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Math Help - Fourier row

  1. #1
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    Fourier row

    I need to decide whether this trigonometrial row

    \Sum_{n=-25}^{50} (n^3+1)e^(I*n*x)

    is a Fourier row for a continous 2\pi periodic function?

    I dont know what to do when the row doesnt go from -\infty till \infty??

    Thanks for the help.
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  2. #2
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    Quote Originally Posted by teazy View Post
    I need to decide whether this trigonometrial row

    \Sum_{n=-25}^{50} (n^3+1)e^(I*n*x)

    is a Fourier row for a continous 2\pi periodic function?

    I dont know what to do when the row doesnt go from -\infty till \infty??

    Thanks for the help.
    [Note: the English word used here is series, not row.]

    The above expression is a finite sum of continuous 2\pi-periodic functions (n^3+1)e^{inx}, and is therefore continuous and 2\pi-periodic. It would not be possible to extend this particular series to an infinite trigonometric series \sum_{n=-\infty}^\infty  (n^3+1)e^{inx} because that series does not converge (the terms become unboundedly large as n\to\infty).
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