A381657 -id:A381657 - cp's OEIS frontend

A381655 Decimal expansion of the multiple zeta value (Euler sum) zetamult(5,1) = zetamult(3, 1, 1, 1).

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

Offset: 0

Artur Jasinski, Mar 11 2025

For complete list of formulas of the positive multiple zeta values up to weight 6 see A381651.

			0.04053689727151973782904590793969648...

Cf. A381651, A381652, A381653, A381654, A381656, A381657.

RealDigits[3*Zeta[6]/4 - Zeta[3]^2/2, 10, 106][[1]]

PARI
```
zetamult([3,1,1,1])
```

zetamult(5,1) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^5*n)) = 3*zeta(6)/4 - zeta(3)^2/2 = zetamult(3,1,1,1).

A381656 Decimal expansion of the multiple zeta value (Euler sum) zetamult(3,2,1).

Original entry on oeis.org

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

Offset: 0

Artur Jasinski, Mar 11 2025

			0.0323090289916698816984064916802...

Cf. A381651, A381652, A381653, A381654, A381655, A381657

RealDigits[-203 Zeta[6]/48 + 3 Zeta[3]^2, 10, 106][[1]]

PARI
```
zetamult([3,2,1])
```

Equals -203*zeta(6)/48 + 3*zeta(3)^2.

cp's OEIS Frontend

A381655 Decimal expansion of the multiple zeta value (Euler sum) zetamult(5,1) = zetamult(3, 1, 1, 1).

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