(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 :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Fourier series and reimann zeta

**Physics Forums | Science Articles, Homework Help, Discussion**