A274419 Decimal expansion of V_4N, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with four masses (non-adjacent case).

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

Offset

1,1

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=1..103.

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_4N = 6 zeta(3 - 14 zeta(4) - 16 U, where U is A255685.

Example

-6.054167858590219739369399569161448794813115362003582403652113814498...

Mathematica

U = A255685 = Pi^4/180 + (Pi^2/12)*Log[2]^2 - (1/12)*Log[2]^4 - 2*PolyLog[4, 1/2];
V4N = 6 Zeta[3] - 14 Zeta[4] - 16 U;
RealDigits[V4N, 10, 103][[1]]

Crossrefs

Cf. A274412 (V_1), A274413 (V_2A), A274414 (V_2N), A274415 (V_3T), A274416 (V_3S), A274417 (V_3L), A274418 (V_4A), A274420 (V_5), A274421 (V_6).

Sequence in context: A275933 A079540 A011492 * A131329 A165954 A340576

Adjacent sequences: A274416 A274417 A274418 * A274420 A274421 A274422

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 21 2016

Status

approved