Package org.apache.commons.numbers.gamma
Class LanczosApproximation
java.lang.Object
org.apache.commons.numbers.gamma.LanczosApproximation
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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Field Summary
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Constructor Summary
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Method Summary
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Field Details
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LANCZOS_G
private static final double LANCZOS_G\( g = \frac{607}{128} \).- See Also:
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LANCZOS
private static final double[] LANCZOSLanczos coefficients.
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Constructor Details
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LanczosApproximation
private LanczosApproximation()Private constructor.
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Method Details
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value
public static double value(double x) Computes the Lanczos approximation.- Parameters:
x
- Argument.- Returns:
- the Lanczos approximation.
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g
public static double g()- Returns:
- the Lanczos constant \( g = \frac{607}{128} \).
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