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

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, 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, 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

Offset

2,4

References

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

Links

Table of n, a(n) for n=2..102.

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

V6 = 6 zeta(3) - 13 zeta(4) - 8 U - 4 C^2, where U is A255685 and C A143298.

Example

-10.03527847976878917191470068515890023865033349600275134054452580...

Mathematica

C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);
U = A255685 = Pi^4/180 + (Pi^2/12)*Log[2]^2 - (1/12)*Log[2]^4 - 2*PolyLog[4, 1/2];
V6 = 6 Zeta[3] - 13 Zeta[4] - 8 U - 4 C0^2;
RealDigits[V6, 10, 101][[1]]

Crossrefs

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).

Sequence in context: A120683 A210042 A338872 * A079313 A125132 A352849

Adjacent sequences: A274418 A274419 A274420 * A274422 A274423 A274424

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 21 2016

Status

approved