Fourier Series of Periodic Function

[he1senberg]

Homework Statement

http://imageshack.us/photo/my-images/824/50177563.png/
I need to find the Fourier coefficients and estimate the series for certain values of n. (4, 20 and 100)

Homework Equations

http://imageshack.us/photo/my-images/839/32591148.png/

The Attempt at a Solution

I was unsure about what to do and found the equation above. So I used it and b coefficient was 0. I set the period 2L as 3, and set -L -3/2 and L as 3/2. So the total value I found was
a0 + Σ(3/(n*pi) - 27/(2*(n*n*n)*(pi*pi*pi)))*sin(2*n*pi/3)+ 9*cos(2*n*pi/3)/(2*(n*n)*(pi*pi))*(cos(2n*pi*x/3)

I managed to get some result but I am not sure if my results are correct, as the graph of the function is discontinuous at the ends of parabola. So, do you think my answer is correct? If not, how can I fix it?

 

[vela]

I have Mathematica crank out the integral, and it produced almost the same result. The only difference is that there shouldn't be 2 in the denominator of the last term.

What did you get for a₀?

 

[he1senberg]

Thanks for reply.

I think a0 was 2/9 or 4/9, I don't have the paper with me right now. I think that last 2 should be 4. Other than that, do you think my procedure to deal with problem is correct? Because I couldn't really make sure that I solved the problem correctly.

 

[vela]

Yes, your method sounds fine. It's just getting the math right now. a₀ is the average value of the function over one period, so it should be 2/9.