reviewed

approved

proposed

reviewed

editing

proposed

Khinchin's constant is K_0. (A002210).

Wikipedia, <a href="http://en.wikipedia.org/wiki/Khinchin%27s_constant">Khinchin's constant</a>

Equals (Sum_{n>=1} -log2(1 - 1/(n+1)^2) * n^(-1))^(-1). - Jianing Song, Aug 08 2021

approved

editing

reviewed

approved

proposed

reviewed

editing

proposed

RealDigits[Log[2]/NSum[Log[(1 - 1/(n + 1)^2)^(-1/n)], {n, Infinity}, NSumTerms -> 10^4, WorkingPrecision -> 250, PrecisionGoal -> 110]][[1, ;; 100]] (* Eric W. Weisstein, Dec 10 2017 *)

Decimal expansion of the Khinchin harmonic mean K_{-1}.

digits = 102; exactEnd = 1000; f[n_] = (1 - 1/(n + 1)^2)^(-1/n); s[n_] = Series[Log[f[n] ], {]], {n, Infinity, digits}] // Normal // N[#, digits]&; ] &; exactSum = Sum[Log[f[n]] , {]], {n, 1, exactEnd}] // N[#, digits]&; ] &; extraSum = Sum[s[n] , {], {n, exactEnd + 1, Infinity}] // N[#, digits]&; ] &; A087491 = Log[2]/(exactSum + extraSum) // RealDigits // First (* Jean-François Alcover, Feb 06 2013 *)

approved

editing

editing

approved