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A261027
Decimal expansion of Cl_2(Pi/6), where Cl_2 is the Clausen function of order 2.
7
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
0,1
LINKS
Eric Weisstein's MathWorld, Clausen Function
Eric Weisstein's MathWorld, Clausen's Integral
Eric Weisstein's MathWorld, Barnes G-Function
Wikipedia, Clausen function
FORMULA
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.
EXAMPLE
0.8643791310538927496250363151902194786681885764036897041820...
MATHEMATICA
Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[Pi/6] // Re, 10, 104] // First
CROSSREFS
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)).
Sequence in context: A093019 A175573 A296494 * A296041 A008569 A219863
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved