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Math Help - Fourier Series Help

  1. #1
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    Fourier Series Help

    So I found the complex version of the fourier series of e^x.

    \sum_{n=-\infty}^{\infty}(-1)^n(\frac{l+in\pi}{l^2+n^2{\pi}^2})(sinh(l))e^{\f  rac{in{\pi}x}{l}}

    I was wondering if there is a way to convert this to the real full fourier series form.

    Thanks
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  2. #2
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    (Pretend all the following functions are well-behaved).

    Let f(x) = \sum_{n=-\infty}^{\infty} a_n e^{inx} where f(x) is a 2\pi-periodic function.
    We can write,
    f(x) = a_0 + \sum_{n=1}^{\infty} [(a_n+a_{-n})\cos nt + i (a_n + a_{-n}) \sin nt ]
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