tgamma, tgammaf, tgammal - true gamma function

```
#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
```

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)

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.

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**.

These functions first appeared in glibc in version 2.1.

For an explanation of the terms used in this section, see attributes(7).

Interface | Attribute | Value |

tgamma(), tgammaf(), tgammal() | Thread safety | MT-Safe |

C99, POSIX.1-2001, POSIX.1-2008.

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).

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`

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.

This page is part of release 4.15 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/.