I want to write the exponential form of furiour series of the function $f(x)=x^2$ where $x\in[0,2\pi]$ and T=$2\pi$. I know it is in the form, $$f(x)=\sum_{n=-\infty}^{+\infty}c_n e^{\tfrac{in\pi x}l}$$ But I've been told that we can sometimes evaluate $c_0$ separately and add this to the RHS of the above equation. So I got,
$$f(x)=\frac{4\pi^2}3+\sum_{n=-\infty}^{+\infty}\frac{2+2n\pi i}{n^2}e^{inx}$$But it doesn't look right to me since for $n=0$, $\dfrac{2+2n\pi i}{n^2}$ is undefined and I think it is necessary to exclude the case $n=0$ from the summation. Am I right? And if this is the case, is there any notation to denote the exclusion of $n=0$ in $\sum_{n=-\infty}^{+\infty}\frac{2+2n\pi i}{n^2}e^{inx}$?