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, $\displaystyle f(x)=\frac{a_0}{2}+\sum_{n=1}^{\infty}a_n\cos(nx)+ b_n\sin(nx)$ where the Fourier coefficients are found as follows:
$\displaystyle a_0=\frac{1}{\pi}\int_0^{2\pi}f(x)\,dx$
$\displaystyle a_n=\frac{1}{\pi}\int_0^{2\pi}f(x)\cos(nx)\,dx$
$\displaystyle b_n=\frac{1}{\pi}\int_0^{2\pi}f(x)\sin(nx)\,dx$
Try to find these Fourier Coefficients when $\displaystyle f(x)=x$...or is this where you're stuck?
--Chris