# Fourier Series Problem.

Printable View

• April 9th 2012, 09:12 PM
stripe501
Fourier Series Problem.
I have this question on my assignment:
Write the Fourier series for the 2-periodic function defined
as f(x) = |x| on [-1, 1] and then by choosing the correct value of x,
find the sum form j = 0 to infinity [1/(2j+1)^2].
Plot your result on the same axes as the
function to compare.

I got got the Fourier Series and have plotted them and compared them ez. But I'm not sure what the part about find the correct value of x to solve the sum is talking about. Please help.
• April 9th 2012, 11:27 PM
a tutor
Re: Fourier Series Problem.
Without doing the work I'm guessing that with the right choice of x value you will get

|x| = constant + constant * (your sum)
• April 10th 2012, 12:59 AM
stripe501
Re: Fourier Series Problem.
I haven no idea what you are talking about :S
• April 10th 2012, 01:02 AM
stripe501
Re: Fourier Series Problem.
I know what the Fourier Series is if that helps at all, it's:
f(x) = (1/2)+sum k=1 to infinity 2[((-1)^k-1)/(pi^2*k^2))*cos(k*pi*x)]
• April 10th 2012, 05:22 AM
stripe501
Re: Fourier Series Problem.
halp? :(
• April 10th 2012, 05:26 AM
a tutor
Re: Fourier Series Problem.
Strange, I make it $\frac{1}{2}-\frac{4}{\pi^2}\left(\cos(\pi x)+\frac{\cos(3\pi x)}{9}+\frac{\cos(5\pi x}{25}...\right)$ and with x=1 it certainly gives the correct answer for the sum.