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A242494 Decimal expansion of Sum_{k > 0} (-1)^k*log(k)^2/k. 3

%I #10 Jan 15 2018 13:51:02

%S 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,

%T 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,

%U 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

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

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

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

%e 0.065372592558898599146207399388201...

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

%o (PARI) sumalt(k=1,(-1)^k*log(k)^2/k) \\ _Charles R Greathouse IV_, Mar 10 2016

%Y Cf. A091812.

%K nonn,cons

%O 0,2

%A _Jean-François Alcover_, May 16 2014

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