= Radial moments of an isotropic Gaussian vector
{title2=$\mathbb E|\mathbf X|^{2n}=2^n\Gamma(n+d/2)v^n/\Gamma(d/2)$}
For $d$ independent centered <normal random variables> of common <variance> $v$, $|\mathbf X|^2/v$ has a <chi-squared distribution> with $d$ degrees of freedom. Its density gives the displayed moments by a <Gamma integral>. In three dimensions, $\mathbb E|\mathbf X|^{2n}=(2n+1)!!v^n$. Radial odd moments need not vanish, although any odd Cartesian product does.
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