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Math Help - Fourier Series Problem.

  1. #1
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    Question 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.
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  2. #2
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    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)
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  3. #3
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    Re: Fourier Series Problem.

    I haven no idea what you are talking about :S
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  4. #4
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    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)]
    Last edited by stripe501; April 10th 2012 at 02:04 AM. Reason: Added missing bracket to function
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  5. #5
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    Re: Fourier Series Problem.

    halp?
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  6. #6
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    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.
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