---
name: "tgamma"
section: "3"
platform: "linux"
package: "man-pages"
version: "6.19-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/tgamma"
---

# tgamma(3)

true gamma function

## NAME

tgamma, tgammaf, tgammal - true gamma function

## LIBRARY

Math library (*libm*, *-lm*)

## SYNOPSIS

```
#include <math.h>
```

**double tgamma(double** *x***);** **float tgammaf(float** *x***);** **long double tgammal(long double** *x***);**

Feature Test Macro Requirements for glibc (see [**feature\_test\_macros**(7)](/feature_test_macros/7.md)):

**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)](/math_error/7.md) 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**.

## ATTRIBUTES

For an explanation of the terms used in this section, see [**attributes**(7)](/attributes/7.md).

| | | |
| --- | --- | --- |
| **Interface** | **Attribute** | **Value** |
| **tgamma**(), **tgammaf**(), **tgammal**() | Thread safety | MT-Safe |

## STANDARDS

C11, POSIX.1-2008.

## HISTORY

glibc 2.1. C99, POSIX.1-2001.

## NOTES

This function had to be called "true gamma function" since there is already a function [**gamma**(3)](/gamma/3.md) that returns something else (see [**gamma**(3)](/gamma/3.md) for details).

## BUGS

Before glibc 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.

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)](/gamma/3.md), [**lgamma**(3)](/lgamma/3.md)