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stunner5000pt
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[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!
[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!
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