As goes to infinity at a constant we have: .
\ln (1/\Gamma(z)) \sim -z \ln (z) + z + \tfrac{1}{2} \ln \left (\frac{z}{2\pi} \right ) - \frac{1}{12z} + \frac{1}{360z^3} -\frac{1}{1260 z^5}\qquad \qquad \text{for}\quad |\arg(z)| < \pi .