Let $f$ be an analytic function in the annulus $ \{ 0<|z|
Is it true that the Laurent series expansion of $f$ about $0$ has a finite number of negative coefficients?
It came to my mind since $0=r=\limsup_{n\rightarrow\ \infty}|a_{n}|^{1/n}$ and therefore $|a_{n}|$ must be $0$ at some point.
Am I correct?