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

%I A261028 #15 Feb 16 2025 08:33:26
%S A261028 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,
%T A261028 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,
%U A261028 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
%N A261028 Decimal expansion of Cl_2(5*Pi/6), where Cl_2 is the Clausen function of order 2.
%H A261028 G. C. Greubel, <a href="/A261028/b261028.txt">Table of n, a(n) for n = 0..10000</a>
%H A261028 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausenFunction.html">Clausen Function</a>
%H A261028 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausensIntegral.html">Clausen's Integral</a>
%H A261028 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H A261028 Wikipedia, <a href="https://en.wikipedia.org/wiki/Clausen_function">Clausen function</a>
%H A261028 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A261028 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.
%e A261028 0.356908327849065937114435038052959335697343922638539808173...
%t A261028 Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[5*Pi/6] // Re, 10, 104] // First
%Y A261028 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)).
%K A261028 nonn,cons,easy
%O A261028 0,1
%A A261028 _Jean-François Alcover_, Aug 07 2015