## table of contents

tgamma(3) | Library Functions Manual | tgamma(3) |

# NAME¶

tgamma, tgammaf, tgammal - true gamma function

# LIBRARY¶

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

# SYNOPSIS¶

#include <math.h>

double tgamma(doublex);float tgammaf(floatx);long double tgammal(long doublex);

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

_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

# DESCRIPTION¶

These functions calculate the Gamma function of *x*.

The Gamma function is defined by

It is defined for every real number except for nonpositive
integers. For nonnegative integral *m* one has

and, more generally, for all *x*:

Furthermore, the following is valid for all values of *x*
outside the poles:

# 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**.

# ATTRIBUTES¶

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

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) that returns something else (see gamma(3) 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¶

2024-05-02 | Linux man-pages 6.8 |