org.apache.commons.numbers.gamma

Class RegularizedGamma.Q

java.lang.Object

org.apache.commons.numbers.gamma.RegularizedGamma.Q

Enclosing class:

RegularizedGamma

public static final class RegularizedGamma.Q
extends Object

Creates the \( Q(a, x) \equiv 1 - P(a, x) \) regularized Gamma function. Class is immutable.

Method Summary

Modifier and Type	Method and Description
static double	value(double a, double x) Computes the regularized gamma function \( Q(a, x) = 1 - P(a, x) \).
static double	value(double a, double x, double epsilon, int maxIterations) Computes 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

value

public static double value(double a,
                           double x)

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

Parameters:

a - Argument.

x - Argument.

Returns:

\( Q(a, x) \).

Throws:

ArithmeticException - if the continued fraction fails to converge.

value

public static double value(double a,
                           double x,
                           double epsilon,
                           int maxIterations)

Computes 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 - Argument.

x - Argument.

epsilon - Tolerance in continued fraction evaluation.

maxIterations - Maximum number of iterations in continued fraction evaluation.

Returns:

\( Q(a, x) \).

Throws:

ArithmeticException - if the continued fraction fails to converge.