- #1

- 3

- 0

## Homework Statement

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]

## Homework Equations

Parsevals Theorom,

Real Fourier series

## 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 :)

Last edited: