Let the z-axis be the symmetry axis for an infinite number of identical rings, each with charge Q and radius R. There is one ring in each of the planes z = 0, z = ±b, z = ±2b, etc. Exploit the Fourier expansion in Example 1.6 to find the potential everywhere in space. Check that your solution makes sense in the limit that the cylindrical variable ρ >> R, b.

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I(y)Ka(y) — Ia(y)K'(y) = 1/y.