# lmvgamma: Multivariate Gamma Function In CholWishart: Cholesky Decomposition of the Wishart Distribution

## Description

A special mathematical function related to the gamma function, generalized for multivariate gammas. `lmvgamma` is the log of the multivariate gamma, `mvgamma`.

The multivariate gamma function for a dimension p is defined as:

Gamma_p(a)=π^{p(p-1)/4}* Prod_{j=1}^{p} Γ[a+(1-j)/2]

For p = 1, this is the same as the usual gamma function.

## Usage

 ```1 2 3``` ```lmvgamma(x, p) mvgamma(x, p) ```

## Arguments

 `x` non-negative numeric vector, matrix, or array `p` positive integer, dimension of a square matrix

## Value

For `lmvgamma` log of multivariate gamma of dimension `p` for each entry of `x`. For non-log variant, use `mvgamma`.

## Functions

• `mvgamma`: Multivariate gamma function.

## References

A. K. Gupta and D. K. Nagar 1999. Matrix variate distributions. Chapman and Hall.

Multivariate gamma function. In Wikipedia, The Free Encyclopedia,from https://en.wikipedia.org/w/index.php?title=Multivariate_gamma_function

`gamma` and `lgamma`
 ```1 2 3 4``` ```lgamma(1:12) lmvgamma(1:12, 1L) mvgamma(1:12, 1L) gamma(1:12) ```