Package org.apache.commons.numbers.gamma

Class LanczosApproximation

java.lang.Object

org.apache.commons.numbers.gamma.LanczosApproximation

public class LanczosApproximation
extends java.lang.Object

Lanczos approximation to the Gamma function. It is related to the Gamma function by the following equation \[ \Gamma(x) = \sqrt{2\pi} \, \frac{(g + x + \frac{1}{2})^{x + \frac{1}{2}} \, e^{-(g + x + \frac{1}{2})} \, \mathrm{lanczos}(x)} {x} \] where \( g \) is the Lanczos constant. See equations (1) through (5), and Paul Godfrey's Note on the computation of the convergent Lanczos complex Gamma approximation.

Constructor Summary

Constructors

Constructor	Description
LanczosApproximation()

Method Summary

Modifier and Type	Method	Description
static double	g()
static double	value(double x)	Computes the Lanczos approximation.

Methods inherited from class java.lang.Object

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

Constructor Detail

LanczosApproximation

public LanczosApproximation()

Method Detail

value

public static double value(double x)

Computes the Lanczos approximation.

Parameters:

x - Argument.

Returns:

the Lanczos approximation.

g

public static double g()

Returns:

the Lanczos constant \( g = \frac{607}{128} \).