A258987 Decimal expansion of the multiple zeta value (Euler sum) zetamult(3,3).

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

Offset

0,1

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Index to constants which are multiple zeta values (3,3)

Formula

zetamult(3,3) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^3*n^3)) = (1/2)*zeta(3)^2 - (1/2)*zeta(6). - [Corrected by Detlef Meya, Jun 06 2025 ]

Example

0.213798868224592547099583574508033649640958957865517556144512748947...

Mathematica

RealDigits[(1/2)*Zeta[3]^2 - (1/2)*Zeta[6], 10, 103] // First (* Corrected by Detlef Meya, Jun 06 2025 *)

Prog

(PARI) zetamult([3, 3]) \\ Charles R Greathouse IV, Jan 21 2016

Crossrefs

Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)), A258984 (4,2), A258985 (5,2), A258947 (6,2), A258986 (2,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).

Sequence in context: A112027 A174400 A178079 * A174254 A384755 A024404

Adjacent sequences: A258984 A258985 A258986 * A258988 A258989 A258990

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 16 2015

Status

approved