cp's OEIS Frontend

A256923 Decimal expansion of Sum_{k>=1} (zeta(2k)/k)*(1/3)^(2k).

%I A256923 #17 Feb 16 2025 08:33:25
%S A256923 1,8,9,9,5,8,6,3,3,4,0,7,1,8,0,9,4,6,4,6,7,7,9,1,6,1,7,4,2,7,4,4,6,7,
%T A256923 2,2,7,5,1,5,5,9,1,1,0,5,4,1,4,4,2,6,4,8,0,3,2,2,6,1,5,8,0,5,0,9,2,8,
%U A256923 9,9,5,2,0,2,6,6,0,7,3,4,5,0,7,9,0,6,2,9,6,5,0,5,1,3,1,0,2,6,2,0,6,2,0,5,6
%N A256923 Decimal expansion of Sum_{k>=1} (zeta(2k)/k)*(1/3)^(2k).
%D A256923 H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 272.
%H A256923 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>
%H A256923 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%F A256923 Equals log(Gamma(2/3)*Gamma(4/3)).
%F A256923 Equals log(2*Pi/(3*sqrt(3))).
%F A256923 Equals log(A248897).
%F A256923 Equals -Sum_{k>=1} log(1 - 1/(3*k)^2). - _Amiram Eldar_, Aug 12 2020
%e A256923 0.189958633407180946467791617427446722751559110541442648...
%t A256923 RealDigits[Log[2*Pi/(3*Sqrt[3])], 10, 105] // First
%Y A256923 Cf. A073006, A202623, A248897, A256924.
%K A256923 nonn,cons,easy
%O A256923 0,2
%A A256923 _Jean-François Alcover_, Apr 13 2015