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  1. #1
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    Post fourier

    Solve this!!



    ∞∑n=0 (sin2nө/n!)
    Last edited by kamaksh_ice; August 10th 2007 at 05:06 AM. Reason: note: the limit is from n=0 to n= ∞
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    Quote Originally Posted by kamaksh_ice View Post
    Solve this!!



    ∞∑n=0 (sin2nө/n!)
    I'm very rusty on this, but assume we have a function f(x) such that the Fourier sine series for f is
    F[f(x)] = \sum_{n = 0}^{\infty}\frac{1}{n!}sin(2n \theta)

    Then we need to invert the Fourier sine series, which if I remember correctly means that
    f(x) = \frac{1}{2 \pi} \int_{-\infty}^{\infty} \sum_{n = 0}^{\infty}\frac{1}{n!}sin(2n\theta) sin(x \theta) d \theta

    Someone needs to check me on that result, but it's going to be something of the sort. (The best way for you, kamaksh_ice, to check me is to do the problem then take the Fourier sine series of the result and see if you get your original series back.)

    -Dan
    Last edited by topsquark; August 10th 2007 at 05:27 AM. Reason: Cleaned up some details
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