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