A143298 -id:A143298 - cp's OEIS frontend

A340576 Decimal expansion of Product_{primes p == 5 (mod 6)} 1/(1-1/p^2).

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

Offset: 1

Jean-François Alcover, Jan 12 2021

The four similar sequences for products of primes mod 6 are these:
  A175646 for Product_{primes p == 1 (mod 6)} 1/(1-1/p^2),
  A340576 for Product_{primes p == 5 (mod 6)} 1/(1-1/p^2),
  A340577 for Product_{primes p == 1 (mod 6)} 1/(1+1/p^2),
  A340578 for Product_{primes p == 5 (mod 6)} 1/(1+1/p^2).

			1.06054829316911072817412636430987203493077130204487163127994372...

R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, arXiv:1008.2547 [math.NT], 2010-2015, Zeta_{6,5}(2) in section 3.2.

Similar constants: A175646, A175647, A248930, A248938, A301429, A333240, A334826, A335963, A340577, A340578.

Cf. A259548.

a := n -> 3^(2^(-n-2))*((1-3^(-2^(n+1)))/2)^(2^(-n-1)):
b := n -> Zeta(n)/Im(polylog(n, (-1)^(2/3))):
c := n -> a(n)*b(2^(n+1))^(1/2^(n+1)):
Digits := 107: evalf((3/4)*mul(c(n), n=0..9)); # Peter Luschny, Jan 14 2021

digits = 105;
precision = digits + 10;
prodeuler[p_, a_, b_, expr_] := Product[If[a <= p <= b, expr, 1], {p, Prime[Range[PrimePi[a], PrimePi[b]]]}];
Lv3[s_] := prodeuler[p, 1, 2^(precision/s), 1/(1 - KroneckerSymbol[-3, p]*p^-s)] // N[#, precision] &;
Lv4[s_] := 2*Im[PolyLog[s, Exp[2*I*Pi/3]]]/Sqrt[3];
Lv[s_] := If[s >= 10000, Lv3[s], Lv4[s]];
gv[s_] := (1 - 3^(-s))*Zeta[s]/Lv[s];
pB = (3/4)*Product[gv[2^n*2]^(2^-(n+1)), {n, 0, 11}] // N[#, precision]&;
RealDigits[pB, 10, digits][[1]] (* Most of this code is due to Artur Jasinski *)
S[m_, n_, s_] := (t = 1; sums = 0; difs = 1; While[Abs[difs] > 10^(-digits - 5) || difs == 0, difs = (MoebiusMu[t]/t) * Log[If[s*t == 1, DirichletL[m, n, s*t], Sum[Zeta[s*t, j/m]*DirichletCharacter[m, n, j]^t, {j, 1, m}]/m^(s*t)]]; sums = sums + difs; t++]; sums);
P[m_, n_, s_] := 1/EulerPhi[m] * Sum[Conjugate[DirichletCharacter[m, r, n]] * S[m, r, s], {r, 1, EulerPhi[m]}] + Sum[If[GCD[p, m] > 1 && Mod[p, m] == n, 1/p^s, 0], {p, 1, m}];
Z[m_, n_, s_] := (w = 1; sumz = 0; difz = 1; While[Abs[difz] > 10^(-digits - 5), difz = P[m, n, s*w]/w; sumz = sumz + difz; w++]; Exp[sumz]);
$MaxExtraPrecision = 1000; digits = 121; RealDigits[Chop[N[Z[6,5,2], digits]], 10, digits-1][[1]] (* Vaclav Kotesovec, Jan 15 2021 *)

g = A143298 = (9 - PolyGamma(1, 2/3) + PolyGamma(1, 4/3))/(4 sqrt(3));
h = A301429;
Equals (3*sqrt(3)*h^2)/2.
Equals (3/4)*A333240.
A340577 = Pi^4/(243*g*h^2);
A340578 = (45*g*h^2)/(2*Pi^2).
Equals Pi^2/(9*A175646). - Artur Jasinski, Jan 11 2021
Equals Sum_{k>=1} 1/A259548(k)^2. - Amiram Eldar, Jan 24 2021

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

Original entry on oeis.org

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

Jean-François Alcover, Jun 21 2016

			-2.860862224139327350272784567773241917561441462020100039500166119667...

Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.

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.

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).

