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%I A258753 #8 Apr 06 2024 13:43:17
%S A258753 7,2,0,1,2,8,3,9,2,2,9,9,7,7,0,5,2,8,7,2,1,0,4,9,7,0,2,2,3,3,3,6,2,6,
%T A258753 7,5,3,4,1,6,2,7,8,4,2,5,2,2,0,0,5,8,8,5,0,3,4,0,8,0,6,4,5,3,8,5,0,4,
%U A258753 8,3,4,6,5,5,5,6,3,4,5,7,9,3,2,5,5,0,8,5,2,8,6,9,4,8,0,9,9,2,5,9,1,9
%N A258753 Decimal expansion of Ls_7(Pi), the value of the 7th basic generalized log-sine integral at Pi (negated).
%H A258753 Jonathan M. Borwein, Armin Straub, <a href="https://carmamaths.org/resources/jon/logsin3.pdf">Special Values of Generalized Log-sine Integrals</a>.
%F A258753 -Integral_{0..Pi} log(2*sin(t/2))^6 dx = -(275/1344)*Pi^7 - (45/2)*Pi*Zeta[3]^2.
%F A258753 Also equals 6th derivative of -Pi*binomial(x, x/2) at x=0.
%e A258753 -720.128392299770528721049702233362675341627842522005885034080645385...
%t A258753 RealDigits[-(275/1344)*Pi^7 - (45/2)*Pi*Zeta[3]^2 , 10, 102] // First
%Y A258753 Cf. A258749 (Ls_3(Pi)),  A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)),A258754 (Ls_8(Pi)).
%K A258753 nonn,cons,easy
%O A258753 3,1
%A A258753 _Jean-François Alcover_, Jun 09 2015

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