lines. As a consequence, the extra term is expressed as an infinite series, which can become logarithmically divergent. Regularization of the series results in ambiguity whenever ${\rm arg}\,z \!=\! (\pm M \!-\! 1/2) \pi$ or at the Stokes lines, of which there are two in each domain of convergence. This ambiguity indicates that $\ln \Gamma(z)$ is discontinuous at the Stokes lines and is resolved by adopting the Zwaan-Dingle principle [@kow09], which states that an initially real function cannot suddenly become imaginary. Hence, the real value of the regularized value of the infinite series is chosen to yield the value of $\ln \Gamma(z)$ at Stokes lines.

As indicated previously, the LogGamma routine only evaluates $\ln \Gamma(z)$ for $z$ situated in the principal branch. Yet the Borel-summed and MB-regularized asymptotic forms presented in Secs. 2 and 4 cover all values of ${\rm arg}\,z$. This is particularly useful if we wish to evaluate $\ln \Gamma(z^3)$ for $z$ lying in the principal branch despite the fact that the LogGamma routine will only yield values for $-\pi/3 \!<\! {\rm arg}\,z \!\leq\! \pi/3$. Sec. 5 begins by presenting the MB-regularized asymptotic forms for $\ln \Gamma(z^3)$. In this instance there are seven domains of convergence spanning the 