Category:Gaussian Integral

This category contains results about Gaussian Integral.
Definitions specific to this category can be found in Definitions/Gaussian Integral.

Gaussian Integral of Two Variables

The Gaussian Integral (of two variables) is the following definite integral, considered as a real-valued function:

$\phi_2: \set {\tuple {a, b} \in \R^2: a \le b} \to \R$:

$\map {\phi_2} {a, b} = \ds \int_a^b \frac 1 {\sqrt {2 \pi} } \map \exp {-\frac {t^2} 2} \rd t$

where $\exp$ is the real exponential function.

Gaussian Integral of 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.