Difference between revisions of "Holomorphic function"
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==Definition== |
==Definition== |
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| − | Assume, for any |
+ | 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 |
| − | : |
+ | :\(\displaystyle f'(z)= \lim_{t \rightarrow 0,~ t\in \mathbb C}~ \frac{f(z\!+\!t)-f(z)}{t} |
| − | + | \) |
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| − | Then, function |
+ | Then, function \(f\) is called holomorphic on \(C\). |
| + | ==Cauchi-Riemann== |
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| − | ==Cauchi–Riemann== |
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==Infinite detivatives== |
==Infinite detivatives== |
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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
