tgamma, tgammaf, tgammal - true gamma function

Synopsis

Description

Return Value

Errors

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Notes

Bugs

Colophon

#include <math.h>

double tgamma(doublex);

float tgammaf(floatx);

long double tgammal(long doublex);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;

orcc -std=c99

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

mone hasGamma(m+1) = m!

and, more generally, for all

x:Gamma(x+1) = x * Gamma(x)

Furthermore, the following is valid for all values of

xoutside the poles:Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

On success, these functions return Gamma(x).If

xis a NaN, a NaN is returned.If

xis positive infinity, positive infinity is returned.If

xis 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, 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.

If

xis -0 or +0, a pole error occurs, and the functions returnHUGE_VAL,HUGE_VALF, orHUGE_VALL, respectively, with the same sign as the 0.

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 overflow errnois 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.

These functions first appeared in glibc in version 2.1.

C99, POSIX.1-2001.

This function had to be called "true gamma function" since there is already a functiongamma(3) that returns something else (seegamma(3) for details).

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.

gamma(3),lgamma(3)

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GNU |
TGAMMA (3) | 2010-09-20 |