org.apache.commons.math.special
Class Gamma

java.lang.Object
  org.apache.commons.math.special.Gamma

All Implemented Interfaces:

Serializable

public class Gamma

extends Object

implements Serializable

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

Version:

$Revision: 1.22 $ $Date: 2004/10/08 05:53:18 $

See Also:

Serialized Form

Method Summary

static double	logGamma(double x) Returns the natural logarithm of the gamma function Γ(x).
static double	regularizedGammaP(double a, double x) Returns the regularized gamma function P(a, x).
static double	regularizedGammaP(double a, double x, double epsilon, int maxIterations) Returns the regularized gamma function P(a, x).
static double	regularizedGammaQ(double a, double x) Returns the regularized gamma function Q(a, x) = 1 - P(a, x).
static double	regularizedGammaQ(double a, double x, double epsilon, int maxIterations) Returns the regularized gamma function Q(a, x) = 1 - P(a, x).

Methods inherited from class java.lang.Object

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

Method Detail

logGamma

public static double logGamma(double x)

Returns the natural logarithm of the gamma function Γ(x). The implementation of this method is based on:

• Gamma Function, equation (28).
• Lanczos Approximation, equations (1) through (5).
• Paul Godfrey, A note on the computation of the convergent Lanczos complex Gamma approximation

Parameters:

x - the value.

Returns:

log(Γ(x))

regularizedGammaP

public static double regularizedGammaP(double a,
                                       double x)
                                throws MathException

Returns the regularized gamma function P(a, x).

Parameters:

a - the a parameter.

x - the value.

Returns:

the regularized gamma function P(a, x)

Throws:

MathException - if the algorithm fails to converge.

regularizedGammaP

public static double regularizedGammaP(double a,
                                       double x,
                                       double epsilon,
                                       int maxIterations)
                                throws MathException

Returns the regularized gamma function P(a, x). The implementation of this method is based on:

• Regularized Gamma Function, equation (1).
• Incomplete Gamma Function, equation (4).
• Confluent Hypergeometric Function of the First Kind, equation (1).

Parameters:

a - the a parameter.

x - the value.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

maxIterations - Maximum number of "iterations" to complete.

Returns:

the regularized gamma function P(a, x)

Throws:

MathException - if the algorithm fails to converge.

regularizedGammaQ

public static double regularizedGammaQ(double a,
                                       double x)
                                throws MathException

Returns the regularized gamma function Q(a, x) = 1 - P(a, x).

Parameters:

a - the a parameter.

x - the value.

Returns:

the regularized gamma function Q(a, x)

Throws:

MathException - if the algorithm fails to converge.

regularizedGammaQ

public static double regularizedGammaQ(double a,
                                       double x,
                                       double epsilon,
                                       int maxIterations)
                                throws MathException

Returns the regularized gamma function Q(a, x) = 1 - P(a, x). The implementation of this method is based on:

• Regularized Gamma Function, equation (1).
• Regularized incomplete gamma function: Continued fraction representations (formula 06.08.10.0003)

Parameters:

a - the a parameter.

x - the value.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

maxIterations - Maximum number of "iterations" to complete.

Returns:

the regularized gamma function P(a, x)

Throws:

MathException - if the algorithm fails to converge.