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

%I A261027 #16 Feb 16 2025 08:33:26
%S A261027 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,
%T A261027 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,
%U A261027 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
%N A261027 Decimal expansion of Cl_2(Pi/6), where Cl_2 is the Clausen function of order 2.
%H A261027 G. C. Greubel, <a href="/A261027/b261027.txt">Table of n, a(n) for n = 0..10000</a>
%H A261027 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausenFunction.html">Clausen Function</a>
%H A261027 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausensIntegral.html">Clausen's Integral</a>
%H A261027 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H A261027 Wikipedia, <a href="https://en.wikipedia.org/wiki/Clausen_function">Clausen function</a>
%H A261027 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A261027 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.
%e A261027 0.8643791310538927496250363151902194786681885764036897041820...
%t A261027 Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[Pi/6] // Re, 10, 104] // First
%Y A261027 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)).
%K A261027 nonn,cons,easy
%O A261027 0,1
%A A261027 _Jean-François Alcover_, Aug 07 2015