tgamma, tgammaf, tgammal - true gamma function
#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():
_ISOC99_SOURCE ||
_POSIX_C_SOURCE >= 200112L
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)
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.
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.
These functions first appeared in glibc in version 2.1.
For an explanation of the terms used in this section, see
attributes(7).
Interface |
Attribute |
Value |
tgamma (), tgammaf (), tgammal () |
Thread safety |
MT-Safe |
C99, POSIX.1-2001, POSIX.1-2008.
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).
Before version 2.18, the glibc implementation of these functions did not set
errno to
EDOM when
x is negative infinity.
Before glibc 2.19, the glibc implementation of these functions did not set
errno to
ERANGE on an underflow range error.
x
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.
gamma(3),
lgamma(3)