A261025 Decimal expansion of Cl_2(Pi/4), where Cl_2 is the Clausen function of order 2.

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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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(7/8)/G(1/8)) - 2*Pi*LogGamma(1/8) + (Pi/4) * log(2*Pi/sqrt(2-sqrt(2))), where G is the Barnes G function.

Example

0.9818721510502033567179245430601956671307909716607304615766131...

Mathematica

Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[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)), A261026 (Cl_2(3*Pi/4)), A261027 (Cl_2(Pi/6)), A261028 (Cl_2(5*Pi/6)).

Sequence in context: A008570 A244978 A114864 * A340207 A185260 A275615

Adjacent sequences: A261022 A261023 A261024 * A261026 A261027 A261028

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 07 2015

Status

approved