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# Landau Constant

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 Robinson (1938, unpublished) and Rademacher (1943) derived the bounds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.

Bloch Constant, Landau-Kolmogorov Constants, Landau-Ramanujan Constant

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## 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."

Landau Constant

## Cite this as:

Weisstein, Eric W. "Landau Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LandauConstant.html