Package dev.nm.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.
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 \(\log (\Gamma(z))\)