cp's OEIS Frontend

A274421 Decimal expansion of V_6, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with six masses.

%I A274421 #5 Jun 21 2016 10:11:53
%S A274421 1,0,0,3,5,2,7,8,4,7,9,7,6,8,7,8,9,1,7,1,9,1,4,7,0,0,6,8,5,1,5,8,9,0,
%T A274421 0,2,3,8,6,5,0,3,3,3,4,9,6,0,0,2,7,5,1,3,4,0,5,4,4,5,2,5,8,0,0,6,6,3,
%U A274421 9,1,4,1,2,4,1,3,2,6,9,5,4,1,9,0,6,3,4,9,2,4,4,6,4,1,0,3,0,3,0,6,8
%N A274421 Decimal expansion of V_6, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with six masses.
%D A274421 Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.
%H A274421 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 A274421 V6 = 6 zeta(3) - 13 zeta(4) - 8 U - 4 C^2, where U is A255685 and C A143298.
%e A274421 -10.03527847976878917191470068515890023865033349600275134054452580...
%t A274421 C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);
%t A274421 U = A255685 = Pi^4/180 + (Pi^2/12)*Log[2]^2 - (1/12)*Log[2]^4 - 2*PolyLog[4, 1/2];
%t A274421 V6 = 6 Zeta[3] - 13 Zeta[4] - 8 U - 4 C0^2;
%t A274421 RealDigits[V6, 10, 101][[1]]
%Y A274421 Cf. A274412 (V_1), A274413 (V_2A), A274414 (V_2N), A274415 (V_3T), A274416 (V_3S), A274417 (V_3L), A274418 (V_4A), A274419 (V_4N), A274420 (V_5).
%K A274421 nonn,cons
%O A274421 2,4
%A A274421 _Jean-François Alcover_, Jun 21 2016