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