A387773 Decimal expansion of the multiple zeta value (Euler sum) zetamult(7,4).

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

Offset

-2,1

Links

Table of n, a(n) for n=-2..103.

Jonathan Borwein and Roland Girgensohn, Evaluation of triple Euler Sums, Elec. Jour. of Comb., Vol. 3, Issue 1, 1996. Article R23, page 2.

Richard E. Crandall, Joe P. Buhler, On the evaluation of Euler Sums, Exp. Math. 3 (4) (1994) 275-285.

Eric Weisstein's MathWorld, Multivariate Zeta Function.

Wikipedia, Multiple zeta function.

Formula

Equals Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^7*n^4)).

Equals 4*Pi^6*zeta(5)/945 + 7*Pi^4*zeta(7)/30 + 14*Pi^2*zeta(9) - 331*zeta(11)/2.

Example

0.0083838913540956950043242502904368792814481710830078340177709...

Maple

evalf(4*Pi^6*Zeta(5)/945 + 7*Pi^4*Zeta(7)/30 + 14*Pi^2*Zeta(9) - 331*Zeta(11)/2, 111)

Mathematica

RealDigits[-331/2*Zeta[11] + 4*Zeta[5]*Zeta[6] + 21*Zeta[7]*Zeta[4] + 84*Zeta[9]*Zeta[2], 10, 120][[1]]

Prog

(PARI) zetamult([7, 4])

Crossrefs

Cf. A258986.

Sequence in context: A097079 A021548 A199598 * A011106 A386734 A131641

Adjacent sequences: A387770 A387771 A387772 * A387774 A387775 A387776

Keyword

nonn,cons

Author

Vaclav Kotesovec, Sep 08 2025

Status

approved