(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the Fourier series expansion for f(x)=[itex]x^{3}[/itex], a periodic function on -[itex]\pi[/itex]<x<[itex]\pi[/itex]

Use this to compute [itex]\zeta[/itex](6)=[itex]\sum\frac{1}{n^{6}}[/itex]

2. Relevant equations

Parsevals Theorom,

Real Fourier series

3. The attempt at a solution

I got the Fourier series to be [itex]\sum\frac{2(-1)^{n}(6-n^{2}\pi^{2})}{n^{3}}[/itex]sin(nx)

Using Parsevals theorom I got that [itex]\frac{\pi^{6}}{7}[/itex]=[itex]\sum\frac{4(6-(n\pi)^{2})^{2}}{n^{6}}[/itex]

The answer is supposed to be [itex]\frac{\pi^{6}}{945}[/itex] I think, I can't see where I went wrong :S

Thanks in advance :)

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# Homework Help: Fourier series and reimann zeta

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