A258752 Decimal expansion of Ls_6(Pi), the value of the 6th basic generalized log-sine integral at Pi.

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

Offset: 3

Author

Jean-François Alcover, Jun 09 2015

Keywords

• nonn
• cons
• easy

Examples

			119.8852400579281896736967018589288678430302320347399435542106179...
		

Links

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

Crossrefs

Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).

Programs

Mathematica

RealDigits[(45/2)*Pi*Zeta[5] + (5/4)*Pi^3*Zeta[3], 10, 105] // First

Formula

-Integral_{0..Pi} log(2*sin(t/2))^5 dx = (45/2)*Pi*zeta(5) + (5/4)*Pi^3*zeta(3).

Also equals 5th derivative of -Pi*binomial(x, x/2) at x=0.