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