(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the Fourier series corresponding to the following functions that are periodic over the

interval [tex][-\pi,\pi][/tex]

[tex] f(x) = 1, -\pi/2 < x< \pi/2; f(x) [/tex] otherwise.

2. Relevant equations

Fourier Series:

[tex] f(x) = \frac{1}{2}a_0 + \sum^\infty_{n=1}a_n cos\frac{2*\pi*n*x}{l} + \sum^\infty_{n=1} b_n sin\frac{2*\pi*n*x}{l}[/tex]

[tex] \frac{1}{l}\int^{l/2}_{-l/2}f(x) dx [/tex]

[tex] a_n = \frac{1}{l}\int^{l/2}_{-l/2}f(x) cos frac{2*\pi*n*x}{l}dx [/tex]

[tex] a_n = \frac{1}{l}\int^{l/2}_{-l/2}f(x) sin frac{2*\pi*n*x}{l}dx [/tex]

3. The attempt at a solution

So far I have:

[tex] a_0 = 1 [/tex]

[tex] a_n = \frac{1}{\pi n}[sin(nx)]^{\pi/2}_{-\pi/2} [/tex]

[tex] b_n = -\frac{1}{\pi n}[cos(nx)]^{\pi}_{-\pi} [/tex]

But I am not sure what to do now. I seem to be mainly confused about the n's

TFM

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# Homework Help: Fourier Series Question

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