the multiplier behaves as a step-function there. In fact, close to a Stokes line, smoothing implies that the Stokes multiplier is almost equal to 1/2, not zero just before it or unity just past it. Therefore, one should not be able to obtain exact values for $\ln \Gamma(z)$ according to the conventional view if Stokes smoothing is valid. Since a Stokes line occurs at ${\rm arg}\,z \!=\! \pi/2$ in the Borel-summed asymptotic forms of Thm. 2.1, the numerical investigation in Sec. 3 is concluded by evaluating $\ln \Gamma(z)$ for $z \!=\! |z| \exp(i(1/2 +\delta)\pi)$, where $|z|$ is large and $\delta$ is both positive and negative with its magnitude ranging from 1/10 to $1/20\,000$. If the smoothing concept is correct, then the Stokes multiplier should be close to $1/2$ and the Stokes discontinuity term will be close to its value at $\theta
\!=\! \pi/2$. However, by using the asymptotic forms above and below the Stokes line, viz. the first and third forms in Eq. (\[fiftyeight\]), we obtain exact values of $\ln \Gamma(z)$ for all values of $\delta$ in Table \[tab5\], thereby confirming the step-function behaviour of the Stokes multiplier close to a Stokes line. Consequently, the conventional view of the Stokes 