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Math Help - Fourier series question

  1. #1
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    Fourier series question

    Hi, i'm having trouble with this problem. The question is: expand the function f(x)=x where x belongs to [0,2pi] into a real fourier series. Any help would be much appreciated thanks.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mbbx5va2 View Post
    Hi, i'm having trouble with this problem. The question is: expand the function f(x)=x where x belongs to [0,2pi] into a real fourier series. Any help would be much appreciated thanks.
    By definition of the Fourier Series, f(x)=\frac{a_0}{2}+\sum_{n=1}^{\infty}a_n\cos(nx)+  b_n\sin(nx) where the Fourier coefficients are found as follows:

    a_0=\frac{1}{\pi}\int_0^{2\pi}f(x)\,dx

    a_n=\frac{1}{\pi}\int_0^{2\pi}f(x)\cos(nx)\,dx

    b_n=\frac{1}{\pi}\int_0^{2\pi}f(x)\sin(nx)\,dx

    Try to find these Fourier Coefficients when f(x)=x...or is this where you're stuck?

    --Chris
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  3. #3
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    Hi, thanks for the reply but i've just found a thread from someone else concerning the same question.
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