Log-gamma function

Summary

The log-gamma function is the logarithm of the gamma function: $\ln\Gamma(x)$ for real $x > 0$, and its holomorphic extension $\operatorname{Log}\Gamma$ to the slit plane $\C \setminus (-\infty, 0]$. It is used because $\Gamma$ grows faster than any exponential, so its logarithm is easier to compute and to estimate. Its derivative is the digamma function, and its asymptotic expansion is Stirling's series.