= Dipole Green tensor angular cancellation
{title2=$K=\frac{I}{3b}\delta-\operatorname{pv}\frac{3n\otimes n-I}{4\pi b r^3}$}
For the three-dimensional reference Green function $g(r)=1/(4\pi br)$, the distributional mixed Hessian $K=\nabla_x\nabla_{x'}g$ has the displayed contact and principal-value parts. Since the spherical mean of $n\otimes n$ is $I/3$, its ordinary dipole part has zero angular integral. Radial weighting therefore isolates the contact term, provided boundary truncation is absent or negligible in the bulk limit.
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