Gamma functions. More...
Include dependency graph for gamma.c:
Macros | |
| #define | EGF_EPS ldexp(1, -54) |
| epsilon for cutoff around integers. | |
Enumerations | |
| enum | dom { pt , qt , cf , ua , rek } |
| enum for the choice of algorithm for the upper incomplete gamma function. | |
Functions | |
| enum dom | egf_domain (double a, double x) |
| set type of algorithm to use depending on the parameters. | |
| enum dom | egf_ldomain (double a, double x) |
| double | egf_pt (double a, double x) |
| calculate upper gamma function with the recursion formula. | |
| double | egf_qt (double a, double x) |
| calculate the upper incomplete gamma function as in Gautschi. | |
| double | egf_rek (double a, double x) |
| calculate the upper incomplete gamma function as in Gautschi. | |
| double | egf_cf (double a, double x) |
| calculate the upper incomplete gamma function as in Gautschi. | |
| double | egf_ua_r (double a, double eta) |
| calculate the upper incomplete gamma function as in Gautschi. | |
| double | egf_ua (double a, double x) |
| calculate the upper incomplete gamma function as in Gautschi. | |
| double | egf_ugamma (double a, double x) |
| calculate the upper incomplete gamma function as in Gautschi. | |
| double | egf_gammaStar (double a, double x) |
| calculate the upper incomplete gamma function as in Gautschi. | |
Detailed Description
Gamma functions.
Calculates the gamma function, the incomplete upper gamma function and the regularized lower incomplete gamma function for evaluations of Crandall's formula.
- See also
- Walter Gautschi. “A Computational Procedure for Incomplete Gamma Func-257 tions”. In: ACM Trans. Math. Softw. 5 (1979), pp. 466–481 for basic principles some improvements were made to increase accuracy
Function Documentation
◆ egf_cf()
| double egf_cf | ( | double | a, |
| double | x ) |
calculate the upper incomplete gamma function as in Gautschi.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- function value of the upper incomplete gamma function.
◆ egf_domain()
| enum dom egf_domain | ( | double | a, |
| double | x ) |
set type of algorithm to use depending on the parameters.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- enum for the type of algorithm to use.
◆ egf_gammaStar()
| double egf_gammaStar | ( | double | a, |
| double | x ) |
calculate the upper incomplete gamma function as in Gautschi.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- function value of the upper incomplete gamma function.
◆ egf_pt()
| double egf_pt | ( | double | a, |
| double | x ) |
calculate upper gamma function with the recursion formula.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- function value of the upper incomplete gamma function.
◆ egf_qt()
| double egf_qt | ( | double | a, |
| double | x ) |
calculate the upper incomplete gamma function as in Gautschi.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- function value of the upper incomplete gamma function.
◆ egf_rek()
| double egf_rek | ( | double | a, |
| double | x ) |
calculate the upper incomplete gamma function as in Gautschi.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- function value of the upper incomplete gamma function.
◆ egf_ua()
| double egf_ua | ( | double | a, |
| double | x ) |
calculate the upper incomplete gamma function as in Gautschi.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- function value of the upper incomplete gamma function.
◆ egf_ua_r()
| double egf_ua_r | ( | double | a, |
| double | eta ) |
calculate the upper incomplete gamma function as in Gautschi.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- function value of the upper incomplete gamma function.
◆ egf_ugamma()
| double egf_ugamma | ( | double | a, |
| double | x ) |
calculate the upper incomplete gamma function as in Gautschi.
- Parameters
-
[in] a exponent of the upper incomplete gamma function. [in] x lower integral boundary of the upper incomplete gamma function.
- Returns
- function value of the upper incomplete gamma function.
