\begin{definition}[Definition:Gaussian Integral/One Variable]
The '''Gaussian Integral''' (of one variable) is the following improper integral, considered as a real function:
:$\phi_1: \R \to \R$:
:$\map {\phi_1} x = \ds \int_{\mathop \to -\infty}^x \frac 1 {\sqrt {2 \pi} } \map \exp {-\frac {t^2} 2 } \rd t$
where $\exp$ is the real exponential function.
\end{definition}