### 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**(): _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE; or
*cc -std=c99*

### DESCRIPTION

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 non-positive integers.
For non-negative 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.
| |

errno is not set for this case.
| |

### VERSIONS

These functions first appeared in glibc in version 2.1.

### CONFORMING TO

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

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.

### SEE ALSO

### COLOPHON

This page is part of release 3.23 of the Linux
*man-pages* project.
A description of the project,
and information about reporting bugs,
can be found at
http://www.kernel.org/doc/man-pages/.