Definition:Inverse Secant/Complex/Arcsecant

Definition
The principal branch of the complex inverse secant function is defined as:
 * $\forall z \in \C_{\ne 0}: \arcsec \paren z := \dfrac 1 i \Ln \paren {\dfrac {1 + \sqrt {1 - z^2} } z}$

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 Complex Arcsecant from Inverse Secant Multifunction