OFFSET
1,1
REFERENCES
Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.
LINKS
David J. Broadhurst, Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity, arXiv:hep-th/9803091, 1998; p. 18.
EXAMPLE
-8.21685981750873806291339833860108582496950833917257503683557579115...
MATHEMATICA
digits = 101;
C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);
v[k_] := ((-1)^k*((24*(k - 1)*(3*k - 4))/(3*k - 2)^3 + (8*(3*k*(3*k - 5) + 4))/(27*(k - 1)^3) + PolyGamma[2, (3*k)/2 - 1] - PolyGamma[2, (3*(k - 1))/2]))/(48*(k - 1)*(3*k - 4)*(3*k - 2));
V = A274400 = 3 Zeta[3]/8 - 1/2 + NSum[v[k], {k, 2, Infinity}, WorkingPrecision -> digits + 10, Method -> "AlternatingSigns"];
V5 = 6 Zeta[3] - 469/27 Zeta[4] + 8/3 C0^2 - 16 V;
RealDigits[V5, 10, digits][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 21 2016
STATUS
approved