It is very interesting that the cn in (6) can be derived directly by a method similar to that for an and bn in Sec. 11.1. For this, multiply the series in (6) by e-imx with fixed integer m, and integrate term wise from ?? ? to ? on both sides (allowed, for instance, in the case of uniform convergence) to get show that the integral on the right equals 2 ? when n = m and 0 when n ? m [use 3b)], so that you get the coefficient formula in (6).

[ f(x) e-imx dx = n=-5 Cn ein-m)x dx.