Definition:Isolated Singularity/Pole/Definition 1
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Definition
Let $U$ be an open subset of a Riemann surface.
Let $z_0 \in U$.
Let $f: U \setminus \set {z_0} \to \C$ be a holomorphic function.
Let $z_0$ be an isolated singularity of $f$.
Then $z_0$ is a pole if and only if:
- $\ds \lim_{z \mathop \to z_0} \cmod {\map f z} \to \infty$
Also see
- Results about poles in the context of Complex Analysis can be found here.
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): pole (in analysis)
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): pole (in complex analysis)