cp's OEIS Frontend

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

%I A258947 #18 Feb 22 2025 12:39:54
%S A258947 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,
%T A258947 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,
%U A258947 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
%N A258947 Decimal expansion of the multiple zeta value (Euler sum) zetamult(6,2).
%H A258947 Richard E. Crandall, Joe P. Buhler, <a href="https://projecteuclid.org/journals/experimental-mathematics/volume-3/issue-4/On-the-evaluation-of-Euler-sums/em/1048515810.full">On the evaluation of Euler Sums</a>, Exp. Math. 3 (4) (1994) 275-285 Table 1.
%H A258947 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/MultivariateZetaFunction.html">Multivariate Zeta Function</a>
%H A258947 Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiple_zeta_function">Multiple zeta function</a>
%F A258947 zetamult(6,2) = Sum_{m>=2} (sum_{n=1..m-1} 1/(m^6*n^2)).
%F A258947 Equals Sum_{m>=2} H(m-1, 2)/m^6, where H(n,2) is the n-th harmonic number of order 2.
%e A258947 0.01781974041683598836265953024872461216871313711029118841882136191761348...
%t A258947 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]
%o A258947 (PARI) zetamult([6,2]) \\ _Charles R Greathouse IV_, Jan 21 2016
%o A258947 (PARI) zetamult([2, 2, 1, 1, 1, 1]) \\ _Charles R Greathouse IV_, Feb 04 2025
%Y A258947 Cf. A072691, A197110.
%K A258947 nonn,cons
%O A258947 0,3
%A A258947 _Jean-François Alcover_, Jun 15 2015