Definition:Gaussian Integral
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Definition
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.
Also see
Source of Name
This entry was named for Carl Friedrich Gauss.