# GammaMultiLog: Evaluates logarithm of the multivariate gamma function of... In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

 GammaMultiLog R Documentation

## Evaluates logarithm of the multivariate gamma function of order p

### Description

`GammaMultiLog(z, p, funmode)` evaluates logarithm of the multivariate gamma function of order `p`, the argument `z` may be complex and of any size.

Multivariate gamma function of order `p`, say `gamma_p(z)`, is defined as `gamma_p(z) = pi^(p*(p-1)/2) * prod_{j=1}^p gamma(z-(j-1)/2)`. Hence, the logarithm of multivariate gamma is given by `log(gamma_p(z))=(p*(p-1)/2)*log(pi) + sum_{j=1}^p log(gamma(z-(j-1)/2))`.

### Usage

``````GammaMultiLog(z, p, funmode)
``````

### Arguments

 `z` complex argument, of any size (vector, matrix). `p` order of the multivariate gamma, if empty, default value is `p = 1`. `funmode` function mode: If `funmode = 0` `f = log[gamma_p(z))`. If `funmode = 1` `f = gamma_p(z)`.

### Value

Function returns values of the logarithm of multivariate gamma function of order `p` evaluated in points `z`.

### Note

Ver.: 18-Sep-2019 17:14:16 (consistent with Matlab CharFunTool v1.3.0, 17-Aug-2018 19:45:37).

Other Utility Function: `ChebCoefficients()`, `ChebPoints()`, `ChebPolyValues()`, `ChebPoly()`, `ChebValues()`, `GammaLog()`, `GammaMulti()`, `GammaZX()`, `Hypergeom1F1MatApprox()`, `Hypergeom1F1Mat()`, `Hypergeom2F1Mat()`, `Hypergeom2F1()`, `HypergeompFqMat()`, `InterpChebValues()`, `hypergeom1F1()`, `interpBarycentric()`

### Examples

``````## EXAMPLE 1
t <- seq(-10, 10, length.out = 101)
z <- 1i * t
p <- 10
f <- GammaMultiLog(z, p)

## EXAMPLE 2
t <- seq(-10, 10, length.out = 101)
z <- 1i * t
p <- 10
funmode <- 1
f <- GammaMultiLog(z, p, funmode)
``````

gajdosandrej/CharFunToolR documentation built on Aug. 22, 2023, 9:58 a.m.