com.numericalmethod.suanshu.analysis.function.special
Class Gamma

java.lang.Object
  com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction
      com.numericalmethod.suanshu.analysis.function.special.Gamma

All Implemented Interfaces:

Function, RealScalarFunction

public class Gamma
extends UnivariateRealFunction

This computes an approximation to the Gamma function, Γ(z), for real numbers.

       ∞
       /
 Γ(z)= | tz-1e-t dt
       /
       0
 

Γ(z) is an extension of the factorial function to real and complex numbers, with its argument shifted down by 1.

We provide a few ways to compute Γ(z). Each method differs in accuracy and speed. For example,

The full Lanczos approximation can be made arbitrarily precise because it is computed using BigDecimal.

The quick Lanczos approximation is quick but could be less precise because the computations are done in double precision.

See Also:

• Wikipedia: Gamma function
• Wikipedia: Lanczos approximation
• Wikipedia: Stirling's approximation
• Wikipedia: Spouge's approximation

Nested Class Summary

static class

Gamma.Method the methods available to compute Γ(z)

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Constructor Summary

Gamma()
Construct an instance to compute for Gamma function using Lanczos approximation with default settings.

Gamma(double g, int n, int scale)
Construct an instance to compute for Gamma function using Lanczos approximation.

Gamma(Gamma.Method method)
Construct an instance to compute for Gamma function using a specified method with default settings.

Method Summary

double

evaluate(double x) Compute for the Gamma function in the Real domain.

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.UnivariateRealFunction

dimension4Domain, dimension4Range, evaluate

Methods inherited from class java.lang.Object

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

Constructor Detail

Gamma

public Gamma()

Construct an instance to compute for Gamma function using Lanczos approximation with default settings.

See Also:

Wikipedia: Lanczos approximation

Gamma

public Gamma(double g,
             int n,
             int scale)

Construct an instance to compute for Gamma function using Lanczos approximation.

Recommended settings are

g = 607.0 / 128.0 n = 15 scale = 30

Parameters:

g - g

n - n

scale - precision

See Also:

Wikipedia: Lanczos approximation

Gamma

public Gamma(Gamma.Method method)

Construct an instance to compute for Gamma function using a specified method with default settings.

Parameters:

method - the algorithm to use, c.f., Gamma.Method

Method Detail

evaluate

public double evaluate(double x)

Compute for the Gamma function in the Real domain.

Specified by:

evaluate in class UnivariateRealFunction

Parameters:

x - a real number

Returns:

Γ(x)