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  "body": "\n## Summary\n\nThe logarithmic kernel is the function $k(z, w) = \\log(1/\\abs{z - w})$ of two points of the plane.\nIt is the planar counterpart of the [[Newtonian kernel|6TJTWQ5HCR]].\nIt equals $2\\pi$ times the [[fundamental solution of the Laplacian|BSJ8X2XRN9]] of the plane, translated to the pole $w$.\nIntegrating it against a measure gives the logarithmic potential, which links potential theory with complex analysis, polynomial approximation and the distribution of zeros of polynomials.\nUnlike the Newtonian kernel, it takes negative values when the two points are more than one unit apart.\n\n## Explanations\n\n### L1 human\n\nIn the plane, the potential of a point charge does not decay like one over the distance.\nIt changes like the logarithm of the distance, which grows without bound but very slowly.\nThe logarithmic kernel is $\\log(1/\\abs{z - w})$: it is large and positive near $w$, zero on the unit circle around $w$, and negative farther out.\nFor example, at distance $e$ from the pole its value is $-1$.\n",
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