Definition:Inverse Cosecant/Complex/Arccosecant

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

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 Complex Arccosecant from Inverse Cosecant Multifunction