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

%I A261026 #17 Feb 16 2025 08:33:26
%S A261026 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,
%T A261026 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,
%U A261026 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
%N A261026 Decimal expansion of Cl_2(3*Pi/4), where Cl_2 is the Clausen function of order 2.
%H A261026 G. C. Greubel, <a href="/A261026/b261026.txt">Table of n, a(n) for n = 0..10000</a>
%H A261026 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausenFunction.html">Clausen Function</a>
%H A261026 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausensIntegral.html">Clausen's Integral</a>
%H A261026 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H A261026 Wikipedia, <a href="https://en.wikipedia.org/wiki/Clausen_function">Clausen function</a>
%H A261026 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A261026 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.
%e A261026 0.52388935396159384919062278559400361174371628451989439444336407484...
%t A261026 Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[3*Pi/4] // Re, 10, 105] // First
%Y A261026 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)).
%K A261026 nonn,cons,easy
%O A261026 0,1
%A A261026 _Jean-François Alcover_, Aug 07 2015