
TGAMMA(3) Linux Programmer's Manual TGAMMA(3)
NAME
tgamma, tgammaf, tgammal  true gamma function
SYNOPSIS
#include <math.h>
double tgamma(double x);
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
DESCRIPTION
The Gamma function is defined by
Gamma(x) = integral from 0 to infinity of t^(x1) 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 cor
rect 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 floatingpoint exception (FE_INVALID) is raised
(but see BUGS).
Pole error: x is +0 or 0
errno is set to ERANGE. A dividebyzero floatingpoint exception (FE_DIVBYZERO)
is raised.
Range error: result overflow
errno is set to ERANGE. An overflow floatingpoint exception (FE_OVERFLOW) is
raised.
glibc also gives the following error which is not specified in C99 or POSIX.12001.
Range error: result underflow
An underflow floatingpoint exception (FE_UNDERFLOW) is raised.
errno is not set for this case.
VERSIONS
These functions first appeared in glibc in version 2.1.
CONFORMING TO
C99, POSIX.12001.
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).
BUGS
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.
SEE ALSO
gamma(3), lgamma(3)
COLOPHON
This page is part of release 3.55 of the Linux manpages project. A description of the
project, and information about reporting bugs, can be found at
http://www.kernel.org/doc/manpages/.
GNU 20100920 TGAMMA(3) 
