jmathlib.toolbox.specfun._private
Class Gamma

java.lang.Object
  extended by jmathlib.toolbox.specfun._private.Gamma

public class Gamma
extends java.lang.Object

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


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:

Parameters:
x - the value.
Returns:
log(Γ(x))

regularizedGammaP

public static double regularizedGammaP(double a,
                                       double x)
                                throws java.lang.Exception
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.
java.lang.Exception

regularizedGammaP

public static double regularizedGammaP(double a,
                                       double x,
                                       double epsilon,
                                       int maxIterations)
                                throws java.lang.Exception
Returns the regularized gamma function P(a, x). The implementation of this method is based on:

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.
java.lang.Exception

regularizedGammaQ

public static double regularizedGammaQ(double a,
                                       double x)
                                throws java.lang.Exception
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.
java.lang.Exception

regularizedGammaQ

public static double regularizedGammaQ(double a,
                                       double x,
                                       double epsilon,
                                       int maxIterations)
                                throws java.lang.Exception
Returns the regularized gamma function Q(a, x) = 1 - P(a, x). The implementation of this method is based on:

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.
java.lang.Exception