\begin{definition}[Definition:Hyperbolic Cotangent/Definition 3]
The '''hyperbolic cotangent''' function is defined on the complex numbers as:
:$\coth: X \to \C$:
:$\forall z \in X: \coth z := \dfrac {e^{2 z} + 1} {e^{2 z} - 1}$
where:
:$X = \set {z : z \in \C, \ e^{2 z} - 1 \ne 0}$
\end{definition}