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Date: 11-8-2020
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Let be the set of complex analytic functions defined on an open region containing the closure of the unit disk satisfying and . For each in , let be the supremum of all numbers such that contains a disk of radius . Then
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 Robinson (1938, unpublished) and Rademacher (1943) derived the bounds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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