Definition:Singular Point/Complex

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.