= Error-function logarithmic switchback
{title2=$-\tfrac14\varepsilon\log\varepsilon\operatorname{erf}z$}
If an <outer expansion> contains $-(\varepsilon/2)\log x$ and the layer coordinate is $x=\sqrt\varepsilon z$, its overlap contains $-(\varepsilon/2)\log z-(\varepsilon/4)\log\varepsilon$. Matching forces an <inner expansion> term $-(\varepsilon/4)\log\varepsilon\operatorname{erf}z$ when that homogeneous profile tends to one in the overlap and vanishes at the boundary. The logarithm multiplies the matching profile, rather than an arbitrary constant.
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