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A261027
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Decimal expansion of Cl_2(Pi/6), where Cl_2 is the Clausen function of order 2.
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7
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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
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OFFSET
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0,1
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LINKS
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FORMULA
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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.
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EXAMPLE
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0.8643791310538927496250363151902194786681885764036897041820...
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MATHEMATICA
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Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[Pi/6] // Re, 10, 104] // First
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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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