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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).
3
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
Eric Weisstein's World of Mathematics, Multivariate Zeta Function, eq. 14.
FORMULA
Equals Pi^2*log(2)/4 - 13*zeta(3)/8.
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
KEYWORD
cons,nonn
AUTHOR
Artur Jasinski, Jan 03 2025
STATUS
approved