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**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(): _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

**DESCRIPTION**

These functions calculate the Gamma function ofx. 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, anderrnois set toERANGE.

**VERSIONS**

These functions first appeared in glibc in version 2.1.

**ATTRIBUTES**

For an explanation of the terms used in this section, seeattributes(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 functiongamma(3) that returns something else (seegamma(3) for details).

**BUGS**

Before version 2.18, the glibc implementation of these functions did not seterrnotoEDOMwhenxis negative infinity. Before glibc 2.19, the glibc implementation of these functions did not seterrnotoERANGEon an underflow range error.xIn 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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