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 A240947 Decimal expansion of the moment of order 1 at Pi/3 of Ls_4, where Ls_4 is a generalized log-sine integral. 0

%I

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

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

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

%N Decimal expansion of the moment of order 1 at Pi/3 of Ls_4, where Ls_4 is a generalized log-sine integral.

%H Jonathan M. Borwein, Armin Straub, <a href="http://arxiv.org/abs/1103.3893">Log-sine evaluations of Mahler measures</a>, arXiv:1103.3893 [math.CA], (20-March-2011)

%F -integral_(0..Pi/3) t*log(2*sin(t/2))^2 dt.

%F -(1/2)*sum_(k=1..infinity) 1/(Binomial(2*k, k)*k^4).

%F -17*Pi^4/6480.

%e -0.255548541292907628552389761683331310377371752536366...

%t RealDigits[-17*Pi^4/6480, 10, 105] // First

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Aug 04 2014

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Last modified June 21 23:37 EDT 2021. Contains 345367 sequences. (Running on oeis4.)