If $f$ is analytic on $B(z_0, R)$, does that imply $f$ has a power series expansion centered at $z_0$ with radius of convergence $R$?

Question

I know that if a power series $f:=\sum_{n=0}^{\infty}a_n(z-z_0)^n$ has radius of convergence $R$, then $f$ is analytic on $B(z_0,R)$. I wonder if the converse of this statement is true. That is, suppose that a function $f:\mathbb{C} \to \mathbb{C}$ is analytic on $B(z_0,R)$ and that there exists a point $\xi\in\partial B(z_0,R)$ at which $f$ is not analytic. Then does it follow that $f$ has a power series expansion around $z_0$ with radius of convergence $R$?