different program is required to evaluate the various terms belonging to $\ln \Gamma(z)$. For the Stokes line given by $\theta=\pi/2$, $|z|$ is set equal to 3, while for $\theta =-\pi/2$, it is set equal to 1/10. In both cases the truncated series and regularized remainder are purely imaginary, while the Stokes discontinuity term is purely real, which is consistent with the rules for the Stokes phenomenon presented in Ch. 1 of Ref. [@din73]. As found previously, the truncated sum and regularized value of the remainder are very small when $N<20$ for the large value of $|z|$, but begin to diverge from thereon, while for $|z|=1/10$, they dominate for $N>3$. In addition, for $|z|=3$, the Stokes discontinuity is very small ($O(10^{-9}$), while for $|z|=1/10$, it represents a sizeable contribution to the real part of $\ln \Gamma(-i/10)$, although it is still not as significant as the real of the leading terms in the Stirling approximation. Nevertheless, all terms are necessary in order to obtain $\ln \Gamma(z)$ to thirty decimal figures/places.

The numerical studies of Sec. 3 demonstrate that it is indeed possible to obtain exact values of a function from its asymptotic expansion based on the conventional view of the Stokes phenomenon. 