Koebe function


The analytic functionMathworldPlanetmath


on the unit disc in the complex planeMathworldPlanetmath is called the Koebe function. For some |α|=1, the functions


are called rotations of the Koebe function.

Firstly note that f1=f, and next note that f is a map from the open unit disc onto \(-,-1/4]. The maps fα(z) can be also given as fα(z)=α¯f1(αz). Further note that the power seriesMathworldPlanetmath representation of these functions is given by


Also note that these functions belong to the class of Schlicht functionsMathworldPlanetmath.


  • 1 John B. Conway. . Springer-Verlag, New York, New York, 1995.
Title Koebe function
Canonical name KoebeFunction
Date of creation 2013-03-22 14:23:30
Last modified on 2013-03-22 14:23:30
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 6
Author jirka (4157)
Entry type Definition
Classification msc 30C45
Synonym Köbe function
Defines rotation of the Koebe function
Defines rotation of the Köbe function