*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

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 Robinson (1938, unpublished) and Rademacher (1943) derived the bounds

where is the Gamma Function, and conjectured that the second inequality is actually an equality,

**References**

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/bloch/bloch.html

Rademacher, H. ``On the Bloch-Landau Constant.'' *Amer. J. Math.* **65**, 387-390, 1943.

© 1996-9

1999-05-26