cp's OEIS Frontend

A258761 Decimal expansion of Ls_5(Pi/3), the value of the 5th basic generalized log-sine integral at Pi/3 (negated).

%I A258761 #8 Apr 06 2024 13:41:50
%S A258761 2,4,0,1,2,5,3,3,1,2,5,5,1,6,9,1,4,6,1,5,0,1,5,7,1,3,9,6,3,6,3,1,6,2,
%T A258761 6,7,9,5,0,2,8,8,4,8,4,1,0,6,4,6,3,1,5,0,2,1,9,0,1,6,2,0,7,8,2,3,3,9,
%U A258761 2,9,9,8,2,1,7,6,3,6,8,1,4,4,4,7,2,8,9,5,8,5,8,6,4,9,1,9,0,0,1,6,3,5,2
%N A258761 Decimal expansion of Ls_5(Pi/3), the value of the 5th basic generalized log-sine integral at Pi/3 (negated).
%H A258761 Jonathan M. Borwein, Armin Straub, <a href="https://carmamaths.org/resources/jon/logsin3.pdf">Special Values of Generalized Log-sine Integrals</a>.
%F A258761 -Integral_{0..Pi/3} log(2*sin(x/2))^4 dx = -1543*Pi^5/19440 + 6*Gl_{4, 1}(Pi/3), where Gl is the multiple Glaisher function.
%F A258761 Also equals -24 * 6F5(1/2,1/2,1/2,1/2,1/2,1/2; 3/2,3/2,3/2,3/2,3/2; 1/4) (with 6F5 the hypergeometric function).
%e A258761 -24.01253312551691461501571396363162679502884841064631502190162...
%t A258761 RealDigits[-24*HypergeometricPFQ[Table[1/2, {6}], Table[3/2, {5}], 1/4], 10, 103] // First
%Y A258761 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 A258761 Cf. A143298 (Ls_2(Pi/3)), A258759 (Ls_3(Pi/3)), A258760 (Ls_4(Pi/3)), A258762 (Ls_6(Pi/3)), A258763 (Ls_7(Pi/3)).
%K A258761 nonn,cons,easy
%O A258761 2,1
%A A258761 _Jean-François Alcover_, Jun 09 2015