I need help finding the Fourier coefficients of:
$f(x) =\begin{cases} \sum_{n=0}^\infty{\frac{e^{inx}}{1+n^2}} & \text{if } x\neq 2k\pi \\0& \text{if } x= 2k\pi \end{cases}$
And my main problem is that I know how to find the coefficients for each case separately, but how do I reach a final answer for the whole function?