**NAME**

tgamma, tgammaf, tgammal - true gamma function

**SYNOPSIS**

#include<math.h>doubletgamma(doublex);floattgammaf(floatx);longdoubletgammal(longdoublex);Link with-lm. Feature Test Macro Requirements for glibc (seefeature_test_macros(7)):tgamma(),tgammaf(),tgammal(): _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L; orcc-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 nonpositive integers. For nonnegative integralmone has Gamma(m+1) = m! and, more generally, for allx: Gamma(x+1) = x * Gamma(x) Furthermore, the following is valid for all values ofxoutside the poles: Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

**RETURN** **VALUE**

On success, these functions return Gamma(x). Ifxis a NaN, a NaN is returned. Ifxis positive infinity, positive infinity is returned. Ifxis 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 returnHUGE_VAL,HUGE_VALF, orHUGE_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. Ifxis -0 or +0, a pole error occurs, and the functions returnHUGE_VAL,HUGE_VALF, orHUGE_VALL, respectively, with the same sign as the 0.

**ERRORS**

Seemath_error(7) for information on how to determine whether an error has occurred when calling these functions. The following errors can occur: Domain error:xis a negative integer, or negative infinityerrnois set toEDOM. An invalid floating-point exception (FE_INVALID) is raised (but see BUGS). Pole error:xis +0 or -0errnois set toERANGE. A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised. Range error: result overflowerrnois set toERANGE. 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.errnois 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 functiongamma(3) that returns something else (seegamma(3) for details).

**BUGS**

Ifxis negative infinity,errnois not set (it should be set toEDOM). In glibc versions 2.3.3 and earlier, an argument of +0 or -0 incorrectly produced a domain error (errnoset toEDOMand anFE_INVALIDexception raised), rather than a pole error.

**SEE** **ALSO**

gamma(3),lgamma(3)

**COLOPHON**

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