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TGAMMA

Section: Linux Programmer's Manual (3)
Updated: 2015-03-02
Index Return to Main Contents
 

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^(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 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 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.
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).
InterfaceAttributeValue
tgamma(), tgammaf(), tgammal() Thread safetyMT-Safe
 

CONFORMING TO

C99, POSIX.1-2001.  

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

This page is part of release 3.81 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 http://www.kernel.org/doc/man-pages/.


 

Index

NAME
SYNOPSIS
DESCRIPTION
RETURN VALUE
ERRORS
VERSIONS
ATTRIBUTES
CONFORMING TO
NOTES
BUGS
SEE ALSO
COLOPHON


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