Search: id:A131688
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%I A131688
%S A131688 1,2,5,7,7,4,6,8,8,6,9,4,4,3,6,9,6,3,0,0,0,9,8,9,9,8,3,0,4,9,5,8,8,1,5,
%T A131688 2,8,5,1,1,5,4,0,8,9,0,5,0,8,8,8,4,8,6,8,9,7,7,5,4,0,8,3,3,5,2,2
%N A131688 Decimal expansion of the constant sum_{k=1..infinity} log(k+1)/k/(k+1).
%C A131688 Equals Sum[ -Zeta'[1 + k], {k, 1, Infinity}], where Zeta' is the derivative 
               of Riemann Zeta function. [From Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), 
               Dec 28 2008]
%H A131688 M. W. Coffey, <a href="http://www.arXiv.org/abs/0706.0345">Series of 
               zeta values, the Stieltjes constants and a sum S_gamma(n)</a>, arXiv:math-ph/
               0706.0345, eq (38a).
%F A131688 Equals sum_{s=1..infinity} (-1)^(s+1)*zeta(s+1)/s.
%e A131688 1.257746886944369630009899830495881528511540890508884868977540833522...
%t A131688 Sum[ -Zeta'[1 + k], {k, 1, Infinity}] [From Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), 
               Dec 28 2008]
%o A131688 (PARI) sumalt(s=1, (-1)^(s+1)/s*zeta(s+1) );
%Y A131688 Sequence in context: A078320 A141430 A021392 this_sequence A096624 A145378 
               A069887
%Y A131688 Adjacent sequences: A131685 A131686 A131687 this_sequence A131689 A131690 
               A131691
%K A131688 cons,nonn
%O A131688 1,2
%A A131688 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 14 2007

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