What is an analytic function?

This thread is just a bit more fun with pure maths of the kind they never bothered to teach you at school. You might though recall covering power series and the concept of convergence, e.g. the classic x^2 series which as you sum all terms to infinity it approaches a distinct value if x < 1. Even easier maybe is the one where if you go half the distance home and then you go half of the half and so on, you will never get home but will get infinitely close to it. Some series though go to infinity as our terms go to infinity. Now that is all well and good, but then we can get into more complicated series if we use complex numbers, so now we are operating in 2D. This is where we come across the difference between analytic functions and their non-analytic counterpart. An analytic function can be extrapolated, but a non-analytic one goes crazy at some point. See the video to see it in action. By the way, this guy is a really good maths teacher if you want to learn "real maths" as they say.