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Unformatted text preview: , otherwise. The Fourier coeﬃcient c j of the Fourier series ∑ ∞ j =-∞ c j e 2 πijx for f is given by c j = Z 1 / 2-1 / 2 f ( x ) e-2 πijx dx. Evaluate the integral to show that c = 1 and if j 6 = 0, c j = 0 if j is even and c j = 2(-1) k π (2 k + 1) 1 2 if j = 2 k + 1 is odd. Note: You can evaluate the integral by breaking it into real and imagi-nary parts, but you can also use the fact that the antiderivative of e-2 πijx is e-2 πijx / (-2 πij )....
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- Fall '11
- Fourier Series, Leonhard Euler