A379826 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).

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, 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, 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

Offset

0,1

Comments

Sometimes called U(2,1) in literature.

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Multivariate Zeta Function, eq. 14.

Formula

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

Equals Integral_{x=0..1} -(log(x)*log(1 - x))/(1 + x) dx. - Kritsada Moomuang, May 27 2025

Example

-0.243070351670061577562704723967582217168..

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A048644 A246713 A106137 * A213381 A127651 A019641

Adjacent sequences: A379823 A379824 A379825 * A379827 A379828 A379829

Keyword

cons,nonn

Author

Artur Jasinski, Jan 03 2025

Status

approved