Category:Definitions/Analytic Complex Functions

This category contains definitions related to Analytic Complex Functions.
Related results can be found in Category:Analytic Complex Functions.

Let $U \subset \C$ be an open set.

Let $f : U \to \C$ be a complex function.

Then $f$ is analytic in $U$ if and only if for every $z_0 \in U$ there exists a sequence $\sequence {a_n}: \N \to \C$ such that the series:

$\ds \sum_{n \mathop = 0}^\infty a_n \paren {z - z_0}^n$

converges to $\map f z$ in a neighborhood of $z_0$ in $U$.