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Landau's constants
In complex analysis, Landau's constants are certain mathematical constants that describe the behaviour of holomorphic functions defined on the unit disk. Consider the set F of all those holomorphic functions f on the unit disk for which
- f'(0) = 1.
We define Lf to be the radius of the largest disk contained in the image of f, and Bf to be the radius of the largest disk that is the biholomorphic image of a subset of a unit disk.
Landau's constants are then defined as the infimum of Lf or Bf, where f is any holomorphic function or any injective holomorphic function on the unit disk with
- f'(0) = 1.
The three resulting constants are abbreviated L, B, and A (for injective functions), respectively.
The exact values of L, B, and A are not known, but it is known that
Last updated: 05-23-2005 07:12:55
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details