# Fourier Series Proof

1. Nov 2, 2005

### stunner5000pt

Show that
$$\lim_{n \rightarrow \infty} \int_{0}^{\pi} Ln(x) Sin(nx) dx$$

i was told to use this identity
given that $int f^2 \rho dx$ is finite then
$$c_{n}^2 \int_{a}^{b} \phi_{n}^2 \rho dx = \frac{(\int_{a}^{b} f \phi_{n} \rho dx)^2}{\int_{a}^{b} \phi_{n}^2 \rho dx} \rightarrow 0$$ 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?

Last edited: Nov 2, 2005
2. Nov 3, 2005

### stunner5000pt

can anyone help with this question?

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