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():

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 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¶

gamma(3), lgamma(3)

COLOPHON¶

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