While reading a text about the application of complex analysis to elasticity, I thought about the following problem:
Let $f$ be a holomorphic function in all $\mathbb{C}$. Is $f$ uniquely determined by the list of its poles and zeros (and their orders, of course)?
EDIT: By "the list of its poles and zeros" I include also the point at $\infty$. I assume that $f$ has a proper limit at infinity.
I guess that if that was true it was an undergrad theorem that I'm supposed to know.