Lévy Constant

Let $p_n/q_n$ be the $n$th Convergent of a Real Number $x$. Then almost all Real Numbers satisfy

$$L\equiv \lim_{n\to\infty} (q_n)^{1/n}=e^{\pi^2/(12\ln 2)}=3.27582291872\ldots.$$

See also Khintchine's Constant, Khintchine-Lévy Constant

References

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 51, 1983.