cp's OEIS Frontend

A258986 Decimal expansion of the multiple zeta value (Euler sum) zetamult(2,3).

%I A258986 #19 Aug 08 2025 00:47:50
%S A258986 7,1,1,5,6,6,1,9,7,5,5,0,5,7,2,4,3,2,0,9,6,9,7,3,8,0,6,0,8,6,4,0,2,6,
%T A258986 1,2,0,9,2,5,6,1,2,0,4,4,3,8,3,3,9,2,3,6,4,9,2,2,2,2,4,9,6,4,5,7,6,8,
%U A258986 6,0,8,5,7,4,5,0,5,8,2,6,5,1,1,5,4,2,5,2,3,4,4,6,3,6,0,0,7,9,8,9,6,4,1
%N A258986 Decimal expansion of the multiple zeta value (Euler sum) zetamult(2,3).
%H A258986 Dominique Manchon, <a href="http://arxiv.org/abs/1603.01498">Arborified multiple zeta values</a>, arXiv:1603.01498 [math.CO], 2016.
%H A258986 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/MultivariateZetaFunction.html">Multivariate Zeta Function</a>
%H A258986 Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiple_zeta_function">Multiple zeta function</a>
%F A258986 zetamult(2,3) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^2*n^3)) = (9/2)*zeta(5) - 2*zeta(2)*zeta(3).
%F A258986 Equals Sum_{i, j >= 1} 1/(i^3*j^2*binomial(i+j, i)). More generally, for n >= 2, Sum_{i, j >= 1} 1/(i^n*j^2*binomial(i+j, i)) = zeta(2)*zeta(n) - zeta(n+2) - zeta(n,2). - _Peter Bala_, Aug 05 2025
%e A258986 0.711566197550572432096973806086402612092561204438339236492222496457686...
%t A258986 RealDigits[(9/2)*Zeta[5] - 2*Zeta[2]*Zeta[3], 10, 103] // First
%o A258986 (PARI) zetamult([2,3]) \\ _Charles R Greathouse IV_, Jan 21 2016
%Y A258986 Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)), A258984 (4,2), A258985 (5,2), A258947 (6,2), A258987 (3,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).
%Y A258986 Cf. A013663 (zeta(5)), A183699 (zeta(2)*zeta(3)).
%K A258986 nonn,cons,easy
%O A258986 0,1
%A A258986 _Jean-François Alcover_, Jun 16 2015