accuracy sought throughout this work. For $\theta >\pi/2$ and $\theta<-\pi/2$, which represent the adjacent Stokes sectors to $|\theta|< \pi/2$, the Stokes discontinuity is non-zero, but is $O(10^{-7})$. Therefore, it only affects the accuracy beyond the seventh decimal place. Similarly, the remainder is very small.

The $|z|=1/10$ situation, however, is completely different. Except for the values of the truncation parameter $N$ close to zero, the regularized value of the remainder and the truncated sum dominate, although when combined, they cancel many decimal places. For $|\theta|<\pi/2$, the Stokes discontinuity term vanishes as for the $|z|=3$ case, but outside the sector, it makes a substantial contribution to $\ln \Gamma(z)$, which cannot be neglected. Therefore, whilst the $|z|=1/10$ case exhibits completely different behaviour to $|z|=3$, when all the contributions are combined, it is able to yield the values of $\ln \Gamma(z)$ to the 30 decimal places specified by the Mathematica module/program as in the $|z|=3$ case.

For $z$ situated on the Stokes lines of $\theta=\pm \pi/2$, the asymptotic forms possess Cauchy principal value integrals for their regularized remainder in addition to a Stokes discontinuity term that is calculated by summing semi-residue contributions rather than full residue contributions in the adjacent Stokes sectors. Consequently, a 