A258985 Decimal expansion of the multiple zeta value (Euler sum) zetamult(5,2).

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

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(5,2) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^5*n^2)) = 5*zeta(2)*zeta(5) + 2*zeta(3)*zeta(4) - 11*zeta(7).

Example

0.03857512434275325550592546437299557001973484169890900833104937293358...

Mathematica

Join[{0}, RealDigits[5*Zeta[2]*Zeta[5] + 2*Zeta[3]*Zeta[4] - 11*Zeta[7], 10, 104] // First]

Prog

(PARI) zetamult([5, 2]) \\ Charles R Greathouse IV, Jan 21 2016

Crossrefs

Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)), A258984 (4,2), A258947 (6,2), A258986 (2,3), A258987 (3,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).

Sequence in context: A379975 A236229 A343920 * A077151 A375596 A342934

Adjacent sequences: A258982 A258983 A258984 * A258986 A258987 A258988

Keyword

nonn,cons,easy,changed

Author

Jean-François Alcover, Jun 16 2015

Status

approved