PROJECT. Complex Fourier Coefficients. It is very
Chapter 11, Problem 11.4(choose chapter or problem)
PROJECT. Complex Fourier Coefficients. It is very interesting that the Cn in (6) can be derived directly by a method sinlllar 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 -7r to 7r on both sides (allowed, for instance, in the case of uniform convergence) to get I7T f(x)e-imx dx = ~ cn I7T ei(n-m)x dx. -7r n=-OO-71" Show that the integral on the right equals 27r when n = m and 0 when n =1= m [use (3b)], so that you get the coefficient formula in (6).
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