A258763 Decimal expansion of Ls_7(Pi/3), the value of the 7th basic generalized log-sine integral at Pi/3 (negated).

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

Offset: 3

Author

Jean-François Alcover, Jun 09 2015

Keywords

• nonn
• cons
• easy

Examples

			-720.1245682263318010530293318351565689006935502658088138930137116778...
		

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)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).

Cf. A143298 (Ls_2(Pi/3)), A258759 (Ls_3(Pi/3)), A258760 (Ls_4(Pi/3)), A258761 (Ls_5(Pi/3)), A258762 (Ls_6(Pi/3)).

Programs

Mathematica

RealDigits[-720*HypergeometricPFQ[Table[1/2, {7}], Table[3/2, {6}], 1/4], 10, 103] // First

Formula

-Integral_{0..Pi/3} log(2*sin(x/2))^5 dx = -74369*Pi^7/326592 - (15/2) * Pi * Zeta[3]^2 + 135*Gl_{6, 1}(Pi/3), where Gl is the multiple Glaisher function.

Also equals -720 * 7F6(1/2,1/2,...; 3/2,3/2,...; 1/4) (with 7F6 the hypergeometric function).