I have the following fuction with T=2 and x defined for [-1,1]
$f(x) = \begin{cases} 2(x+1) & -1 \leq x\leq -0.5 \\ 1 & -0.5 \leq x\leq 0.5 \\ 2(1-x) & 0.5 \leq x\leq 1 \\ \end{cases} $
Now I have this question:
Is it true that the coefficients of the exponential Fourier series of $f(x) $ satisfy $c_n = ic_{-n}$?
I'm not really sure how to prove this is true or false.