A258750 Decimal expansion of Ls_4(Pi), the value of the 4th basic generalized log-sine integral at Pi.

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

Offset: 1

Author

Jean-François Alcover, Jun 09 2015

Keywords

• nonn
• cons
• easy

Examples

			5.6645597042446183908052136898788142322518455591949799463744298643...
		

Links

• Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals.

Crossrefs

Cf. A258749 (Ls_3(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).

Programs

Mathematica

RealDigits[(3/2)*Pi*Zeta[3], 10, 105] // First

Formula

-Integral_{0..Pi} log(2*sin(t/2))^3 dx = (3/2)*Pi*zeta(3).

Also equals 3rd derivative of -Pi*binomial(x, x/2) at x=0.