= Error-function smoothing of a Stokes multiplier
{title2=$\operatorname{erfc}(\mu/2)$}
The pole contour in a <Gaussian saddle coalescing with a simple pole> changes the multiplier smoothly. For the lower contour, $\int_{\mathcal C_-}e^{-u^2-i\mu u}\,du/u=i\pi\operatorname{erfc}(\mu/2)$. This follows by integrating $-i\sqrt\pi e^{-\mu^2/4}$ and adding the indentation contribution $i\pi$. The transition width is inverse square root of the large parameter; on a <Stokes line> the multiplier takes half its switched-on value.
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