A379273 Decimal expansion of the generalized log-sine integral with k = 0, n = 3, m = 3, from {0 .. 2*Pi/3} (negated).

1, 9, 4, 0, 3, 9, 1, 9, 8, 2, 0, 7, 2, 0, 5, 9, 6, 9, 7, 9, 3, 6, 4, 9, 2, 5, 5, 9, 1, 3, 1, 0, 6, 3, 7, 1, 6, 1, 1, 9, 1, 8, 4, 1, 8, 7, 8, 3, 6, 2, 5, 4, 5, 2, 6, 9, 4, 3, 2, 6, 0, 7, 6, 2, 9, 4, 4, 8, 5, 7, 1, 3, 2, 3, 5, 9, 3, 4, 5, 8, 6, 7, 4, 5, 8, 9, 4, 9, 5, 4, 5, 5, 7, 2, 3, 2, 4, 8, 7, 3

Offset

1,2

Links

Table of n, a(n) for n=1..100.

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; alternative link.

Armin Straub, A Mathematica package for evaluating log-sine integrals.

Formula

Equals -Integral_{0..2*Pi/3} log(3*sin(x/2))^2 dx.

Equals (1/162)*(-4*Pi^3 + 324*Im(PolyLog(3, 1 - (-1)^(2/3))) - 108*Pi*log(3/2)^2 + 27*Pi*log(3)^2 + 12*sqrt(3)*Pi^2*log(27/4) - 18*sqrt(3)*log(27/4)*PolyGamma(1, 2/3)). (This formula was suggested by Mathematica.)

Example

-1.9403919820720596979364925591310637161191841878362545269432607629448...

Mathematica

RealDigits[(1/162)*(-4*Pi^3 + 324*Im[PolyLog[3, 1 - (-1)^(2/3)]] - 108*Pi*Log[3/2]^2 + 27*Pi*Log[3]^2 + 12*Sqrt[3]*Pi^2*Log[27/4] - 18*Sqrt[3]*Log[27/4]*PolyGamma[1, 2/3]), 10, 105] // First

Prog

(PARI) -intnum(x = 0, 2*Pi/3, log(3*sin(x/2))^2) \\ Amiram Eldar, Jun 29 2026

Crossrefs

Cf. A379042.

Sequence in context: A359285 A355283 A198111 * A194562 A239349 A198675

Adjacent sequences: A379270 A379271 A379272 * A379274 A379275 A379276

Keyword

nonn,cons,changed

Author

Detlef Meya, Dec 19 2024

Status

approved