A379829 Decimal expansion of the alternating double sum zeta(-5,-3) = Sum_{i>=2} (Sum_{j=1..i-1} (-1)^(i+j)/(i^5*j^3)) (negated).

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

Offset

-1,1

Links

Table of n, a(n) for n=-1..103.

Formula

Equals 207*zeta(3,3,2)/416 - 22397*Pi^8/31449600 - 621*Pi^2*zeta(3)^2/1664 + 1005*zeta(3)*zeta(5)/104.

Equals -23*zeta(-6,-2)/16 + 3373*Pi^8/38707200 - 45*zeta(3)*zeta(5)/64.

Equals -207*zeta(3,2,3)/1280 - 1139*Pi^8/2419200 - 207*Pi^2*zeta(3)^2/1280 + 13863*zeta(3)*zeta(5)/2560.

Equals -207*zeta(6,2)/128 - 1103*Pi^8/4838400 - Li(8,-1/2)/4 - Li(8,-1/4)/4 + Li(8,1/16)/512 - 127*Li(8,1/4)/512 - Li(8,1/2)/4 + 57*zeta(3)*zeta(5)/32, where Li are polylogarhitms.

Example

-0.02833366128004690229673823715754..

Prog

(PARI) polylogmult([5, 3], [-1, -1])

Crossrefs

Cf. A076788 (-zeta(-1,-1)), A255685 (-zeta(-3,-1)), A379826 (-zeta(-2,-1)), A379827 (-zeta(-5,-1)).

Sequence in context: A381898 A214072 A016640 * A385569 A321984 A397293

Adjacent sequences: A379826 A379827 A379828 * A379830 A379831 A379832

Keyword

nonn,cons

Author

Artur Jasinski, Jan 03 2025

Status

approved