Definition:Gaussian Integral/One Variable

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


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


 * $\phi_1\left({x}\right) = \displaystyle \int_{\to -\infty}^x \frac 1 {\sqrt{2\pi}} \exp \left({-\frac 1 2t^2 }\right) \, \mathrm dt$

where $\exp$ is the real exponential function.