Definition:Gaussian Integral/One Variable

Definition
The Gaussian Integral (of one variable) is the following improper integral, considered as a real function:


 * $\phi_1: \R \to \R$:


 * $\map {\phi_1} x = \displaystyle \int_{\mathop \to -\infty}^x \frac 1 {\sqrt {2 \pi} } \map \exp {-\frac {t^2} 2 } \rd t$

where $\exp$ is the real exponential function.