cp's OEIS Frontend

A368551 Decimal expansion of 6*gamma/Pi^2 - 72*zeta'(2)/Pi^4.

%I A368551 #31 Jan 26 2024 05:48:44
%S A368551 1,0,4,3,8,9,4,5,1,5,7,1,1,9,3,8,2,9,7,4,0,4,5,6,3,4,3,8,5,0,9,0,0,2,
%T A368551 4,9,3,5,2,5,5,7,5,9,6,2,7,3,4,1,4,5,8,9,5,0,3,7,6,9,0,6,8,0,5,2,5,5,
%U A368551 8,2,6,3,3,7,3,4,0,7,0,6,0,3,1,6,4,1,5,8,8,6,2,5,5,8,7,8,0,3,5,8,0,6,5,6,6
%N A368551 Decimal expansion of 6*gamma/Pi^2 - 72*zeta'(2)/Pi^4.
%C A368551 Also the Wolf-Kawalec constant of index 0.
%C A368551 For the Wolf-Kawalec constant of index 1 see A368547.
%C A368551 For the Wolf-Kawalec constant of index 2 see A368568.
%C A368551 Let g(n) be the Wolf-Kawalec constant of index n; then the function
%C A368551   zeta(x)/zeta(2*x) - 6/(Pi^2*(x-1))
%C A368551 has the expansion
%C A368551   Sum_{n>=0} (-1)^n*(g(n)/n!)*(x-1)^n
%C A368551 at x=1.
%H A368551 Artur Kawalec, <a href="https://arxiv.org/abs/2312.16811">On the series expansion of a square-free zeta series</a>, arXiv:2312.16811 [math.NT], 2023.
%H A368551 Marek Wolf, <a href="https://cmst.eu/articles/numerical-determination-of-a-certain-mathematical-constant-related-to-the-mobius-function">Numerical Determination of a Certain Mathematical Constant Related to the Mobius Function</a>, Computational Methods in Science and Technology, Volume 29 (1-4) 2023, 17-20 see formulas (26) and (27).
%F A368551 Equals (6/Pi^2)*(24*Glaisher - gamma - 2*log(2*Pi)) where Glaisher is A074962.
%F A368551 Equals lim_{x->oo} {(Sum_{n=1..x} abs(mu(n))/n) - 6*log(x)/Pi^2}.
%e A368551 1.0438945157119382974...
%t A368551 RealDigits[6 EulerGamma/Pi^2 - 72 Zeta'[2]/Pi^4, 10, 105][[1]]
%Y A368551 Cf. A000796, A001620, A008683, A073002, A074962, A368547, A368568.
%K A368551 nonn,cons
%O A368551 1,3
%A A368551 _Artur Jasinski_, Dec 29 2023