A255987 - OEIS

%I #5 Mar 13 2015 14:16:08

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

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

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

%N Decimal expansion of sum_{m,n >= 1} (-1)^(m + n)*log(m)*log(n)/(m*n*(m + n)).

%H David H. Bailey and Jonathan M. Borwein, <a href="http://www.davidhbailey.com/dhbpapers/mtw3.pdf">Computation and structure of character polylogarithms</a>.

%e 0.008465459183243566000220465483622880709825883487695051...

%t digits = 104; s = NSum[(-1)^(m + n)*Log[m]*Log[n]/(m*n*(m + n)), {m, 1, Infinity}, {n, 1, Infinity}, WorkingPrecision -> digits + 10, Method -> "AlternatingSigns"]; Join[{0, 0}, RealDigits[s, 10, digits] // First]

%K nonn,cons

%O 0,3

%A _Jean-François Alcover_, Mar 13 2015