# Notes - Complex Analysis MT23, Analytic functions

### Flashcards

What does it mean for a function $f : U \to \mathbb C$ where $U$ open to be analytic?

For every $z _ 0 \in U$ there exists $r > 0$ with $B(z _ 0, r) \subseteq U$ such that there is a power series $f(z) = \sum^\infty _ {k=0} a _ k(z - z _ 0)^k$ with radius of convergence at least $r$.