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%I #8 Apr 06 2024 13:43:37
%S 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,
%T 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,
%U 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
%N Decimal expansion of Ls_6(Pi), the value of the 6th 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_{0..Pi} log(2*sin(t/2))^5 dx = (45/2)*Pi*zeta(5) + (5/4)*Pi^3*zeta(3).
%F Also equals 5th derivative of -Pi*binomial(x, x/2) at x=0.
%e 119.8852400579281896736967018589288678430302320347399435542106179...
%t RealDigits[(45/2)*Pi*Zeta[5] + (5/4)*Pi^3*Zeta[3], 10, 105] // First
%Y Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).
%K nonn,cons,easy
%O 3,3
%A _Jean-François Alcover_, Jun 09 2015