If I am given a function
$$ f(x) = \left\{ \begin{array}{ll} 2 & \quad x \in (0,6) \\0 & \quad x\in(0,-6) \end{array} \right. $$
$I=(-6,6)$
and I want to find the complex series representation, is it correct that
$\mathbb{C}_n=\frac{1}{12} \int_0^6(2*\exp(-\frac{-xni\pi}{12})) dx$?
Because the first half of interval contribution would just be $0$, Right?
To The MODERATOR .. I am not fully sure about it, but hope it improves upon earlier..
The complex Fourier series is defined as: \begin{equation} f(x)=\sum_{-\infty}^{+\infty} c_n e^{i n x \frac{2 \pi}{L}} \end{equation} where \begin{equation} c_n=\frac{1}{L} \int_{0}^{L} f(x) e^{-i n x \frac{2 \pi}{L}} dx \end{equation} In your case $L=3$. Of course the Fourier series is periodic.