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%I #13 Apr 06 2024 13:43:03
%S 5,0,4,0,0,3,9,8,7,9,1,1,5,0,4,5,1,6,4,3,4,5,6,2,1,4,3,8,3,3,5,3,9,3,
%T 1,5,9,3,0,5,3,7,5,9,6,1,6,7,7,4,8,2,0,0,2,0,0,2,1,3,8,5,3,9,1,6,1,3,
%U 4,1,1,9,9,0,5,7,5,1,4,0,6,2,1,5,8,9,5,4,2,4,5,3,0,3,2,2,3,3,5,7,0,5,3,8,6
%N Decimal expansion of Ls_8(Pi), the value of the 8th basic generalized log-sine integral at Pi.
%H Jonathan M. Borwein, Armin Straub, <a href="https://carmamaths.org/resources/jon/logsin3.pdf">Special Values of Generalized Log-sine Integrals</a>.
%F -Integral_{t=0..Pi} log(2*sin(t/2))^7 = (2835/4)*Pi*zeta(7) + (315/8)*Pi^3*zeta(5) + (133/32)*Pi^5*zeta(3).
%F Also equals 7th derivative of -Pi*binomial(x, x/2) at x=0.
%e 5040.03987911504516434562143833539315930537596167748200200213853916...
%t RealDigits[(2835/4)*Pi*Zeta[7] + (315/8)*Pi^3*Zeta[5] + (133/32)*Pi^5*Zeta[3], 10, 105] // First
%o (PARI) -intnum(t=0,Pi,log(2*sin(t/2))^7) \\ _Hugo Pfoertner_, Jul 22 2020
%Y Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)).
%K nonn,cons,easy,changed
%O 4,1
%A _Jean-François Alcover_, Jun 09 2015
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