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]]

V_3S = 6 zeta(3) - 11/2 zeta(4) - 4 C^2, where C is A143298.

A274417 Decimal expansion of V_3L, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with three masses (line case).

Original entry on oeis.org

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

Jean-François Alcover, Jun 21 2016

			-3.027009493987652019786374701758957286150741786417375620053670876...

Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.

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.

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).

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]]

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

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

A274418 Decimal expansion of V_4A, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with four masses (adjacent case).

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Jun 21 2016

			-5.9132047838840205304957178925354050268834109915339807072082741172...

Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.

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.

Cf. A274412 (V_1), A274413 (V_2A), A274414 (V_2N), A274415 (V_3T), A274416 (V_3S), A274417 (V_3L), A274419 (V_4N), A274420 (V_5), A274421 (V_6).

C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);
V4A = 6 Zeta[3] - 77/12 Zeta[4] - 6 C0^2;
RealDigits[V4A, 10, 100][[1]]

V_4A = 6 zeta(3) - 77/12 zeta(4) - 6 C^2, where C is A143298.

A274420 Decimal expansion of V_5, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with five masses.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Jun 21 2016

			-8.21685981750873806291339833860108582496950833917257503683557579115...

Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.

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.

Cf. A274412 (V_1), A274413 (V_2A), A274414 (V_2N), A274415 (V_3T), A274416 (V_3S), A274417 (V_3L), A274418 (V_4A), A274419 (V_4N), A274421 (V_6).

digits = 101;
C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);
v[k_] := ((-1)^k*((24*(k - 1)*(3*k - 4))/(3*k - 2)^3 + (8*(3*k*(3*k - 5) + 4))/(27*(k - 1)^3) + PolyGamma[2, (3*k)/2 - 1] - PolyGamma[2, (3*(k - 1))/2]))/(48*(k - 1)*(3*k - 4)*(3*k - 2));
V = A274400 = 3 Zeta[3]/8 - 1/2 + NSum[v[k], {k, 2, Infinity}, WorkingPrecision -> digits + 10, Method -> "AlternatingSigns"];
V5 = 6 Zeta[3] - 469/27 Zeta[4] + 8/3 C0^2 - 16 V;
RealDigits[V5, 10, digits][[1]]

V_5 = 6 zeta(3) - 469/27 zeta(4) + 8/3 C^2 - 16 V, where C is A143298 and V A274400.

A274421 Decimal expansion of V_6, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with six masses.

Original entry on oeis.org

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

Offset: 2

Jean-François Alcover, Jun 21 2016

			-10.03527847976878917191470068515890023865033349600275134054452580...

Jonathan Borwein and Peter Borwein, Experimental and Computational Mathematics: Selected Writings, Perfectly Scientific Press, 2010, p. 106.

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.

Cf. A274412 (V_1), A274413 (V_2A), A274414 (V_2N), A274415 (V_3T), A274416 (V_3S), A274417 (V_3L), A274418 (V_4A), A274419 (V_4N), A274420 (V_5).

C0 = A143298 = (9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]);
U = A255685 = Pi^4/180 + (Pi^2/12)*Log[2]^2 - (1/12)*Log[2]^4 - 2*PolyLog[4, 1/2];
V6 = 6 Zeta[3] - 13 Zeta[4] - 8 U - 4 C0^2;
RealDigits[V6, 10, 101][[1]]

V6 = 6 zeta(3) - 13 zeta(4) - 8 U - 4 C^2, where U is A255685 and C A143298.

A261024 Decimal expansion of Cl_2(2*Pi/3), where Cl_2 is the Clausen function of order 2.

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Aug 07 2015

			0.676627737606435750014135036183013523961126205020199861344992737851...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's MathWorld, Clausen Function.
Eric Weisstein's MathWorld, Clausen's Integral.
Eric Weisstein's MathWorld, Barnes G-Function.
Wikipedia, Clausen function.
Wikipedia, Barnes G-function.

Cf. A006752 (Cl_2(Pi/2) = Catalan's constant), A143298 (Cl_2(Pi/3) = Gieseking's constant), A261025 (Cl_2(Pi/4)), A261026 (Cl_2(3*Pi/4)), A261027 (Cl_2(Pi/6)), A261028 (Cl_2(5*Pi/6)).

Cf. A252798, A252799, A263416, A263417.

Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[2*Pi/3] // Re, 10, 105] // First

clausen(n, x) = my(z = polylog(n, exp(I*x))); if (n%2, real(z), imag(z));
clausen(2, 2*Pi/3) \\ Gheorghe Coserea, Sep 30 2018

Equals 2*Pi*log(G(2/3)/G(1/3)) - 2*Pi*LogGamma(1/3) + (2*Pi/3)*log(2*Pi/sqrt(3)), where G is the Barnes G function.

A261027 Decimal expansion of Cl_2(Pi/6), where Cl_2 is the Clausen function of order 2.

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Aug 07 2015

			0.8643791310538927496250363151902194786681885764036897041820...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's MathWorld, Clausen Function
Eric Weisstein's MathWorld, Clausen's Integral
Eric Weisstein's MathWorld, Barnes G-Function
Wikipedia, Clausen function
Wikipedia, Barnes G-function

Cf. A006752 (Cl_2(Pi/2) = Catalan's constant), A143298 (Cl_2(Pi/3) = Gieseking's constant), A261024 (Cl_2(2*Pi/3)), A261025 (Cl_2(Pi/4)), A261026 (Cl_2(3*Pi/4)), A261028 (Cl_2(5*Pi/6)).

Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[Pi/6] // Re, 10, 104] // First

Equals 2*Pi*log(G(11/12)/G(1/12)) - 2*Pi*LogGamma(1/12) + (Pi/6) * log(2*Pi*sqrt(2)/(sqrt(3)-1)), where G is the Barnes G function.

A261028 Decimal expansion of Cl_2(5*Pi/6), where Cl_2 is the Clausen function of order 2.

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Aug 07 2015

			0.356908327849065937114435038052959335697343922638539808173...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's MathWorld, Clausen Function
Eric Weisstein's MathWorld, Clausen's Integral
Eric Weisstein's MathWorld, Barnes G-Function
Wikipedia, Clausen function
Wikipedia, Barnes G-function

Cf. A006752 (Cl_2(Pi/2) = Catalan's constant), A143298 (Cl_2(Pi/3) = Gieseking's constant), A261024 (Cl_2(2*Pi/3)), A261025 (Cl_2(Pi/4)), A261026 (Cl_2(3*Pi/4)), A261027 (Cl_2(Pi/6)).

Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[5*Pi/6] // Re, 10, 104] // First

Equals 2*Pi*log(G(7/12)/G(5/12)) - 2*Pi*LogGamma(5/12) + (5*Pi/6) * log(2*Pi*sqrt(2)/(sqrt(3)+1)), where G is the Barnes G function.

A261025 Decimal expansion of Cl_2(Pi/4), where Cl_2 is the Clausen function of order 2.

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Aug 07 2015

			0.9818721510502033567179245430601956671307909716607304615766131...

G. C. Greubel, Table of n, a(n) for n = 0..1000
Eric Weisstein's MathWorld, Clausen Function
Eric Weisstein's MathWorld, Clausen's Integral
Eric Weisstein's MathWorld, Barnes G-Function
Wikipedia, Clausen function
Wikipedia, Barnes G-function

Cf. A006752 (Cl_2(Pi/2) = Catalan's constant), A143298 (Cl_2(Pi/3) = Gieseking's constant), A261024 (Cl_2(2*Pi/3)), A261026 (Cl_2(3*Pi/4)), A261027 (Cl_2(Pi/6)), A261028 (Cl_2(5*Pi/6)).

Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[Pi/4] // Re, 10, 105] // First

Equals 2*Pi*log(G(7/8)/G(1/8)) - 2*Pi*LogGamma(1/8) + (Pi/4) * log(2*Pi/sqrt(2-sqrt(2))), where G is the Barnes G function.

cp's OEIS Frontend

A340576 Decimal expansion of Product_{primes p == 5 (mod 6)} 1/(1-1/p^2).

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

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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).

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A274418 Decimal expansion of V_4A, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with four masses (adjacent case).

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A274420 Decimal expansion of V_5, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with five masses.

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A274421 Decimal expansion of V_6, a Quantum Field Theory constant [negated] related to the coloring of the tetrahedron with six masses.

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A261024 Decimal expansion of Cl_2(2*Pi/3), where Cl_2 is the Clausen function of order 2.

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