# Manpage of TGAMMA

# 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
*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, 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**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*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.

## SEE ALSO

**gamma**(3),

**lgamma**(3)

## Index

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