A381651 Decimal expansion of the multiple zeta value (Euler sum) zetamult(4,1).

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

Offset: 0

Author

Artur Jasinski, Mar 03 2025

Keywords

• nonn
• cons

Examples

			0.0965511599894437344656455314289...
		

Links

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

Programs

Mathematica

RealDigits[2 Zeta[5] - Zeta[2] Zeta[3], 10, 105][[1]]
(* slowly convergent *)
sum = 0; Monitor[Do[Do[sum = sum + N[1/(m^4 n)], {n, 1, m - 1}, 50], {m, 2, 10000}], m]; Print[sum]

PARI

zetamult([4,1])

Formula

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