datatable.math.gamma()¶
Euler Gamma function of x.
The gamma function is defined for all x
except for the negative
integers. For positive x
it can be computed via the integral
\[\Gamma(x) = \int_0^\infty t^{x-1}e^{-t}dt\]
For negative x
it can be computed as
\[\Gamma(x) = \frac{\Gamma(x + k)}{x(x+1)\cdot...\cdot(x+k-1)}\]
where \(k\) is any integer such that \(x+k\) is positive.
If x
is a positive integer, then \(\Gamma(x) = (x - 1)!\).