cp's OEIS Frontend

A340440 Decimal expansion of Sum_{k>=2} log(k)/(k^2-1).

%I A340440 #28 Aug 25 2021 13:02:27
%S A340440 1,0,2,3,1,3,8,7,2,6,4,2,7,9,3,9,2,9,5,5,3,5,0,8,8,0,7,6,9,7,5,2,1,8,
%T A340440 0,9,7,4,9,2,1,4,5,2,7,9,3,6,6,0,8,3,2,5,9,3,6,6,3,4,8,6,1,7,9,1,2,1,
%U A340440 6,5,3,1,9,2,2,8,5,2,3,2,7,8,9,2,2,7,5,3,1,9,7,2,4,1,2,1,7,0,8,7,5,0,1,0,7
%N A340440 Decimal expansion of Sum_{k>=2} log(k)/(k^2-1).
%H A340440 R. J. Mathar, <a href="https://arxiv.org/abs/0902.0789">The series limit of sum_k 1/(k log k (log log k)^2)</a>, arXiv:0902.0789 [math.NA], 2009-2021, version 3, App. B.
%F A340440 Equals Sum_{i>=1} -zeta'(2i) = A073002 + A261506 - Sum_{i>=3} zeta'(2i).
%F A340440 Sum_{k>=2} log(k)/(k^2-s) = -Sum_{i>=1} s^(i-1)*zeta'(2i) for |s|<4. - _R. J. Mathar_, May 03 2021
%F A340440 Equals log(2)/2 + Sum_{k>=1} (zeta(2*k)-1)/(2*k-1). - _Amiram Eldar_, Jun 08 2021
%e A340440 1.0231387264279392955...
%o A340440 (PARI) sumpos(k=2, log(k)/(k^2-1)) \\ _Michel Marcus_, Jan 09 2021
%Y A340440 Cf. A073002, A261506, A340485, A340484.
%K A340440 nonn,cons
%O A340440 1,3
%A A340440 _R. J. Mathar_, Jan 07 2021