Namespaces
Variants
Actions

Difference between revisions of "Regular function"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
m (TeX encoding is done)
Line 1: Line 1:
 +
{{TEX|done}}
 +
 
''in a domain''
 
''in a domain''
  
A function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080720/r0807201.png" /> of a complex variable <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080720/r0807202.png" /> which is single-valued in this domain and which has a finite derivative at every point (see [[Analytic function|Analytic function]]). A regular function at a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080720/r0807203.png" /> is a function that is regular in some neighbourhood of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080720/r0807204.png" />.
+
A function $f(z)$ of a complex variable $z$ which is single-valued in this domain and which has a finite derivative at every point (see [[Analytic function|Analytic function]]). A regular function at a point $a$ is a function that is regular in some neighborhood of $a$.
 
 
 
 
  
====Comments====
 
  
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G. Springer,  "Introduction to Riemann surfaces" , Addison-Wesley  (1957)  pp. 60; 169; 173</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G. Springer,  "Introduction to Riemann surfaces" , Addison-Wesley  (1957)  pp. 60; 169; 173</TD></TR></table>

Revision as of 06:03, 23 December 2012


in a domain

A function $f(z)$ of a complex variable $z$ which is single-valued in this domain and which has a finite derivative at every point (see Analytic function). A regular function at a point $a$ is a function that is regular in some neighborhood of $a$.


References

[a1] G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley (1957) pp. 60; 169; 173
How to Cite This Entry:
Regular function. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Regular_function&oldid=29262
This article was adapted from an original article by Yu.D. Maksimov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article