A258991 Decimal expansion of the multiple zeta value (Euler sum) zetamult(4,4).

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

Offset

0,2

Links

Table of n, a(n) for n=0..106.

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Formula

zetamult(4,4) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^4*n^4)) = (1/2)*(zeta(4)^2 - zeta(8)).

Example

0.08367311301649536161489043654238770543824673255415416836075918355438...

Mathematica

Join[{0}, RealDigits[(1/2)*(Zeta[4]^2 - Zeta[8]), 10, 106] // First]

Prog

(PARI) zetamult([4, 4]) \\ Charles R Greathouse IV, Jan 21 2016
(PARI) (zeta(4)^2-zeta(8))/2 \\ Charles R Greathouse IV, Jan 20 2022

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), A258987 (3,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4).

Sequence in context: A228211 A010522 A197332 * A132035 A153813 A316166

Adjacent sequences: A258988 A258989 A258990 * A258992 A258993 A258994

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 16 2015

Status

approved