Category:Gaussian Integral

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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:

$\phi_2: \left\{{\left({a, b}\right) \in \R^2: a \le b}\right\} \to \R$:
$\phi_2 \left({a, b}\right) = \displaystyle \int_a^b \frac 1 {\sqrt{2 \pi}} \exp \left({- \frac {t^2} 2}\right) \ \mathrm d t$

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:

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

where $\exp$ is the real exponential function.

Pages in category "Gaussian Integral"

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