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