# Difference between revisions of "Holomorphic function"

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Then, function \(f\) is called holomorphic on \(C\). |
Then, function \(f\) is called holomorphic on \(C\). |
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==Infinite detivatives== |
==Infinite detivatives== |

## Latest revision as of 21:08, 25 January 2021

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

## Contents

## 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 \(C\).

## Cauchi-Riemann

## Infinite detivatives

## Other notations

## Examples

## 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