I am working on computing the Fourier Series for the function $$f(x) = \ \begin{cases} x,\hspace{0.5cm} -L<x<L \newline 0, \hspace{0.5cm} x \in \{-L,L\} \end{cases} \ $$
I know how to compute the coefficients for a Fourier Series using the formulas, however this function definition does not make sense to me. It seems that when f(x) is between -L and L, it is equal to both x and 0 simultaneously. Could someone please clarify this for me? Many thanks!