Definition:Inverse Hyperbolic Cosecant/Complex/Definition 2

Definition
The inverse hyperbolic cosecant is a multifunction defined as:


 * $\forall z \in \C: \operatorname{csch}^{-1} \left({z}\right) = \ln \left({\dfrac 1 z + \sqrt{\dfrac 1 {z^2} + 1} }\right)$

where $\ln$ denotes the complex natural logarithm considered as a multifunction.

Also see

 * Equivalence of Definitions of Inverse Hyperbolic Cosecant


 * Definition:Inverse Hyperbolic Sine
 * Definition:Inverse Hyperbolic Cosine
 * Definition:Inverse Hyperbolic Tangent
 * Definition:Inverse Hyperbolic Cotangent
 * Definition:Inverse Hyperbolic Secant