Definition:Inverse Hyperbolic Cotangent/Complex/Definition 2

Definition
Let $S$ be the subset of the complex plane:
 * $S = \C \setminus \left\{{-1 + 0 i, 1 + 0 i}\right\}$

The inverse hyperbolic cotangent is a multifunction defined on $S$ as:


 * $\forall z \in S: \coth^{-1} \left({z}\right) := \left\{{\dfrac 1 2 \ln \left({\dfrac {z + 1} {z - 1} }\right) + k \pi i: k \in \Z}\right\}$

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

Also see

 * Equivalence of Definitions of Complex Inverse Hyperbolic Cotangent


 * Definition:Inverse Cotangent/Complex/Definition 2