Sine/Complex/Principal Branch

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

where:
 * $\Ln$ 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