A256923 - OEIS

%I #16 Aug 12 2020 04:39:40

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

%D H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 272.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>

%F Equals log(Gamma(2/3)*Gamma(4/3)).

%F Equals log(2*Pi/(3*sqrt(3))).

%F Equals log(A248897).

%F Equals -Sum_{k>=1} log(1 - 1/(3*k)^2). - _Amiram Eldar_, Aug 12 2020

%e 0.189958633407180946467791617427446722751559110541442648...

%t RealDigits[Log[2*Pi/(3*Sqrt[3])], 10, 105] // First

%Y Cf. A073006, A202623, A248897, A256924.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Apr 13 2015