- #1
TFM
- 1,026
- 0
Homework Statement
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.
Homework 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]
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