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

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

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

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

Adjacent sequences: A261024 A261025 A261026 * A261028 A261029 A261030

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 07 2015

Status

approved