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

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

0,1

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(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.

Example

0.356908327849065937114435038052959335697343922638539808173...

Mathematica

Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[5*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)), A261027 (Cl_2(Pi/6)).

Sequence in context: A335110 A152989 A308051 * A195481 A199730 A016612

Adjacent sequences: A261025 A261026 A261027 * A261029 A261030 A261031

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 07 2015

Status

approved