Two-dimensional modified Helmholtz fundamental solution
= Two-dimensional modified Helmholtz fundamental solution
{title2=$\Gamma_m(r)=K_0(mr)/(2\pi)$}
For $m>0$, the decaying fundamental solution of $-\Delta+m^2$ in two dimensions is $K_0(mr)/(2\pi)$, with $K_0$ the <Modified Bessel function of the second kind>. <Green second identity> reconstructs an interior solution from its <Dirichlet boundary condition> $f$ and outward <normal derivative> $h$ as $q(r)=\int_{\partial\Omega}(\Gamma_m h-f\partial_n\Gamma_m)ds$.