A258750 - OEIS

%I #8 Apr 06 2024 13:44:18

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

%T 2,3,2,2,5,1,8,4,5,5,5,9,1,9,4,9,7,9,9,4,6,3,7,4,4,2,9,8,6,4,3,2,6,8,

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

%N Decimal expansion of Ls_4(Pi), the value of the 4th 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))^3 dx = (3/2)*Pi*zeta(3).

%F Also equals 3rd derivative of -Pi*binomial(x, x/2) at x=0.

%e 5.6645597042446183908052136898788142322518455591949799463744298643...

%t RealDigits[(3/2)*Pi*Zeta[3], 10, 105] // First

%Y Cf. A258749 (Ls_3(Pi)),  A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Jun 09 2015