\begin{definition}[Definition:Hyperbolic Secant/Definition 2]
The '''hyperbolic secant''' function is defined on the complex numbers as:
:$\sech: X \to \C$:
:$\forall z \in X: \sech z := \dfrac 1 {\cosh z}$
where:
:$\cosh$ is the hyperbolic cosine
:$X = \set {z: z \in \C, \ \cosh z \ne 0}$
\end{definition}