I think I have some understanding of what an analytic function is — it is a function that can be approximated by a Taylor power series. But why is the notion of "analytic function" so important?
I guess being analytic entails some more interesting knowledge rather than just that it can be approximated by Taylor power series, right?
Or, maybe I don't understand (underestimate) how a Taylor power series is important? Is it more than just a means of approximation?
