# Fourier series question

• Nov 24th 2008, 06:51 AM
mbbx5va2
Fourier series question
Hi, i'm having trouble with this problem. The question is: expand the function f(x)=x where x belongs to [0,2pi] into a real fourier series. Any help would be much appreciated thanks.
• Nov 24th 2008, 08:12 AM
Chris L T521
Quote:

Originally Posted by mbbx5va2
Hi, i'm having trouble with this problem. The question is: expand the function f(x)=x where x belongs to [0,2pi] into a real fourier series. Any help would be much appreciated thanks.

By definition of the Fourier Series, $f(x)=\frac{a_0}{2}+\sum_{n=1}^{\infty}a_n\cos(nx)+ b_n\sin(nx)$ where the Fourier coefficients are found as follows:

$a_0=\frac{1}{\pi}\int_0^{2\pi}f(x)\,dx$

$a_n=\frac{1}{\pi}\int_0^{2\pi}f(x)\cos(nx)\,dx$

$b_n=\frac{1}{\pi}\int_0^{2\pi}f(x)\sin(nx)\,dx$

Try to find these Fourier Coefficients when $f(x)=x$...or is this where you're stuck?

--Chris
• Nov 24th 2008, 08:35 AM
mbbx5va2
Hi, thanks for the reply but i've just found a thread from someone else concerning the same question.