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tgamma(3)
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():
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
DESCRIPTION
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)
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 oc‐
curs, 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 math‐
ematical sign.
If the result underflows, a range error occurs, and the functions re‐
turn 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 excep‐
tion (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.
VERSIONS
These functions first appeared in glibc in version 2.1.
ATTRIBUTES
For an explanation of the terms used in this section, see attrib‐
utes(7). allbox; lbw30 lb lb l l l. Interface Attribute Value T{
tgamma(), tgammaf(), tgammal() T} Thread safety MT-Safe
CONFORMING TO
C99, POSIX.1-2001, POSIX.1-2008.
NOTES
This function had to be called "true gamma function" since there is al‐
ready 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.
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 incor‐
rectly produced a domain error (errno set to EDOM and an FE_INVALID ex‐
ception raised), rather than a pole error.
SEE ALSO
gamma(3), lgamma(3)
COLOPHON
This page is part of release 5.02 of the Linux man-pages project. A
description of the project, information about reporting bugs, and the
latest version of this page, can be found at
https://www.kernel.org/doc/man-pages/.
GNU 2017-09-15 TGAMMA(3)