A258759 - OEIS

%I #8 Apr 06 2024 13:42:43

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

%T 5,0,3,8,4,7,9,3,5,3,7,0,0,1,1,0,7,1,7,9,4,9,9,0,8,4,9,6,9,1,9,1,3,3,

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

%N Decimal expansion of Ls_3(Pi/3), the value of the 3rd basic generalized log-sine integral at Pi/3 (negated).

%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/3} log(2*sin(x/2))^2 dx = -7*Pi^3/108.

%e -2.0096660811305439002623537543491645038479353700110717949908496919...

%t RealDigits[-7*Pi^3/108, 10, 105] // First

%Y 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)).

%Y Cf. A143298 (Ls_2(Pi/3)), A258760 (Ls_4(Pi/3)), A258761 (Ls_5(Pi/3)), A258762 (Ls_6(Pi/3)), A258763 (Ls_7(Pi/3)).

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Jun 09 2015