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Fourier Series Proof

  1. Nov 2, 2005 #1
    Show that
    [tex] \lim_{n \rightarrow \infty} \int_{0}^{\pi} Ln(x) Sin(nx) dx [/tex]

    i was told to use this identity
    given that [itex] int f^2 \rho dx [/itex] is finite then
    [tex] c_{n}^2 \int_{a}^{b} \phi_{n}^2 \rho dx = \frac{(\int_{a}^{b} f \phi_{n} \rho dx)^2}{\int_{a}^{b} \phi_{n}^2 \rho dx} \rightarrow 0 [/tex] and n approaches infinity

    here Cn are the Fourier Coefficients

    but how do i relate this to the problem i have
    would rho = log x and phi^2 = sin nx?
    Please help!
    Last edited: Nov 2, 2005
  2. jcsd
  3. Nov 3, 2005 #2
    can anyone help with this question?

    how would you go about solving it given the 'stuff' i have shown?

    Thank you in advance for your help!
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