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:

glibc also gives the following error which is not specified in C99 or POSIX.1-2001.

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)