A274414 Decimal expansion of V_2N, a Quantum Field Theory constant related to the coloring of the tetrahedron with two masses (non-adjacent case).

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

Offset

1,3

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_2N = 6 zeta(3) - 13/2 zeta(4) - 8 U, where U is A255685.

Example

1.1202483970392420822725165482242095262757766719790688973922458664984...

Mathematica

U = A255685 = Pi^4/180 + (Pi^2/12)*Log[2]^2 - (1/12)*Log[2]^4 - 2*PolyLog[4, 1/2];
V2N = 6 Zeta[3] - 13/2 Zeta[4] - 8 U;
RealDigits[V2N, 10, 103][[1]]

Crossrefs

Cf. A274412 (V_1), A274413 (V_2A), A274415 (V_3T), A274416 (V_3S), A274417 (V_3L), A274418 (V_4A), A274419 (V_4N), A274420 (V_5), A274421 (V_6).

Sequence in context: A239229 A058210 A360860 * A079550 A226430 A067648

Adjacent sequences: A274411 A274412 A274413 * A274415 A274416 A274417

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 21 2016

Status

approved