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 P: 169 1. The problem statement, all variables and given/known data The potential inside a spherical shell is given by: $V_{-}(x,y,z)= \frac{V_0}{R^2}(6z^2-3x^2-3y^2)$ $P_n(\cos(\theta ))$ where $\theta$ is the polar angle. The potential on the surface carries a surface charge density $\sigma$. Besides this, ther's no other charges and no outher field. The potential is rotational symmetric around the z-axis inside and outside, and goes to 0 far away from the sphere. b) express the potential inside the spherical shell using a LegendrePolynomial 2. Relevant equations In spherical coordinates i have: $V(r,\theta ) = \sum\limits_{l=0}^{\infty}(A_lr^lP_l(\cos(\theta)) = V_0(\theta)$ 3. The attempt at a solution This is how far i made it. Now i suppose i could multiply it with $P_{l'}(\cos( \theta ))\sin(\theta)$ and integrate, but i cant figure out how to simplify it and extract the solution. I'm aware that the functions' are orthogonal, but the integral of a sum is something i've never done before.