This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379042 #24 Dec 19 2024 07:08:55
%S A379042 1,3,5,8,7,8,0,5,8,8,3,2,6,6,7,4,2,4,5,6,0,5,4,3,1,7,5,7,4,9,6,7,3,3,
%T A379042 6,7,0,4,6,3,1,5,5,6,6,9,9,5,4,6,8,1,1,8,7,8,1,8,8,9,9,1,3,4,7,0,6,5,
%U A379042 1,6,7,6,7,3,4,7,6,3,7,6,7,2,9,5,4,6,2,2,3,2,4,6,5,4,2,3,4,7,7,7,5
%N A379042 Decimal expansion of the generalized log-sine integral with k = 0, n = 3, m = 3, from {0 .. Pi/3} (negated).
%H A379042 Jonathan M. Borwein and Armin Straub, <a href="https://carmamaths.org/resources/jon/logsin3.pdf">Special Values of Generalized Log-sine Integrals</a>, ISSAC '11: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, 2011, pp. 43-50.
%H A379042 Armin Straub, <a href="https://arminstraub.com/software/lstoli">A Mathematica package for evaluating log-sine integrals</a>
%F A379042 -Integral_{0..Pi/3} log(3*sin(x/2))^2 dx = -((7*Pi^3)/108) - (2*Pi^2*Log(3/2))/(3*Sqrt(3)) - (1/3)*Pi*Log(2)^2 + (2/3)*Pi*Log(2)*Log(3) - (1/3)*Pi*Log(3)^2 + (Log(3/2)*PolyGamma(1, 1/3))/Sqrt(3). (This formula was suggested by Mathematica.)
%e A379042 -1.3587805883266742456054317574967336704631556699546811878188991347065...
%p A379042 Digits:= 106: evalf(Int(log(3*sin(x/2))^2, x = 0..Pi/3)); # _Peter Luschny_, Dec 16 2024
%t A379042 RealDigits[-((7*Pi^3)/108) - (2*Pi^2*Log[3/2])/(3*Sqrt[3]) - (1/3)*Pi* Log[2]^2 + (2/3)*Pi*Log[2]*Log[3] - (1/3)*Pi*Log[3]^2 + (Log[3/2]*PolyGamma[1, 1/3])/Sqrt[3], 10, 105] // First
%Y A379042 Cf. A258759 (Ls_3(Pi/3)).
%K A379042 nonn,cons
%O A379042 1,2
%A A379042 _Detlef Meya_, Dec 14 2024