Lévy's constant

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 1936 French mathematician Paul Lévy showed that the denominators "q""n" of the convergents of the continued fraction expansions of almost all real numbers satisfy

:lim_{n o infty}{q_n}^{1/n}=e^{pi^2/(12ln2)} approx 3.2758229ldots

Lévy's constant is the constant on the right hand side of this expression, and is approximately equal to 3.275 822 918 7... The term is also sometimes used to refer to the logarithm of the right hand side of this expression, which is approximately equal to 1.186 569 110 4...

The base-10 logarithm of Lévy's constant, which is approximately 0.51532941..., is half of the reciprocal of the limit in Lochs' theorem.

ee also

*Khinchin's constant

External links

*
* Decimal expansion of Levy's constant: OEIS|id=A086702


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