tgammal (3)
NAME
tgamma, tgammaf, tgammal - true gamma functionSYNOPSIS
#include <math.h> double tgamma(double x);Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
tgamma(), tgammaf(), tgammal():
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
DESCRIPTION
These functions calculate the Gamma function of x. The Gamma function is defined byGamma(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.
- Range error: result underflow
- An underflow floating-point exception (FE_UNDERFLOW) is raised, and errno is set to ERANGE.
VERSIONS
These functions first appeared in glibc in version 2.1.ATTRIBUTES
For an explanation of the terms used in this section, see attributes(7).Interface | Attribute | Value |
tgamma (), tgammaf (), tgammal () | Thread safety | MT-Safe |