From my lecture notes I was given, the definiton of an analytic function was as follows:
A function f is analytic at xo if there exists a radius of convergence bigger than 0 such that f has a power series representation in x-xo which converges absolutely for [x-xo]<R
What I undestand is that for all x values, |x-xo| must be less than R (radius of convergence) in order for f to be analytic at xo.
Convergence in a general sense is when the sequence of partial sums in a series approaches a limit
Is my understanding of convergence and analytic functions correct ?