value of $|z|$ is chosen, viz. $z \!=\! 3$. The truncation parameter $N$ takes on various values between 1 and 50 with the optimal point of truncation occurring around $N_{OP} \!=\!10$. This means for $N \!<\! 15$, the leading terms in Stirling’s approximation or $F(z)$ given by Eq. (\[fiftynine\]) dominate, but for $N \!>\! 30$, the remainder and truncated sum dominate the calculations. Nevertheless, when all the quantities in Eq. (\[fiftyeight\]) are added together, they always yield the exact value of $\ln \Gamma(3)$ regardless of the value of $N$, provided a sufficient number of decimal places has been specified in order to allow the cancellation of decimal places to occur when the truncated sum and the regularized value of its remainder are combined. The same analysis is repeated for $z \!=\! 1/10$, which could never be studied in standard Poincar${\acute {\rm e}}$ asymptotics. For such a value the leading terms in Stirling’s approximation or $F(z)$ are not accurate. Hence, it is vital that the truncated sum of the asymptotic series and the regularized value of its remainder must be included to obtain $\ln\Gamma(1/10)$. In fact, because there is no optimal point of truncation, the remainder and truncated sum diverge far 