I'm studying from my class notes and I don't understand a step. The function is analytic over .
Furthermore . From this I get that the radius of convergence of the function is 1, ok but my problem is how could they write the function log(x+1) as an infinite series whose "center" is 0 while the function isn't analytic there. I know I'm not expressing myself well. I mean why do they used instead of say any number greater than 2 (since the radius of convergence is 1 and the function isn't analytic for any real number lesser or equal than 1).
So it would mean that any function, regardless of analytic or not, can be written in terms of infinite series? It seems to contradict a theorem that I can't find at the moment.
Any help is greatly appreciated, as usual.