Module gamma

Provides the gamma and related functions

Enums

GammaFuncError

Represents the errors that can occur when computing any of the incomplete gamma functions.

Functions

checked_gamma_li

Computes the lower incomplete gamma function gamma(a,x) = int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the upper integral limit.

checked_gamma_lr

Computes the lower incomplete regularized gamma function P(a,x) = 1 / Gamma(a) * int(exp(-t)t^(a-1), t=0..x) for real a > 0, x > 0 where a is the argument for the gamma function and x is the upper integral limit.

checked_gamma_ui

Computes the upper incomplete gamma function Gamma(a,x) = int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the lower intergral limit.

checked_gamma_ur

Computes the upper incomplete regularized gamma function Q(a,x) = 1 / Gamma(a) * int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the lower integral limit.

digamma

Computes the Digamma function which is defined as the derivative of the log of the gamma function. The implementation is based on “Algorithm AS 103”, Jose Bernardo, Applied Statistics, Volume 25, Number 3 1976, pages 315 - 317

gamma

Computes the gamma function with an accuracy of 16 floating point digits. The implementation is derived from “An Analysis of the Lanczos Gamma Approximation”, Glendon Ralph Pugh, 2004 p. 116

gamma_li

Computes the lower incomplete gamma function gamma(a,x) = int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the upper integral limit.

gamma_lr

Computes the lower incomplete regularized gamma function P(a,x) = 1 / Gamma(a) * int(exp(-t)t^(a-1), t=0..x) for real a > 0, x > 0 where a is the argument for the gamma function and x is the upper integral limit.

gamma_ui

Computes the upper incomplete gamma function Gamma(a,x) = int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the lower intergral limit.

gamma_ur

Computes the upper incomplete regularized gamma function Q(a,x) = 1 / Gamma(a) * int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the lower integral limit.

inv_digamma

ln_gamma

Computes the logarithm of the gamma function with an accuracy of 16 floating point digits. The implementation is derived from “An Analysis of the Lanczos Gamma Approximation”, Glendon Ralph Pugh, 2004 p. 116