Khinchin¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

Khinchin
    is Khinchin's constant K (also Khintchine's constant), with numerical
    value ~= 2.68545.
Khinchin's constant is the limiting geometric mean of the partial
quotients in the continued-fraction expansion of almost every real
number, given by the product over s >= 1 of (1 + 1/(s (s + 2)))^Log2[s].
It is a mathematical constant: it has attributes Constant and Protected,
NumericQ[Khinchin] is True, and D[Khinchin, x] is 0. N[Khinchin, prec]
evaluates it to any precision.

Examples¶

No verified examples yet for this function.

Implementation notes¶

Attributes Constant, Protected. `Attributes[Khinchin] = {Constant,

Attributes: Constant, Protected.

Implementation status¶

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References¶

Source: src/info.c
Specification: docs/spec/builtins/mathematical-constants.md

Notes & additional examples¶

Worked examples¶

In[1]:= N[Khinchin]
Out[1]= 2.68545

Khinchin's constant evaluates to arbitrary precision via its convergent product over partial quotients:

In[1]:= N[Khinchin, 60]
Out[1]= 2.685452001065306445309714835481795693820382293994462953051151

It is a true symbolic constant — NumericQ is True and its derivative vanishes:

In[1]:= NumericQ[Khinchin]
Out[1]= True

In[2]:= D[Khinchin, x]
Out[2]= 0

Notes¶

Khinchin is Khinchin's (Khintchine's) constant K ~= 2.68545, the limiting geometric mean of the partial quotients in the continued-fraction expansion of almost every real number: K = Product[(1 + 1/(s (s + 2)))^Log2[s], {s, 1, Infinity}]. It carries the Constant and Protected attributes, so it stays symbolic until N[Khinchin, prec] evaluates it to the requested precision.