| 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:
\[
\gamma(s,x) = \int_0^x t^{s-1}\,e^{-t}\,{\rm d}t = P(s,x)\Gamma(s)
\]
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
pgamma. |
| 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. |
| GammaRegularizedQ |
The Regularized Incomplete Gamma Q function is defined as:
\[
Q(s,x)=\frac{\Gamma(s,x)}{\Gamma(s)}=1-P(s,x), s \geq 0, x \geq 0
\]
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:
\[
\Gamma(s,x) = \int_x^{\infty} t^{s-1}\,e^{-t}\,{\rm d}t = Q(s,x) \times \Gamma(s)
\]
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 log-Gamma 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 methods available to compute \(\log (\Gamma(z))\)
|