A381656 -id:A381656 - 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).

A381657 Decimal expansion of the multiple zeta value (Euler sum) zetamult(4, 1, 1).

Original entry on oeis.org

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

Offset: 0

Artur Jasinski, Mar 19 2025

			0.0174898531690114044259344452675...

Artur Jasinski, Complete list of formulas of the positive multiple zeta values up to weight 6 (2025)
Index to constants which are multiple zeta values (4,1,1)

Cf. A381651, A381652, A381653, A381654, A381655, A381656.

RealDigits[23 Zeta[6]/16 - Zeta[3]^2, 10, 106][[1]]

PARI
```
zetamult([4,1,1])
```

Equals 23*A013664/16 - A002117^2.

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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