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Math Help - convolution fourier series question

  1. #1
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    convolution fourier series question

    P_r is defined as:
    P_r(x)=\frac{1-r^2}{1-2r\cos x +r^2}
    and
    P_r(x)=\frac{1-r^2}{1-2r\cos x +r^2}=\sum_{n=-\infty}^{\infty}r{|n|}e^{inx}
    and
    f(x)=\sum_{-\infty}^{\infty}c_ne^{inx}
    which is continues

    i need to prove that:
    f_r(x)=\frac{1}{2\pi}\int_{-\pi}^{\pi}p_r(t)dt=\sum_{n=1}^{\infty}c_nr^{|n|}e^  {inx}

    the solution says to use the convolution property
    c_n(f)=c_n
    c_n(P_r)=r^{|n|}
    c_n(f_r)=c_n r^{|n|}

    but i cant see how the multiplication of those coefficient gives me the
    expression i needed to prove

    ?

    i only got the right side not the left integral

    ??
    Last edited by transgalactic; December 28th 2009 at 09:23 AM.
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