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Math Help - Fourier series

  1. #1
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    Fourier series

    Define f(t)=e^{-t} on [-\pi,\pi)  and extend f to be 2\pi-periodic.Find the complex Fourier series of f.
    Then, apply Parseval's relation to f to evaluate  /sum {1/(1+k^2)} .
    I know how the complex fourier series looks like but I don't know how to extend it periodically
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  2. #2
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    Quote Originally Posted by AkilMAI View Post
    Define f(t)=e^{-t} on [-\pi,\pi)  and extend f to be 2\pi-periodic.Find the complex Fourier series of f.
    Then, apply Parseval's relation to f to evaluate  /sum {1/(1+k^2)} .
    I know how the complex fourier series looks like but I don't know how to extend it periodically
    The function e^{t} is not peroidic, but when you find its Fourier series on [-\pi,\pi) and then let t \in \mathbb{R} not just the interval you will be a new function that is periodic on all of \mathbb{R} (It will just be translated copies of the series on the original interval)
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  3. #3
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    Quote Originally Posted by AkilMAI View Post
    Define f(t)=e^{-t} on [-\pi,\pi)  and extend f to be 2\pi-periodic.Find the complex Fourier series of f.
    Then, apply Parseval's relation to f to evaluate  /sum {1/(1+k^2)} .
    I know how the complex fourier series looks like but I don't know how to extend it periodically
    http://www.mathhelpforum.com/math-he...em-167764.html

    Kind regards

    \chi \sigma
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  4. #4
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    Quote Originally Posted by AkilMAI View Post
    Define f(t)=e^{-t} on [-\pi,\pi) and extend f to be 2\pi-periodic.Find the complex Fourier series of f.
    Then, apply Parseval's relation to f to evaluate  /sum {1/(1+k^2)} .
    I know how the complex fourier series looks like but I don't know how to extend it periodically
    Thread closed under rule #6: http://www.mathhelpforum.com/math-he...hp?do=vsarules
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