I'm working on a problem concerning fourier, but got stuck at two points.
Here is the question:
3)
Find the fourier series of the function $$f(x) =
\begin{cases}
1, & \text{if $|x|<1$ } \\
0, & \text{if $1\leq|x|<2$ }
\end{cases}$$
Added is the solution:
In the first step I dont get why they use $f(x)=0$ if $-2\leq x\leq -1$ and $f(x)=0$ if $1\leq x\leq 2$
Why smaller/bigger or $\mathbf {equal}$ to $2$ and $-2$? Since in the problem it says $|x|<2$
Then in the final step after the coefficients are calculated I don't understand how they get to this fourier series, normally you use this rule of $a_0+ \sum a_ncos(\frac{n\pi x}{L})+ b_n sin(\frac{n\pi x}{L})$ but here in the final answer there are no cosines.
Thanks in advance :)