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Decimal expansion of V_4A, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with four masses (adjacent case).
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%I #5 Jun 21 2016 10:15:54

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

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

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

%N Decimal expansion of V_4A, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with four masses (adjacent case).

%D Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.

%H David J. Broadhurst, <a href="http://arxiv.org/abs/hep-th/9803091">Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity</a>, arXiv:hep-th/9803091, 1998; p. 18.

%F V_4A = 6 zeta(3) - 77/12 zeta(4) - 6 C^2, where C is A143298.

%e -5.9132047838840205304957178925354050268834109915339807072082741172...

%t C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);

%t V4A = 6 Zeta[3] - 77/12 Zeta[4] - 6 C0^2;

%t RealDigits[V4A, 10, 100][[1]]

%Y Cf. A274412 (V_1), A274413 (V_2A), A274414 (V_2N), A274415 (V_3T), A274416 (V_3S), A274417 (V_3L), A274419 (V_4N), A274420 (V_5), A274421 (V_6).

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Jun 21 2016