java.lang.Object
org.bzdev.math.Functions.GammaFunction
- Enclosing class:
- Functions
Class providing static methods for computing Gamma functions,
their logarithms, and asymptotic values.
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Method Summary
Modifier and TypeMethodDescriptionstatic double
asymptoticValue
(double x) Compute the asymptotic value of the Gamma function.static double
Gamma
(double z) Compute the Gamma function.static double
logAsymptoticValue
(double x) Compute the asymptotic value of the logarithm of the Gamma function.static double
logGamma
(double z) Compute the logarithm of the Gamma function
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Method Details
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Gamma
public static double Gamma(double z) Compute the Gamma function. The function Γ(x) has poles at 0, -1, -2, -3, etc. At a poll, an infinite double-precision number is returned, with the choice of positive or negative infinity based on whether the value at x+δ is positive or negative respectively for δ>0, where δ is an arbitrarily small number.- Parameters:
z
- a real number- Returns:
- the value Γ(z)
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logGamma
public static double logGamma(double z) Compute the logarithm of the Gamma function- Parameters:
z
- a non-negative number- Returns:
- the value of log (Γ(x))
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asymptoticValue
public static double asymptoticValue(double x) Compute the asymptotic value of the Gamma function. The computation uses Nemes' approximation with up to a t6 term. Errors are less than 1 part in 1012 for t \gt; 20.Citation: http://www.ebyte.it/library/downloads/2007_MTH_Nemes_GammaFunction.pdf or http://dx.doi.org/10.3247/sl2math08.005
- Parameters:
x
- the argument, which must be positive- Returns:
- an asymptotic approximation for Γ(x)
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logAsymptoticValue
public static double logAsymptoticValue(double x) Compute the asymptotic value of the logarithm of the Gamma function. The computation uses Nemes' approximation with up to a t6 term. Errors are less than 1 part in 1012 for t \gt; 20.Citation: http://www.ebyte.it/library/downloads/2007_MTH_Nemes_GammaFunction.pdf or http://dx.doi.org/10.3247/sl2math08.005
- Parameters:
x
- the argument, which must be positive- Returns:
- an asymptotic approximation for log (Γ(x))
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