# tgamma - Man Page

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).

InterfaceAttributeValue

## 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.