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Math Help - Fourier series help please

  1. #1
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    Fourier series help please

    Expand the following function in a Fourier series...

    f(x)=x (0 < x < 2pi)


    These fourier series make no freaking sense to me. Please help me.
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  2. #2
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    I guess everyone else hates these too.
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  3. #3
    MHF Contributor chisigma's Avatar
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    Is...

    f(x) = \frac {a_{0}}{2} + \sum_{n=1} ^{\infty} a_{n} \cdot \cos n x + b_{n}\cdot \sin nx (1)

    ... where...

     a_{n} = \frac{1}{\pi} \int _{0}^{2\pi} f(x)\cdot \cos nx\cdot dx

     b_{n} = \frac{1}{\pi} \int _{0}^{2\pi} f(x)\cdot \sin nx\cdot dx (2)

    In your case is f(x)=x so that...

    a_{0} = 2 \pi

    a_{n} =0, n\ge 1

    b_{n} = - \frac {2}{n}, n \ge 1 (3)

    Therefore the (1) becomes...

     f(x) = \pi - 2\cdot \sum _{n=1}^{\infty} \frac {\sin nx}{n} (4)

    Kind regards

    \chi \sigma
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