math.cern

Class GammaFun

java.lang.Object

math.cern.GammaFun

public final class GammaFun
extends Object

This is a utility class that provides computation methods related to the Γ (Gamma) family of functions.

Implementation:

Some code taken and adapted from the Java 2D Graph Package 2.4, which in turn is a port from the Cephes 2.2 Math Library (C). Most Cephes code (missing from the 2D Graph Package) directly ported.

Author:

wolfgang.hoschek@cern.ch

Method Summary

Modifier and Type	Method and Description
static double	digamma(double x) Returns the value of the logarithmic derivative of the Gamma function psi(x) = Gamma’(x) / Gamma(x).
static double	gamma(double x) Returns the Gamma function of the argument.
static double	incompleteGamma(double a, double x) Returns the Incomplete Gamma function.
static double	incompleteGammaComplement(double a, double x) Returns the Complemented Incomplete Gamma function.
static double	lnGamma(double x) Returns the natural logarithm of the gamma function.
static double	trigamma(double x) Returns the value of the trigamma function d(psi(x))/dx, the derivative of the digamma(double) function, evaluated at x.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

gamma

public static double gamma(double x)

Returns the Gamma function of the argument.

Parameters:

x - x value

Returns:

gamma(x)

lnGamma

public static double lnGamma(double x)

Returns the natural logarithm of the gamma function.

Parameters:

x - x value

Returns:

ln(gamma(x))

incompleteGamma

public static double incompleteGamma(double a,
                                     double x)

Returns the Incomplete Gamma function.

Parameters:

a - the parameter of the gamma distribution.

x - the integration end point.

Returns:

the incomplete gamma of x

incompleteGammaComplement

public static double incompleteGammaComplement(double a,
                                               double x)

Returns the Complemented Incomplete Gamma function.

Parameters:

a - the parameter of the gamma distribution.

x - the integration start point.

Returns:

the complemented incomplete gamma of x

digamma

public static double digamma(double x)

Returns the value of the logarithmic derivative of the Gamma function psi(x) = Gamma’(x) / Gamma(x).

Parameters:

x - x value

Returns:

digamma(x)

trigamma

public static double trigamma(double x)

Returns the value of the trigamma function d(psi(x))/dx, the derivative of the digamma(double) function, evaluated at x.

Parameters:

x - x value

Returns:

trigamma(x)