Inverse gamma function

The inverse gamma function refers to the function that is defined as the inverse of the gamma function. The gamma function, denoted as \(\Gamma(z)\), is a generalization of the factorial function to complex numbers, except for the non-positive integers. It is defined for \(z > 0\) as: \[ \Gamma(z) = \int_0^\infty t^{z-1} e^{-t} \, dt.