A242494 Decimal expansion of Sum_{k > 0} (-1)^k*log(k)^2/k.

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

Offset: 0

Author

Jean-François Alcover, May 16 2014

Keywords

• nonn
• cons

Examples

			0.065372592558898599146207399388201...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 168.

Crossrefs

Cf. A091812.

Programs

Mathematica

-Log[2]^3/3 + EulerGamma*Log[2]^2 +  StieltjesGamma[1]*Log[4] // RealDigits[#, 10, 100]& // First

PARI

sumalt(k=1,(-1)^k*log(k)^2/k) \\ Charles R Greathouse IV, Mar 10 2016

Formula

sum(k>0, (-1)^k*log(k)^2/k) = -log(2)^3/3 + gamma*log(2)^2 + gamma(1)*log(4).