3. Library calls (functions within program libraries)
TGAMMA
Section: Linux Programmer's Manual (3)Updated: 20150419
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NAME
tgamma, tgammaf, tgammal  true gamma functionSYNOPSIS
#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
These functions calculate the Gamma function of x.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 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 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.ATTRIBUTES
For an explanation of the terms used in this section, see attributes(7).Interface  Attribute  Value 
tgamma(), tgammaf(), tgammal()  Thread safety  MTSafe 
CONFORMING TO
C99, POSIX.12001, POSIX.12008.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
Before version 2.18, the glibc implementation of these functions did not set errno to EDOM when x is negative infinity.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
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Index
 NAME
 SYNOPSIS
 DESCRIPTION
 RETURN VALUE
 ERRORS
 VERSIONS
 ATTRIBUTES
 CONFORMING TO
 NOTES
 BUGS
 SEE ALSO
 COLOPHON
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