Definition:Analytic Function/Complex Plane

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Definition

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 $U$.


Also known as

An analytic complex function is also referred to as a holomorphic function.


Also see


Sources