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

Author

Jean-François Alcover, Aug 07 2015

Keywords

• nonn
• cons
• easy

Examples

			0.9818721510502033567179245430601956671307909716607304615766131...
		

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

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)).

Programs

Mathematica

Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[Pi/4] // Re, 10, 105] // First

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.