I am doing a Laplace's equation in spherical coordinates and have come to a part of the problem that has the integral... ∫ P(sub L)*(x) * P(sub L')*(x) dx (-1<x<1) The answer to this integral is given by a Kronecker delta function (δ)... = 0 if L ≠ L' OR.... = 2/(2L+1)*δ if L = L' (where δ = 1) I believe the reason why the integral is equal to zero when L ≠ L' is because of the orthogonality of Legendre polynomials, however i cannot figure out how the integral is equal 2/(2L+1). If L = L' then the integral would equal... ∫ [P(sub L)*(x)]^2 dx I tried to use a simple power rule of integration to solve the above integral, but i am afraid my method is flawed. Any suggestions? Pre-emptive thanks to whomever takes the time to help!!