I calculated the Fourier series of the 2$π$-periodic function $f(x)=e^{ax}$ for $x ∈ [0,2π)$ and it results
$$f(x)=\frac1π\big(e^{2πa}-1\big)\left(\frac1a+\sum^\infty_{n=1}\frac{a\cos(nx)-n\sin(nx)}{n^2 + a^2}\right)$$
Now I have to use this result to calculate $\sum^\infty_{n=1}\frac{1}{n^2+a^2}$
Should I now calculate the series at $x=0$? Or some non-continuous point of the periodic function? I'm a bit confused about this.