Landau Constant
المؤلف:
Finch, S. R.
المصدر:
"Bloch-Landau Constants." §7.1 in Mathematical Constants. Cambridge, England: Cambridge University Press
الجزء والصفحة:
...
22-7-2021
2392
Landau Constant
Let 
be the set of complex analytic functions 
defined on an open region containing the closure of the unit disk ![D=<span style=]()
{z:|z|<1}" src="https://mathworld.wolfram.com/images/equations/LandauConstant/Inline3.gif" style="height:15px; width:88px" /> satisfying 
and 
. For each 
in 
, let 
be the supremum of all numbers 
such that 
contains a disk of radius 
. Then
![L=inf<span style=]() {l(f):f in F}. " src="https://mathworld.wolfram.com/images/equations/LandauConstant/NumberedEquation1.gif" style="height:15px; width:125px" /> |
This constant is called the Landau constant, or the Bloch-Landau constant. Robinson (1938, unpublished) and Rademacher (1943) derived the bounds
(OEIS A081760), where 
is the gamma function, and conjectured that the second inequality is actually an equality.
REFERENCES:
Finch, S. R. "Bloch-Landau Constants." §7.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 456-459, 2003.
Rademacher, H. "On the Bloch-Landau Constant." Amer. J. Math. 65, 387-390, 1943.
Sloane, N. J. A. Sequence A081760 in "The On-Line Encyclopedia of Integer Sequences."
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