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865:{\displaystyle \int _{\mathbb {R} ^{D}}\rho _{\mu ,\Sigma }(x)\cdot \rho _{\mathbf {0} ,\Gamma }(x)\,dx={\frac {\exp \left(-{\frac {1}{2}}(\mu ^{T}\Sigma ^{-1}(\Sigma ^{-1}+\Gamma ^{-1})^{-1}\Gamma ^{-1}\mu )\right)}{\sqrt {(2\pi )^{D}|\Sigma ||\Gamma ||\Sigma ^{-1}+\Gamma ^{-1}|}}}}
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It is not commonly called the normal function but the normal distribution. The function is the
Gaussian function. The current name would also be confusing to people new to integrals, they might think normal functions means the standard functions.
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455:{\displaystyle \rho _{\mu ,\Sigma }(x):={\frac {1}{\sqrt {|2\pi \Sigma |}}}e^{-{\frac {1}{2}}(x-\mu )^{T}\Sigma ^{-1}(x-\mu )}}
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Knowledge. If you would like to participate, please visit the project page, where you can join
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In fact better how about 'List of integrals of
Gaussian functions'.
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Maybe it is worth to add some formulas for multivariate
Gaussians?
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