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Multivariate Gamma FunctionIn mathematics, the multivariate Gamma distribution, , is a generalization of the Gamma function. It is useful in multivariate statistics. It has two equivalent definitions: -
\Gamma_p(a)= \int_{S\in {\mathbf S}} \exp\left( -{\rm trace}(S)\right) \left|S\right|^{a-(p+1)/2} dS where is the set of all positive-definite matrices. The other is more useful in practice: -
\Gamma_p(a)= \pi^{p(p-1)/4}\Pi_{j=1}^p \Gamma\lefta+(1-j)/2\right. Thus -
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and so on.
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