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.
FORMULA
V_3L = 6 zeta(3) - 15/4 zeta(4) - 6 C^2, where C is A143298.
EXAMPLE
-3.027009493987652019786374701758957286150741786417375620053670876...
MATHEMATICA
C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);
V3L = 6 Zeta[3] - 15/4 Zeta[4] - 6 C0^2;
RealDigits[V3L, 10, 102][[1]]
PROG
(PARI)
clausen(n, x) = my(z = polylog(n, exp(I*x))); if (n%2, real(z), imag(z));
6*(zeta(3) - (clausen(2, Pi/3)^2 + (zeta(2)/2)^2)) \\ Gheorghe Coserea, Sep 30 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 21 2016
STATUS
approved