# Holomorphic function

Holomorphic function is concept of the theory of functions of complex variables that refers the the existence of the derivative.

## Definition

Assume, for any $$z \in C\subseteq \mathbb C$$, there is defined function $$f(z) \in \mathbb C$$ such that for any $$z \in C$$ there exist the derivative

$$\displaystyle f'(z)= \lim_{t \rightarrow 0,~ t\in \mathbb C}~ \frac{f(z\!+\!t)-f(z)}{t}$$

Then, function $$f$$ is called holomorphic on $$C$$.

## References

http://en.citizendium.org/wiki/Holomorphic_function
http://en.wikipedia.org/wiki/Holomorphic_function
http://www.proofwiki.org/wiki/Definition:Holomorphic_Function
http://www.proofwiki.org/wiki/Equivalence_of_Definitions_for_Analytic_Function