A258990 Decimal expansion of the multiple zeta value (Euler sum) zetamult(3,4).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Formula

zetamult(3,4) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^3*n^4)) = 10*zeta(2)*zeta(5) + zeta(3)*zeta(4) - 18*zeta(7).

Example

0.20750501461573209590780760549467146544182867955060619041951789656971...

Mathematica

RealDigits[10*Zeta[2]*Zeta[5] + Zeta[3]*Zeta[4] - 18*Zeta[7], 10, 105] // First

Prog

(PARI) zetamult([3, 4]) \\ 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), A258987 (3,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258991 (4,4).

Sequence in context: A011343 A326731 A021486 * A351727 A337450 A228819

Adjacent sequences: A258987 A258988 A258989 * A258991 A258992 A258993

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 16 2015

Status

approved