Return to Revisions

Just solve for the sum in the addition formula (31) of Neumann 1867, p. 65 (also in Watson p. 128, or more conceptually Vilenkin 1968, formula (4) p. 209): $$ J_0\left(2r\sqrt{\frac{1-\cos\theta}2}\right) = J_0(r)^2 + 2\sum_{n=1}^\infty J_n(r)^2\cos(n\theta). $$