login
Decimal expansion of the multiple zeta value (Euler sum) zetamult(2,4).
9

%I #10 Jan 21 2016 14:44:54

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

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

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

%N Decimal expansion of the multiple zeta value (Euler sum) zetamult(2,4).

%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(2,4) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^2*n^4)) = (25/12)*zeta(6) - zeta(3)^2.

%e 0.67452391403396814049156060825742993927838436513788957970691722144377...

%t RealDigits[(25/12)*Zeta[6] - Zeta[3]^2, 10, 103] // First

%o (PARI) zetamult([2,4]) \\ _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), A258990 (3,4), A258991 (4,4).

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Jun 16 2015