tgamma, tgammaf, tgammal − true gamma function
float tgammaf(float x);
long double tgammal(long double x);
Link with −lm.
Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
tgamma(), tgammaf(), tgammal():
_XOPEN_SOURCE >= 600
|| _ISOC99_SOURCE ||
_POSIX_C_SOURCE >= 200112L;
or cc -std=c99
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)
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.
See math_error(7) for information on how to determine whether an error has occurred when calling these functions.
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.
gives the following error which is not specified in C99 or
Range error: result underflow
An underflow floating-point exception (FE_UNDERFLOW) is raised.
errno is not set for this case.
These functions first appeared in glibc in version 2.1.
For an explanation of the terms used in this section, see attributes(7).
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).
If x is negative infinity, errno is not set (it should be set to EDOM).
In glibc versions 2.3.3 and earlier, an argument of +0 or −0 incorrectly produced a domain error (errno set to EDOM and an FE_INVALID exception raised), rather than a pole error.
This page is part of release 3.53 of the Linux man-pages project. A description of the project, and information about reporting bugs, can be found at http://www.kernel.org/doc/man−pages/.