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)
For x < 0.5 one can use
Gamma(x) * Gamma(1-x) = PI/sin(PI*x)
This function returns the value of the Gamma function for the argument x.
It had to be called "true gamma function" since there is already a
function gamma() that returns something else.
In order to check for errors, set errno to zero and call
feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return,
if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO |
FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
A range error occurs if x is too large. A pole error occurs if x is zero. A
domain error (or a pole error) occurs if x is a negative integer.