Definition:Inverse Hyperbolic Cosecant/Complex/Principal Branch

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

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 Area Hyperbolic Cosecant from Inverse Hyperbolic Cosecant Multifunction


 * Definition:Complex Area Hyperbolic Sine
 * Definition:Complex Area Hyperbolic Cosine
 * Definition:Complex Area Hyperbolic Tangent
 * Definition:Complex Area Hyperbolic Cotangent
 * Definition:Complex Area Hyperbolic Secant