= Boundary-decaying Green kernel for an inverse-square differential operator
{title2=$G(x,\xi)=-\min(x,\xi)^2/[3\max(x,\xi)]$}
For $L=d^2/dx^2-2/x^2$ on $x>0$, the homogeneous solutions $x^2,x^{-1}$ satisfy respectively the zero and infinity <boundary conditions>. Their <Wronskian> is $-3$. The displayed <Green's function> is continuous at $x=\xi$ and its first <derivative> has jump one, so $L_xG=\delta(x-\xi)$ in the <distribution> sense. Integration against a compactly supported forcing gives the unique solution decaying at both boundaries.
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