Question

Fourier series

Answer 1

I need find the Fourier Cosine series of f(x) = x for x in [0, π]

Answer 2

what is this ? sawtooth function?

Answer 3

I find \[a_{n}=π/2\]

Answer 4

use integration by parts.

Answer 5

and \[a_{n}=\frac{ 2*(-1)^n-2 }{ π*n^2 }\]

Answer 6

take 2 common, you see that for even values, a_n disappears

Answer 7

just put your series for odd values.

Answer 8

Yes but are my calculations for a.0 and a.n correct?

Answer 9

do you have mathematica?

Answer 10

a_0 seems to be correct

Answer 11

Because when I plot it. It seems not correct

Answer 12

put x=0 and see if you can get this or not
http://www.wolframalpha.com/input/?i=Sum%5B1%2F%282n%2B1%29%5E2%2C+%7Bn%2C+0%2C+Infinity%7D%5D

Answer 13

seems correct ... just get rid of that -1^n thing ... you only have odd terms.