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A274417 Decimal expansion of V_3L, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with three masses (line case). 9
3, 0, 2, 7, 0, 0, 9, 4, 9, 3, 9, 8, 7, 6, 5, 2, 0, 1, 9, 7, 8, 6, 3, 7, 4, 7, 0, 1, 7, 5, 8, 9, 5, 7, 2, 8, 6, 1, 5, 0, 7, 4, 1, 7, 8, 6, 4, 1, 7, 3, 7, 5, 6, 2, 0, 0, 5, 3, 6, 7, 0, 8, 7, 6, 0, 2, 7, 7, 3, 9, 3, 1, 3, 1, 3, 4, 8, 6, 0, 0, 2, 4, 8, 0, 7, 7, 0, 0, 4, 8, 2, 1, 5, 4, 2, 3, 7, 8, 2, 1, 7, 2 (list; constant; graph; refs; listen; history; text; internal format)
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..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

V_3L = 6 zeta(3) - 15/4 zeta(4) - 6 C^2, where C is A143298.

EXAMPLE

-3.027009493987652019786374701758957286150741786417375620053670876...

MATHEMATICA

C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);

V3L = 6 Zeta[3] - 15/4 Zeta[4] - 6 C0^2;

RealDigits[V3L, 10, 102][[1]]

PROG

(PARI)

clausen(n, x) = my(z = polylog(n, exp(I*x))); if (n%2, real(z), imag(z));

6*(zeta(3) - (clausen(2, Pi/3)^2 + (zeta(2)/2)^2)) \\ Gheorghe Coserea, Sep 30 2018

CROSSREFS

Cf. A274412 (V_1), A274413 (V_2A), A274414 (V_2N), A274415 (V_3T), A274416 (V_3S), A274418 (V_4A), A274419 (V_4N), A274420 (V_5), A274421 (V_6).

Sequence in context: A309973 A298058 A298707 * A208764 A209129 A282694

Adjacent sequences:  A274414 A274415 A274416 * A274418 A274419 A274420

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jun 21 2016

STATUS

approved

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Last modified January 24 13:11 EST 2022. Contains 350538 sequences. (Running on oeis4.)