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We re-examine the exponentially improved expansion for $\log\,\g(z)$, firstconsidered in Paris and Wood in 1991, to point out that the recent treatment byKowalenko [Exactification of Stirling's approximation for the logarithm of thegamma function, arXiv:1404.2705] using his procedure of regularisation producesan equivalent result. In addition, we point out an error in his definition ofthe Stokes multiplier that leads him to make the incorrect statement that theStokes phenomenon is a jump discontinuity, rather than a smooth transition. Wesupply a numerical example that clearly demonstrates the smooth transition ofthe leading subdominant exponential $e^{2\pi iz}$ across the Stokes line$\arg\,z=\fs\pi$.

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