This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: , otherwise. The Fourier coecient c j of the Fourier series j =- c j e 2 ijx for f is given by c j = Z 1 / 2-1 / 2 f ( x ) e-2 ijx 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 (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 ijx is e-2 ijx / (-2 ij )....
View Full Document
- Fall '11