Editing Khinchin's constant (section)

==Generalizations==
The Khinchin constant can be viewed as the first in a series of the [[Hölder mean]]s of the terms of continued fractions.  Given an arbitrary series {''a''<sub>''n''</sub>}, the Hölder mean of order ''p'' of the series is given by

:<math>K_p=\lim_{n\to\infty} \left[\frac{1}{n} 
\sum_{k=1}^n a_k^p \right]^{1/p}.</math>
When the {''a''<sub>''n''</sub>} are the terms of a continued fraction expansion, the constants are given by
:<math>K_p=\left[\sum_{k=1}^\infty -k^p 
\log_2\left( 1-\frac{1}{(k+1)^2} \right)
\right]^{1/p}.</math>

This is obtained by taking the ''p''-th mean in conjunction with the [[Gauss–Kuzmin distribution]]. This is finite when <math>p < 1</math>.

The arithmetic average diverges: <math>\lim_{n\to\infty}\frac 1n \sum_{k=1}^n a_k = K_1 = +\infty</math>, and so the coefficients grow arbitrarily large: <math>\limsup_n a_n = +\infty</math>.

The value for ''K''<sub>0</sub> is obtained in the limit of ''p''&nbsp;&rarr;&nbsp;0.

The [[harmonic mean]] (''p''&nbsp;=&nbsp;&minus;1) is
:<math>K_{-1}=1.74540566240\dots</math> {{OEIS|A087491}}.