A258947 Decimal expansion of the multiple zeta value (Euler sum) zetamult(6,2).

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

Offset

0,3

Links

Table of n, a(n) for n=0..99.

Richard E. Crandall, Joe P. Buhler, On the evaluation of Euler Sums, Exp. Math. 3 (4) (1994) 275-285 Table 1.

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Formula

zetamult(6,2) = Sum_{m>=2} (sum_{n=1..m-1} 1/(m^6*n^2)).

Equals Sum_{m>=2} H(m-1, 2)/m^6, where H(n,2) is the n-th harmonic number of order 2.

Example

0.01781974041683598836265953024872461216871313711029118841882136191761348...

Mathematica

digits = 99; zetamult[6, 2] = NSum[HarmonicNumber[m-1, 2]/m^6, {m, 2, Infinity}, WorkingPrecision -> digits+20, NSumTerms -> 200, Method -> {"NIntegrate", "MaxRecursion" -> 18}]; Join[{0}, RealDigits[zetamult[6, 2], 10, digits] // First]

Prog

(PARI) zetamult([6, 2]) \\ Charles R Greathouse IV, Jan 21 2016
(PARI) zetamult([2, 2, 1, 1, 1, 1]) \\ Charles R Greathouse IV, Feb 04 2025

Crossrefs

Cf. A072691, A197110.

Sequence in context: A329219 A093720 A154216 * A360381 A216207 A171274

Adjacent sequences: A258944 A258945 A258946 * A258948 A258949 A258950

Keyword

nonn,cons,changed

Author

Jean-François Alcover, Jun 15 2015

Status

approved