1. The problem statement, all variables and given/known data A chare +Q is distributed uniformly along the z axis from z=-a to z=+a. Find the multipole expansion. 2. Relevant equations Here rho has been changed to lambda, which is just Q/2a and d^3r to dz. 3. The attempt at a solution I have solved the problem correctly (confirmed since the answer is given in the book.) I could not figure out how to solve the problem. Just to see what happened, I took the legendre polynomial factor outside the integral, and I stumbled onto the correct answer. Was my attempt incorrect, and my correct solution a lucky coincidence, or was my method correct? If my method was correct, why are you allowed to take the legendre polynomial outside the integral? It seems to me that theta must certainly depend on z (I was convinced of this based on fig. 3.28 in Griffiths). It can also be seen from: where r corresponds to z in my problem. Certainly in the figure above if you changed r theta would also change.