A087496 Decimal expansion of Khinchin mean K_{-6}.
1, 1, 5, 6, 5, 5, 2, 3, 7, 4, 4, 2, 1, 5, 1, 4, 4, 2, 3, 1, 5, 2, 6, 0, 5, 9, 9, 8, 7, 4, 3, 4, 1, 0, 0, 4, 6, 8, 4, 0, 2, 1, 3, 0, 7, 0, 7, 1, 8, 7, 6, 1, 2, 9, 2, 2, 3, 1, 0, 6, 7, 0, 7, 7, 3, 8, 2, 8, 6, 7, 2, 2, 7, 1, 5, 0, 3, 5, 7, 6, 6, 4, 3, 9, 2, 6, 5, 1, 7, 9, 7, 1, 8, 3, 9, 2, 9, 3, 4, 2
Offset: 1
Examples
1.15655237...
Links
- Eric Weisstein's World of Mathematics, Khinchin's Constant
Crossrefs
Programs
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Mathematica
m = 6; digits = 100; exactEnd = 1000; f[n_] = -(Log[1 - (1 + n)^(-2)]/(n^m*Log[2])); s[n_] = Series[f[n], {n, Infinity, digits}] // Normal // N[#, digits]&; exactSum = Sum[f[n], {n, 1, exactEnd}] // N[#, digits]&; extraSum = Sum[s[n], {n, exactEnd + 1, Infinity}] // N[#, digits]&; (exactSum + extraSum)^(-1/m) // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 14 2013 *)
Extensions
More terms from Charles R Greathouse IV, Jul 16 2007
Edited by Charles R Greathouse IV, Oct 28 2009
More terms from Jean-François Alcover, Feb 14 2013
Comments