The Landau constant, also called the Bloch-Landau constant, is defined using the set 
of analytic functions 
on an open region
containing the set 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
 |
Robinson (1938, unpublished) and Rademacher (1943) derived the bounds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.
Wikström (2026, p. 3) obtained the improved lower bound 
using a computer-assisted proof. Wikström (2026) reports that OpenAI Codex and
Anthropic Claude Code assisted with developing the interval
arithmetic verification scripts.
Restricting the normalized analytic functions to univalent functions defines the univalent
Bloch-Landau constant 
, rather than 
. The disk center remains unrestricted (Landau 1929).
