Poles and Zeroes of Meromorphic Function are of Finite Order

Theorem

Let $f: D \to \C$ be a meromorphic function on the open subset $D$ of $\C$.

Zeroes of Meromorphic Function are of Finite Order

The zeroes of $f$ are of finite order.

Poles of Meromorphic Function are of Finite Order

The poles of $f$ are of finite order.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): meromorphic function