Holomorphic function - Revision history

T: /* Cauchi–Riemann */

2021-01-25T12:08:20Z

Cauchi–Riemann

T: Text replacement - "\$([^\$]+)\$" to "\$\1\$"

2019-07-30T09:25:18Z

Text replacement - "\$([^\$]+)\$" to "\$\1\$"

Maintenance script at 05:32, 20 June 2013

2013-06-20T05:32:48Z

New page

'''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 $C$.

==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

[[Category:Holomorphic functions]]
[[Category:Mathematics]]
[[Category:MatAn]]
[[Category:Articles in English]]

← Older revision		Revision as of 12:08, 25 January 2021
Line 9:		Line 9:
	Then, function \(f\) is called holomorphic on \(C\).		Then, function \(f\) is called holomorphic on \(C\).

		+	==Cauchi-Riemann==
−	==Cauchi–Riemann==

	==Infinite detivatives==		==Infinite detivatives==

@@ Line 3: / Line 3: @@
 ==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
+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}
+:\(\displaystyle  f'(z)= \lim_{t \rightarrow 0,~ t\in \mathbb C}~ \frac{f(z\!+\!t)-f(z)}{t}
+\)
-Then, function $f$ is called holomorphic on $C$.
+Then, function \(f\) is called holomorphic on \(C\).
 ==Cauchi–Riemann==

Holomorphic function - Revision history

T: /* Cauchi–Riemann */

T: Text replacement - "\$([^\$]+)\$" to "\\(\1\\)"

Maintenance script at 05:32, 20 June 2013