GammaMultiLog: Evaluates logarithm of the multivariate gamma function of...

In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

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).

See Also

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 June 3, 2024, 7:46 p.m.