A258983 Decimal expansion of the multiple zeta value (Euler sum) zetamult(3,2).

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

Offset

0,1

Comments

Also zetamult(2, 2, 1). - Charles R Greathouse IV, Jan 04 2017

Links

Table of n, a(n) for n=0..103.

Dominique Manchon, Arborified multiple zeta values, arXiv:1603.01498 [math.CO], 2016.

Jonathan Borwein and Roland Girgensohn, Evaluation of triple Euler Sums, Elec. Jour. of Comb., Vol. 3, Issue 1, 1996. Article R23 (see page 21).

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Formula

Equals Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^3*n^2)) = 3*zeta(2)*zeta(3) - (11/2)*zeta(5).

Example

0.2288103976033537597687461489416887919325093427198821602294071...

Mathematica

RealDigits[3*Zeta[2]*Zeta[3] - (11/2)*Zeta[5], 10, 104] // First

Prog

(PARI) zetamult([3, 2]) \\ Charles R Greathouse IV, Jan 21 2016
(PARI) zetamult([2, 2, 1]) \\ Charles R Greathouse IV, Jan 04 2017

Crossrefs

Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), 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), A258991 (4,4).

Cf. A013663 (zeta(5)), A183699 (zeta(2)*zeta(3)).

Sequence in context: A195299 A095297 A269545 * A195138 A094887 A021441

Adjacent sequences: A258980 A258981 A258982 * A258984 A258985 A258986

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 16 2015

Status

approved