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Aug24-11, 12:13 AM
P: 141
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 ?
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