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A087493
Decimal expansion of Khinchin mean K_{-3}.
10
1, 3, 1, 3, 5, 0, 7, 0, 7, 8, 6, 8, 7, 9, 8, 5, 7, 6, 6, 7, 1, 7, 3, 3, 9, 4, 4, 7, 0, 7, 2, 7, 8, 6, 8, 2, 8, 1, 5, 8, 1, 2, 9, 8, 6, 1, 4, 8, 4, 7, 9, 2, 0, 5, 8, 8, 0, 9, 8, 4, 9, 8, 0, 5, 4, 2, 3, 8, 8, 1, 3, 6, 0, 3, 3, 8, 8, 1, 5, 9, 2, 5, 0, 5, 2, 4, 2, 9, 1, 5, 4, 1, 1, 8, 2, 2, 0, 8, 6, 1, 1, 7, 2
OFFSET
1,2
COMMENTS
Khinchin's constant is K_0.
LINKS
Eric Weisstein's World of Mathematics, Khinchin's Constant
EXAMPLE
1.31350707...
MATHEMATICA
digits = 102; exactEnd = 1000; f[n_] = -(Log[1 - (1 + n)^(-2)]/(n^3*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]&; A087493 = (exactSum + extraSum)^(-1/3) // RealDigits // First (* Jean-François Alcover, Feb 06 2013 *)
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Sep 09 2003
EXTENSIONS
More terms from Jean-François Alcover, Feb 06 2013
STATUS
approved