# Definition:Hyperbolic Cosine

## Definition

The hyperbolic cosine function is defined on the complex numbers as:

$\cosh: \C \to \C$:
$\forall z \in \C: \cosh z := \dfrac {e^z + e^{-z} } 2$

### Real Hyperbolic Cosine

On the real numbers it is defined similarly.

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

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

## Also see

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