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Decimal expansion of the multiple zeta value (Euler sum) zetamult(3,4).
8

%I #10 Jan 21 2016 14:45:08

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

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

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

%N Decimal expansion of the multiple zeta value (Euler sum) zetamult(3,4).

%H Eric Weisstein's MathWorld, <a href="http://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(3,4) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^3*n^4)) = 10*zeta(2)*zeta(5) + zeta(3)*zeta(4) - 18*zeta(7).

%e 0.20750501461573209590780760549467146544182867955060619041951789656971...

%t RealDigits[10*Zeta[2]*Zeta[5] + Zeta[3]*Zeta[4] - 18*Zeta[7], 10, 105] // First

%o (PARI) zetamult([3,4]) \\ _Charles R Greathouse IV_, Jan 21 2016

%Y Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)), A258984 (4,2), A258985 (5,2), A258947 (6,2), A258986 (2,3), A258987 (3,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258991 (4,4).

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Jun 16 2015