Expand description
Provides the gamma and related functions
Enums§
- Gamma
Func Error - 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
wherea
is the argument for the gamma function andx
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
wherea
is the argument for the gamma function andx
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
wherea
is the argument for the gamma function andx
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
wherea
is the argument for the gamma function andx
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
wherea
is the argument for the gamma function andx
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
wherea
is the argument for the gamma function andx
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
wherea
is the argument for the gamma function andx
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
wherea
is the argument for the gamma function andx
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