A396438 - OEIS

%I #5 May 26 2026 04:54:17

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

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

%U 0,0,1,6,6,3,4,4,4,6,6,6,9,2,6,9,4,3,0,2,8,9,9,0,7,8,0,4,2,3,3,0,3,3,4,0,7

%N Decimal expansion of Sum_{k>=1} (zeta(2*k)/k)*(3/5)^(2*k).

%D H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, p. 272, eq. (34).

%F Equals log(6*sqrt(2)*Pi/(5*sqrt(5+sqrt(5)))).

%F Equals log(Gamma(2/5)*Gamma(8/5)).

%e 0.684086052005027982956076086488842223395691645069838...

%t RealDigits[Log[6*Sqrt[2]*Pi/(5*Sqrt[5+Sqrt[5]])], 10, 120][[1]]

%o (PARI) log(6*sqrt(2)*Pi/(5*sqrt(5+sqrt(5))))

%Y Cf. A094642, A255681, A256921, A256922, A256923, A256929, A256930, A377008, A396436, A396437, A396439, A396440, A396441, A396442, A396443, A396444, A396445.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 26 2026