# TGAMMA

Section: Linux Programmer's Manual (3)
Updated: 2017-09-15
Index

## 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 mone 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 xoutside the poles:

Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

## RETURN VALUE

On success, these functions return Gamma(x).

If xis a NaN, a NaN is returned.

If xis positive infinity, positive infinity is returned.

If xis 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 xis -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
errnois set to EDOM. An invalid floating-point exception (FE_INVALID) is raised (but see BUGS).
Pole error: x is +0 or -0
errnois set to ERANGE. A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
Range error: result overflow
errnois 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 errnois 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 attributes(7).
 Interface Attribute Value tgamma(), tgammaf(), tgammal() 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 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 errnoto EDOMwhen xis negative infinity.

Before glibc 2.19, the glibc implementation of these functions did not set errnoto ERANGEon an underflow range error. x

In glibc versions 2.3.3 and earlier, an argument of +0 or -0 incorrectly produced a domain error (errnoset to EDOMand an FE_INVALIDexception raised), rather than a pole error.

## SEE ALSO

gamma(3), lgamma(3)

## Index

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

This document was created by man2html, using the manual pages.
Time: 19:53:54 GMT, October 26, 2017 Click Here!