Is it possible to expand the Green's function for Laplacian (with Dirichlet boundary conditions) in Cartesian coordinates?
$\bigtriangledown ^2G(x,y,z|x^\prime,y^\prime,z^\prime)=\delta(x-x^\prime)\delta(y-y^\prime)\delta(z-z^\prime)$
$G(x,y,z|x^\prime,y^\prime,z^\prime)=\frac{1}{|\vec{r}-\vec{r^\prime}|}+F(x,y,z), \bigtriangledown ^2F(x,y,z)=0$
