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

Author

Jean-François Alcover, Jun 16 2015

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			0.2288103976033537597687461489416887919325093427198821602294071...
		

Links

• 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

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)).

Programs

Mathematica

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

PARI

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

PARI

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

Formula

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