A258986 Decimal expansion of the multiple zeta value (Euler sum) zetamult(2,3).

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

Offset

0,1

Links

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

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

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Formula

zetamult(2,3) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^2*n^3)) = (9/2)*zeta(5) - 2*zeta(2)*zeta(3).

Example

0.711566197550572432096973806086402612092561204438339236492222496457686...

Mathematica

RealDigits[(9/2)*Zeta[5] - 2*Zeta[2]*Zeta[3], 10, 103] // First

Prog

(PARI) zetamult([2, 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), 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: A051422 A201670 A019980 * A086384 A102421 A019620

Adjacent sequences: A258983 A258984 A258985 * A258987 A258988 A258989

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 16 2015

Status

approved