- Landau's constants
In
complex analysis , Landau's constants are certainmathematical constant s that describe the behaviour ofholomorphic function s defined on theunit disk . Consider the set "F" of all those holomorphic functions "f" on the unit disk for which:f'(0) = 1.,
We define "L""f" to be the radius of the largest disk contained in the image of "f", and "B""f" 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 "L""f" or "B""f", where "f" is any holomorphic function or anyinjective 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
:0.4330 + 10^{-14} < B < 0.472 ,!
:0.5 < L < 0.544 ,!
:0.5 < A le 0.7853.
See Also
* Table of selected mathematical constants
External links
*
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