Definition:Inverse Hyperbolic Secant/Complex/Principal Branch

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

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

Also see

 * Derivation of Hyperbolic Arcsecant from Inverse Hyperbolic Secant Multifunction