A087498 Decimal expansion of Khinchin mean K_{-8}.

1, 1, 1, 5, 9, 6, 4, 4, 0, 8, 9, 7, 8, 7, 1, 6, 6, 9, 0, 6, 1, 9, 1, 5, 6, 4, 1, 9, 3, 4, 5, 3, 4, 9, 6, 9, 5, 7, 6, 9, 4, 9, 1, 1, 8, 2, 2, 3, 0, 4, 0, 0, 9, 3, 7, 0, 6, 3, 5, 3, 3, 1, 1, 0, 0, 3, 3, 7, 0, 9, 5, 7, 5, 0, 5, 0, 2, 0, 3, 1, 1, 8, 9, 1, 5, 0, 1, 1, 3, 9, 6, 4, 6, 7, 1, 5, 1, 7, 0, 0

Offset: 1

Author

Eric W. Weisstein, Sep 09 2003

Keywords

• nonn
• cons

Comments

Khinchin's constant is K_0.

Examples

			1.11596440...
		

Links

• Eric Weisstein's World of Mathematics, Khinchin's Constant

Crossrefs

Cf. A002210, A087491, A087492, A087493, A087494, A087495, A087496, A087497, A087498, A087499, A087500.

Programs

Mathematica

m = 8; 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 Jean-François Alcover, Feb 14 2013