Thanks Goddar, as soon as I left it alone for a while the same answer came to me. Interestingly, your first answer sounds similar to what I was initially thinking as well, great minds & all that ;)
The problem: Find the potential between 2 concentric spheres, of radii a & b, where the potential of the spheres are held at Ca*P3(cos(t)) & Cb*P5(cos(t)), where P3 & P5 are the 3rd & 5th Legendre functions, t is theta & Ca & Cb are constants.
The general solution to Laplace with azimuthal...