I'm trying to understand the main differences (if there are) between analytic and holomorphic functions.
I know that a function is holomorphic in a connected open set if it is differentiable in each point.
Also I know that a function is analytic if it can be written in terms of Taylor expansion in each neighborhood of $x_0$.
So which are the differences between these two classes of functions? Or which topic should I use to show they are the same thing?
Thank you!