Lévy's constant
In mathematics Lévy's constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions. In 1935, the Soviet mathematician Aleksandr Khinchin showed that the denominators "q" of the convergents of the continued fraction expansions of almost all real numbers satisfy Soon afterward, in 1936, the French mathematician Paul Lévy found the explicit expression for the constant, namely The term "Lévy's constant" is sometimes used to refer to formula_3 (the logarithm of the above expression), which is approximately equal to 1.1865691104… The  value derives from the asymptotic expectation of the logarithm of the ratio of successive denominators, using the Gauss-Kuzmin distribution. In particular, the ratio has the asymptotic density function formula_4 for formula_5 and zero otherwise. This gives Lévy's constant as formula_6. The base-10 logarithm of Lévy's constant, which is approximately 0.51532041…, is half of the reciprocal of the limit in Lochs' theorem.