Definition:Singular Point/Complex
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Definition
Let $U \subseteq \C$ be an open set.
Let $f : U \to \C$ be a complex function.
A singular point of $f$ is a point at which $f$ is not analytic.
Examples
Reciprocal of $\paren {z - 2}^2$
Let $f$ be the complex function defined as:
- $\map f z = \dfrac 1 {\paren {z - 2}^2}$
Then $f$ has a singular point at $z = 2$.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): singular point (singularity): 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): singular point (singularity): 1.