A258983 - OEIS

%I #16 Feb 16 2025 08:33:25

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

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

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

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

%C Also zetamult(2, 2, 1). - _Charles R Greathouse IV_, Jan 04 2017

%H Dominique Manchon, <a href="http://arxiv.org/abs/1603.01498">Arborified multiple zeta values</a>, arXiv:1603.01498 [math.CO], 2016.

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/MultivariateZetaFunction.html">Multivariate Zeta Function</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiple_zeta_function">Multiple zeta function</a>

%F zetamult(3,2) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^3*n^2)) = 3*zeta(2)*zeta(3) - (11/2)*zeta(5).

%e 0.2288103976033537597687461489416887919325093427198821602294071...

%t RealDigits[3*Zeta[2]*Zeta[3] - (11/2)*Zeta[5], 10, 104] // First

%o (PARI) zetamult([3,2]) \\ _Charles R Greathouse IV_, Jan 21 2016

%o (PARI) zetamult([2,2,1]) \\ _Charles R Greathouse IV_, Jan 04 2017

%Y Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258984 (4,2), A258985 (5,2), A258947 (6,2), A258986 (2,3), A258987 (3,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).

%Y Cf. A013663 (zeta(5)), A183699 (zeta(2)*zeta(3)).

%K nonn,cons,easy,changed

%O 0,1

%A _Jean-François Alcover_, Jun 16 2015