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Homework Help: Fourier series

  1. Sep 23, 2010 #1
    1. The problem statement, all variables and given/known data
    Expand the function in to Fourier series
    [tex] f(x) = coshx, |x|\leq \pi[/tex]



    2. Relevant equations

    Fourier series will be
    [tex] C_{n}=\frac{1}{2\pi}\int_{-\pi}^{\pi}(\frac{e^{x}+e^{-x}}{2}})e^{-inx}}dx[/tex]

    [tex] \frac{1}{4\pi}\int_{-\pi}^{\pi}({e^{x}e^{-inx})dx+ \frac{1}{4\pi}\int_{-\pi}^{\pi}(e^{-x}e^{-inx})dx[/tex]


    3. The attempt at a solution


    I calculate both integrals separately

    [tex] \frac{1}{4\pi}\int_{-\pi}^{\pi}({e^{x}e^{-inx})dx=\frac{1}{4\pi}\int_{-\pi}^{\pi}({e^{x-inx})dx=\frac{1}{4\pi}\frac{e^{x-inx}}{1-in}[/tex]

    I substitute [tex] x=\pm\pi \Rightarrow \frac{(-1)^n}{1-in}[e^{\pi}-e^{-\pi}][/tex]
    1. The problem statement, all variables and given/known data

    and the other one gives me

    [tex]\frac{(-1)^n}{-1-in}[e^{-\pi}-e^{\pi}][/tex]


    is this correct so far?
     
  2. jcsd
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