1. The problem statement, all variables and given/known data A thin spherical shell of radius R carries a surface charge density of the form kcos 3 θ . Find the electric field inside and outside the sphere and demonstrate explicitly that its components satisfy the relevant boundary conditions at the surface 2. Relevant equations The solution to Laplace's equation in spherical coordinates 3. The attempt at a solution I solved Laplace's equation using separation of variables, and got to where I would integrate to find the coefficients of the Fourier series, but that's where I'm stuck. I get that my coeffcient Al = k/2εRl-1∫cos3θ Pl(cos θ) sin θ dθ where Pl(cos θ) are the Legendre polynomials. I don't know how to integrate this, but intuitively shouldn't all terms that aren't P3 give me zero?