A261026 Decimal expansion of Cl_2(3*Pi/4), where Cl_2 is the Clausen function of order 2.

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

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(5/8)/G(3/8)) - 2*Pi*LogGamma(3/8) + (3*Pi/4) * log(2*Pi/sqrt(2+sqrt(2))), where G is the Barnes G function.

Example

0.52388935396159384919062278559400361174371628451989439444336407484...

Mathematica

Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[3*Pi/4] // Re, 10, 105] // 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)), A261027 (Cl_2(Pi/6)), A261028 (Cl_2(5*Pi/6)).

Sequence in context: A353617 A133746 A176319 * A160080 A026247 A354236

Adjacent sequences: A261023 A261024 A261025 * A261027 A261028 A261029

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 07 2015

Status

approved