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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
OFFSET
1,1
REFERENCES
Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.
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 A368479
KEYWORD
nonn,cons
AUTHOR
STATUS
approved