I saw this question on my book (Complex Analysis/Donald & Newman):
Let $f(z)$ be an analytic function in the punctured plane $\{ z \mid z \neq 0 \}$ and assume that $|f(z)| \leq \sqrt{|z|} + \frac{1}{\sqrt{|z|}}$. Show that $f$ is constant.
How I can do it by Cauchy's formula?!