I'm afraid my math in this area is a bit deficient, but what I am trying to do is see if there's a way to simplify the function: but I never really learned how to manipulate factorials algebraically, ...

The first forty-one coefficients of a continued fraction for $\ln \Gamma(z) + z - (z - 1/2) \ln z - \ln \surd \overline {2\pi}$, are given. The computation, based on Wall's algorithm for converting a ...