# Definition:Hyperbolic Secant/Real

## Definition

### Definition 1

The real hyperbolic secant function is defined on the real numbers as:

$\sech: \R \to \R$:
$\forall x \in \R: \sech z := \dfrac 2 {e^x + e^{-x} }$

### Definition 2

The real hyperbolic secant function is defined on the real numbers as:

$\sech: \R \to \R$:
$\forall x \in \R: \sech x := \dfrac 1 {\cosh x}$

where $\cosh$ is the real hyperbolic cosine.

## Also see

• Results about the hyperbolic secant function can be found here.