Package org.apache.commons.numbers.gamma
Class LanczosApproximation
- java.lang.Object
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- org.apache.commons.numbers.gamma.LanczosApproximation
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public final 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.
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Constructor Summary
Constructors Modifier Constructor Description private
LanczosApproximation()
Private constructor.
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Method Summary
All Methods Static Methods Concrete Methods Modifier and Type Method Description static double
g()
Return the Lanczos constant \( g = \frac{607}{128} \).static double
value(double x)
Computes the Lanczos approximation.
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Field Detail
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LANCZOS_G
private static final double LANCZOS_G
\( g = \frac{607}{128} \).- See Also:
- Constant Field Values
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LANCZOS
private static final double[] LANCZOS
Lanczos coefficients.
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