is Khinchin's constant, with numerical value .
Background & Context
- Khinchin is the symbol representing Khinchin's constant , also known as Khintchine's constant. Khinchine is defined as the limiting value for the geometric mean of the terms of a simple continued fraction expansion of a real number , where the value of is independent of the choice of . Khinchin has a numerical value and a closed form product is given by . Khinchin arises most commonly in the theory of continued fractions and in ergodic theory.
- When Khinchin is used as a symbol, it is propagated as an exact quantity.
- It is not currently known if Khinchin is rational (meaning it can be expressed as a ratio of integers), algebraic (meaning it is the root of some integer polynomial), or normal (meaning the digits in its base- expansion are equally distributed) to any base.
- Khinchin can be numerically evaluated using N. However, no efficient formulas for computing large numbers of its digits are currently known. RealDigits can be used to return a list of digits of Khinchin and ContinuedFraction to obtain terms of its continued fraction expansion.
Examplesopen allclose all
Properties & Relations (2)
Various symbolic relations are automatically used:
Various products give results that can be expressed using Khinchin:
Neat Examples (1)
Terms in the continued fraction:
Introduced in 1999