A274416 - OEIS

%I #5 Jun 21 2016 10:15:27

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

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

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

%N Decimal expansion of V_3S, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with three masses (star 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_3S = 6 zeta(3) - 11/2 zeta(4) - 4 C^2, where C is A143298.

%e -2.860862224139327350272784567773241917561441462020100039500166119667...

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

%t V3S = 6 Zeta[3] - 11/2 Zeta[4] - 4 C0^2;

%t RealDigits[V3S, 10, 103][[1]]

%Y Cf. A274412 (V_1), A274413 (V_2A), A274414 (V_2N), A274415 (V_3T), A274417 (V_3L), A274418 (V_4A), A274419 (V_4N), A274420 (V_5), A274421 (V_6).

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Jun 21 2016