satisfies:

so where: . Choose for and for .

so

leading to a total green's functions of:

The z coordinate has been given a special treatment. It'd be nice to have a green function which is symmetric in all coordinates. This can be done using a laplacian eigenfunction expansion. The rectangular eigenfunctions are:

where ... and similar relations

This gives .

Comparing these green functions, you get:

which can be thought of as a fourier expansion or the series can just be summed.

source psfile jl@crush.caltech.edu index