1. The problem statement, all variables and given/known data (Griffith' electrodynamics, problem 3.22): a spherical shell (radius R) carries uniform charge sigma0 on the "northern" hemisphere, –sigma0 on the "southern" one. Find the potential inside and outside the sphere, calculating coefficients explicitly up to A6 and B6. 2. Relevant equations Attached document: i don't know how to paste equations on this page, it's my first time.. for reference, it's the same basic solution developed for example 3.9 of the book, p.142 3. The attempt at a solution the above makes reference the method of separation of variables (in spherical coordinates), with solution in the form of a Fourier series with coefficients involving legendre polynomials (variable = "cosine theta"): since the charge density is constant over each hemisphere, i end-up with no polynomial at all.. While an infinite series seems expected (this would be more clear if i could paste my equations); i guess i don't know where to plug-in the right boundary condition.. Anybody could enlight me?