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A274417
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Decimal expansion of V_3L, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with three masses (line case).
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9
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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
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OFFSET
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1,1
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REFERENCES
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Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.
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LINKS
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FORMULA
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V_3L = 6 zeta(3) - 15/4 zeta(4) - 6 C^2, where C is A143298.
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EXAMPLE
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-3.027009493987652019786374701758957286150741786417375620053670876...
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MATHEMATICA
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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]]
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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