Definition:Bloch's Constant/Historical Note

Historical Note on Bloch's Constant
The precise value of Bloch's constant is unknown.

stated a lower bound for it of $\dfrac 1 {72}$.

However, it is known that $\dfrac 1 {72}$ is not the best possible value for it.

In their $1983$ work, and  give $\dfrac {\sqrt 3} 4$:
 * $\dfrac {\sqrt 3} 4 \approx 0 \cdotp 43301 \, 2701 \ldots$

The best value known at present is $\dfrac {\sqrt 3} 4 + \dfrac 2 {10 \, 000}$ which evaluates to approximately $0 \cdotp 43321 \, 2701$.

This was demonstrated by and  in $1996$.

and demonstrated that:


 * $B \le \sqrt {\dfrac {\sqrt 3 -1} 2} \times \dfrac {\map \Gamma {\frac 1 3} \map \Gamma {\frac {11} {12} } } {\map \Gamma {\frac 1 4} }$

and conjectured that this value is in fact the true value of $B$.

The number is given by and  as $\pi \sqrt 2^{1/4} \dfrac {\map \Gamma {1/3} } {\map \Gamma {1/4} } \paren {\dfrac {\map \Gamma {11/12} } {\map \Gamma {1/12} } }^{1/2}$.