.
.
The expansion of the angular portion of the delta function is: .
The laplacian can be expressed as 
where 
The Green's function will satisfy: 
Applying the poisson equation gives: 
where 
satisfies: 
. Then
for 
and 
for 
.
Some algebra gives 
Integrating the equation for , you get: 
This means 
with 
.
This means 
.