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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 – π to π on both sides (allowed, for instance, in the case of uniform convergence) to get show that the integral on the right equals 2 π when n = m and 0 when n ≠ m [use 3b)], so that you get the coefficient formula in (6). |
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