A274416 Decimal expansion of V_3S, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with three masses (star case).

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, 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, 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

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_3S = 6 zeta(3) - 11/2 zeta(4) - 4 C^2, where C is A143298.

Example

-2.860862224139327350272784567773241917561441462020100039500166119667...

Mathematica

C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);
V3S = 6 Zeta[3] - 11/2 Zeta[4] - 4 C0^2;
RealDigits[V3S, 10, 103][[1]]

Crossrefs

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).

Sequence in context: A183232 A344691 A096417 * A011059 A200284 A019771

Adjacent sequences: A274413 A274414 A274415 * A274417 A274418 A274419

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 21 2016

Status

approved