Interface  Description 

Gamma 
The Gamma function is an extension of the factorial function to real and complex numbers, with its argument shifted down by 1.

Class  Description 

Digamma 
The digamma function is defined as the logarithmic derivative of the gamma function.

GammaGergoNemes 
The Gergo Nemes' algorithm is very simple and quick to compute the Gamma function, if accuracy is not critical.

GammaLanczos 
Lanczos approximation provides a way to compute the Gamma function such that the accuracy can be made arbitrarily precise.

GammaLanczosQuick 
Lanczos approximation, computations are done in
double . 
GammaLowerIncomplete 
The Lower Incomplete Gamma function is defined as:
\[
\gamma(s,x) = \int_0^x t^{s1}\,e^{t}\,{\rm d}t = P(s,x)\Gamma(s)
\]
P(s,x) is the Regularized Incomplete Gamma P function.

GammaRegularizedP 
The Regularized Incomplete Gamma P function is defined as:
\[
P(s,x) = \frac{\gamma(s,x)}{\Gamma(s)} = 1  Q(s,x), s \geq 0, x \geq 0
\]
The R equivalent function is 
GammaRegularizedPInverse 
The inverse of the Regularized Incomplete Gamma P function is defined as:
\[
x = P^{1}(s,u), 0 \geq u \geq 1
\]
When
s > 1 , we use the asymptotic inversion method.
When s <= 1 , we use an approximation of P(s,x) together with a higherorder Newton like method.
In both cases, the estimated value is then improved using Halley's method, c.f., HalleyRoot . 
GammaRegularizedQ 
The Regularized Incomplete Gamma Q function is defined as:
\[
Q(s,x)=\frac{\Gamma(s,x)}{\Gamma(s)}=1P(s,x), s \geq 0, x \geq 0
\]
The algorithm used for computing the regularized incomplete Gamma Q function depends on the values of s and x.

GammaUpperIncomplete 
The Upper Incomplete Gamma function is defined as:
\[
\Gamma(s,x) = \int_x^{\infty} t^{s1}\,e^{t}\,{\rm d}t = Q(s,x) \times \Gamma(s)
\]
The integrand has the same form as the Gamma function, but the lower limit of the integration is a variable.

Lanczos 
The Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964.

LogGamma 
The logGamma function, \(\log (\Gamma(z))\), for positive real numbers, is the log of the Gamma function.

Trigamma 
The trigamma function is defined as the logarithmic derivative of the digamma function.

Enum  Description 

LogGamma.Method 
the available methods to compute \(\log (\Gamma(z))\)

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