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TGAMMA(3) | Linux Programmer's Manual | 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**():

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

*cc -std=c99*# DESCRIPTION¶

The Gamma function is defined byGamma(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.

*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¶

gamma(3), lgamma(3)# COLOPHON¶

This page is part of release 3.74 of the Linux*man-pages*project. A description of the project, information about reporting bugs, and the latest version of this page, can be found at http://www.kernel.org/doc/man-pages/.

2010-09-20 | GNU |