\begin{definition}[Definition:Error Function]
The '''error function''' is the following improper integral, considered as a real function $\erf : \R \to \R$:
:$\map {\erf} x = \ds \dfrac 2 {\sqrt \pi} \int_0^x \map \exp {-t^2} \rd t$
where $\exp$ is the real exponential function.
\end{definition}