A380205 Decimal expansion of the generalized log-sine integral with k = 0, n = 3, m = 3, from {0 .. 4 Pi/3} (negated).
4, 2, 6, 0, 2, 8, 8, 7, 3, 9, 1, 5, 1, 0, 6, 3, 1, 7, 4, 3, 2, 2, 6, 5, 2, 9, 5, 3, 7, 3, 0, 5, 0, 0, 5, 3, 4, 9, 8, 8, 8, 8, 7, 8, 7, 5, 8, 6, 9, 7, 8, 0, 1, 3, 8, 1, 5, 3, 9, 1, 6, 2, 5, 7, 7, 2, 7, 1, 3, 4, 5, 1, 4, 4, 4, 4, 1, 5, 2, 8, 1, 5, 0, 8, 7, 4, 1, 4, 4, 1, 4, 4, 2, 9, 5, 0, 2, 2, 1, 5
Offset: 1
Examples
-4.260288739151063174322652953730500534988887875869780138153916257727...
Links
- Jonathan M. Borwein and Armin Straub, Special Values of Generalized Log-sine Integrals, ISSAC '11: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, 2011, pp. 43-50.
- Armin Straub, A Mathematica package for evaluating log-sine integrals
Programs
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Maple
Digits:= 100: evalf(Int(log(3*sin(x/2))^2, x = 0..4*Pi/3)); # Peter Luschny, Jan 28 2025
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Mathematica
NIntegrate[Log[3*Sin[x/2]]^2, {x, 2*Pi/3, 2*Pi}, WorkingPrecision -> 100]