I've been studying Fourier Series and I think I have a decent understanding of it now, I can work out the Fourier series of most 2-pi periodic functions, however, I came across a question where the function was not 2-pi periodic, the period of the function was '-2 <= x <= 2'.
I've haven't yet figured out how to tackle a question set out like this. I'm just wondering if anyone can explain how to obtain the Fourier series for a function that isn't 2-pi periodic? What are the extra steps we have to take? My initial idea is that we try find a way to transform it into a 2-pi periodic function and then solve as normal but I'm not sure how I would achieve this.
Any help would be appreciated.
The functions $\sin(2\pi nx/L)$ and $\cos(2 \pi nx/L)$ have period of length $L$, and can be used to write a Fourier series for a function with period $L$.