In mathematics, the multivariate gamma function, Γp(·), is a generalization of the gamma function. It is useful in multivariate statistics, appearing in the probability density function of the Wishart and inverse Wishart distributions.
Contents
It has two equivalent definitions. One is given as the following integral over the
The other one, more useful to obtain a numerical result is:
From this, we have the recursive relationships:
Thus
and so on.
Derivatives
We may define the multivariate digamma function as
and the general polygamma function as
Calculation steps
References
Multivariate gamma function Wikipedia(Text) CC BY-SA