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Let f(x)= exp(ix), x = (0,r) plus periodic extension with period = πt. (a) Find the complex Fourier series of f(x). (b) Use Parseval's theorem to show 1 - (2r-1)² 4 (c) From the result of (a), write out Fourier series of cos(x), x € (0, π) plus periodic extension with period = π, sin(x), x € (0, π) plus periodic extension with period = π.

Let f(x)= exp(ix), x = (0,r) plus periodic extension with period = πt. (a) Find the complex Fourier series of f(x). (b) Use Parseval's theorem to show 1 - (2r-1)² 4 (c) From the result of (a), write out Fourier series of cos(x), x € (0, π) plus periodic extension with period = π, sin(x), x € (0, π) plus periodic extension with period = π.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f(x)= exp(ix), x = (0,r) plus periodic extension with period = πt. (a) Find the complex Fourier series of f(x). (b) Use Parseval's theorem to show 1 .(2r-1)² (c) From the result of (a), write out Fourier series of cos(x), x € (0, π) plus periodic extension with period = π, sin(x), x € (0, π) plus periodic extension with period = π.
Transcribed Image Text:Let f(x)= exp(ix), x = (0,r) plus periodic extension with period = πt. (a) Find the complex Fourier series of f(x). (b) Use Parseval's theorem to show 1 .(2r-1)² (c) From the result of (a), write out Fourier series of cos(x), x € (0, π) plus periodic extension with period = π, sin(x), x € (0, π) plus periodic extension with period = π.
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