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

%I A261025 #17 Feb 16 2025 08:33:26
%S A261025 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,
%T A261025 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,
%U A261025 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
%N A261025 Decimal expansion of Cl_2(Pi/4), where Cl_2 is the Clausen function of order 2.
%H A261025 G. C. Greubel, <a href="/A261025/b261025.txt">Table of n, a(n) for n = 0..1000</a>
%H A261025 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausenFunction.html">Clausen Function</a>
%H A261025 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ClausensIntegral.html">Clausen's Integral</a>
%H A261025 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H A261025 Wikipedia, <a href="https://en.wikipedia.org/wiki/Clausen_function">Clausen function</a>
%H A261025 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A261025 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.
%e A261025 0.9818721510502033567179245430601956671307909716607304615766131...
%t A261025 Cl2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); RealDigits[Cl2[Pi/4] // Re, 10, 105] // First
%Y A261025 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)).
%K A261025 nonn,cons,easy
%O A261025 0,1
%A A261025 _Jean-François Alcover_, Aug 07 2015