tgamma3
True gamma function
Usage
#include <math.h>
double tgamma(double x); float tgammaf(float x); long double tgammal(long double x);
Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
tgamma(), tgammaf(), tgammal():
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
Library
Math library (libm, -lm)
Overview
These functions calculate the Gamma function of x.
The Gamma function is defined by
Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
It is defined for every real number except for nonpositive integers. For nonnegative integral m one has
Gamma(m+1) = m!
and, more generally, for all x:
Gamma(x+1) = x * Gamma(x)
Furthermore, the following is valid for all values of x outside the poles:
Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
Return value
On success, these functions return Gamma(x).
If x is a NaN, a NaN is returned.
If x is positive infinity, positive infinity is returned.
If x is a negative integer, or is negative infinity, a domain error occurs, and a NaN is returned.
If the result overflows, a range error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct mathematical sign.
If the result underflows, a range error occurs, and the functions return 0, with the correct mathematical sign.
If x is -0 or +0, a pole error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign as the 0.
Errors
See math_error(7) for information on how to determine whether an error has occurred when calling these functions.
The following errors can occur:
- Domain error: x is a negative integer, or negative infinity
-
errno is set to EDOM. An invalid floating-point exception (
FE_INVALID) is raised (but see BUGS).
- Pole error: x is +0 or -0
-
errno is set to ERANGE. A divide-by-zero floating-point exception (
FE_DIVBYZERO) is raised.
- Range error: result overflow
-
errno is set to ERANGE. An overflow floating-point exception (
FE_OVERFLOW) is raised.
glibc also gives the following error which is not specified in C99 or POSIX.1-2001.
- Range error: result underflow
-
An underflow floating-point exception (
FE_UNDERFLOW) is raised, and errno is set to ERANGE.
Attributes
For an explanation of the terms used in this section, see attributes(7).
| Interface | Attribute | Value |
| tgamma(), tgammaf(), tgammal() | Thread safety | MT-Safe |
Notes
This function had to be called "true gamma function" since there is already a function gamma(3) that returns something else (see gamma(3) for details).
Releases
12 releases since Debian 3.1 (Sarge); the text changed 11 times.