Definition:Inverse Hyperbolic Cotangent/Complex/Principal Branch

Definition
The principal branch of the complex inverse hyperbolic cotangent function is defined as:
 * $\forall z \in \C: \operatorname{Coth}^{-1} \left({z}\right) := \dfrac 1 2 \operatorname{Ln} \left({\dfrac {z + 1} {z - 1} }\right)$

where $\operatorname{Ln}$ denotes the principal branch of the complex natural logarithm.

Also see

 * Derivation of Hyperbolic Arccotangent from Inverse Hyperbolic Cotangent Multifunction