A087493 Decimal expansion of Khinchin mean K_{-3}.

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

Author

Eric W. Weisstein, Sep 09 2003

Keywords

• nonn
• cons

Comments

Khinchin's constant is K_0.

Examples

			1.3135070786879857667173394470727868281581298614...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.8, p. 61.

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

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 *)

Extensions

More terms from Jean-François Alcover, Feb 06 2013