A379826 - OEIS

%I #14 Jan 15 2025 04:17:25

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

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

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

%N Decimal expansion of the alternating double sum zeta(-2,-1) = Sum_{i>=2} (Sum_{j=1..i-1} (-1)^(i+j)/(i^2*j)) (negated).

%C Sometimes called in literature as U(2,1).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultivariateZetaFunction.html">Multivariate Zeta Function</a>, eq. 14.

%F Equals Pi^2*log(2)/4 - 13*zeta(3)/8.

%e -0.243070351670061577562704723967582217168..

%t RealDigits[(-2 Pi^2 Log[2] + 13 Zeta[3])/8, 10, 105]

%o (PARI) polylogmult([2,1],[-1,-1])

%Y Cf. A076788 (-zeta(-1,-1)), A255685 (-zeta(-3,-1)), A379827 (-zeta(-5,-1)), A379829 (-zeta(-5,-3)).

%K cons,nonn,new

%O 0,1

%A _Artur Jasinski_, Jan 03 2025