# tgamma (3)

# 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.

- 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)