A363687 - OEIS

%I #13 Jun 16 2023 05:10:40

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

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

%U 2,8,5,9,4,1,6,8,1,8,1,8,1,0,1,4,2,9,8,3,1,3,5,2,4,2,4,1,6,1,8,6,4,1,3,8,3

%N Decimal expansion of Sum_{k>=1} cos(Pi* log k)/k^2.

%C Sum_{k>=1} sin(Pi*log k)/k^2 = 0.0942944615085... is the associated imaginary part.

%H Math StackExchange, <a href="https://math.stackexchange.com/questions/385694">Closed form for sum n>=1 cos(pi*log(n)/n^2</a>, (2013).

%F Equals Re(zeta(2 + Pi*i)), where i=sqrt(-1).

%e 0.795640206735677517430628328498...

%p Re(Zeta(2+I*Pi)) ;

%p evalf(%) ;

%t RealDigits[Re[Zeta[2 + Pi*I]], 10, 105][[1]] (* _Amiram Eldar_, Jun 16 2023 *)

%o (PARI) real(zeta(2+I*Pi)) \\ _Michel Marcus_, Jun 15 2023

%K cons,nonn

%O 0,1

%A _R. J. Mathar_, Jun 15 2023