In the Feynman Lectures, Volume II, Chapter 7, the final two pages (7-10 and 7-11), Feynman describes an infinite array of parallel charged wires and uses a fourier series to solve for the field above them. He shows that the series can be expressed entirely in terms of cosine terms and that the coefficients have the value F(n)*e^(-z/k) where n is the order of the term, z is the distance from the plane of the wires, and k is a constant. What I don't understand is how one would then find the function F(n) (which he does not show). Later (in chapter 12 of the same volume) says that F(1) is twice the average field strength and that solving for the function F(n) is straightforward (in relation to another, related problem). How would you go about solving for the function? I've found the field via the coulomb interaction at several points where symmetry makes it easy but I'm not sure how this helps. Any help would be appreciated.