# Package com.numericalmethod.suanshu.analysis.function.special.gamma

• Interface Summary
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 Summary
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. When s <= 1, we use an approximation of P(s,x) together with a higher-order 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: $Q(s,x)=\frac{\Gamma(s,x)}{\Gamma(s)}=1-P(s,x), s \geq 0, x \geq 0$ 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 Summary
Enum Description
LogGamma.Method
the available methods to compute $$\log (\Gamma(z))$$