Let there be a function: $$F:\mathbb{R}\rightarrow\mathbb{C}$$ $$F(x)=\sum_{n\in \mathbb{Z}}a_ne^{inx}$$
For some real-valued sequence $(a_n)_{n\in \mathbb{Z}}$
How to extract the zeroth coefficient ($a_0$) ?
I was considering the usage of derivatives in this case, but i didn't figure out how to do this.
Thank you for help.