A258988 Decimal expansion of the multiple zeta value (Euler sum) zetamult(4,3).

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

Offset

0,2

Links

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

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Formula

zetamult(4,3) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^2*n^3)) = 17*zeta(7) - 10*zeta(2)*zeta(5).

Example

0.0851598225348336514068060188723673459573395085868773204671034320533...

Mathematica

Join[{0}, RealDigits[17*Zeta[7] - 10*Zeta[2]*Zeta[5], 10, 104] // First]

Prog

(PARI) zetamult([4, 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), A258986 (2,3), A258987 (3,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).

Sequence in context: A249449 A357466 A334496 * A139721 A307384 A261882

Adjacent sequences: A258985 A258986 A258987 * A258989 A258990 A258991

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 16 2015

Status

approved