tgamma, tgammaf, tgammal − true gamma function

**#include <math.h>**

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

long double tgammal(long double

Link with *−lm*.

Feature Test Macro Requirements for glibc (see **feature_test_macros(7)**):

**tgamma**(), **tgammaf**(), **tgammal**():

_XOPEN_SOURCE >= 600 || _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L;

or *cc -std=c99*

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.

*errno* is not set for this case.

These functions first appeared in glibc in version 2.1.

C99, POSIX.1-2001.

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).

If *x* is negative infinity, *errno* is not set (it should be set to **EDOM**).

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.

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