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%I #21 Feb 13 2017 03:36:05
%S 6,0,4,1,8,8,2,9,0,9,7,7,5,0,9,3,5,2,2,1,5,0,4,2,4,1,3,0,6,7,5,9,9,5,
%T 9,8,5,5,0,8,7,1,0,3,0,5,7,7,4,6,4,1,9,0,7,2,5,8,6,0,1,0,1,5,2,6,0,0,
%U 4,3,0,2,5,4,6,5,5,7,5,8,1,6,0,4,0,4,7,0,8,2,6,5,8,8,2,6,1,6,9,5,1,5,5,8,1
%N Decimal expansion of Pi/8*(6*zeta(3)+Pi^2*log(2)+4*log(2)^3).
%C The absolute value of the integral {x=0..Pi/2} log(sin(x))^3 dx. The absolute value of m=3 of sqrt(Pi)/2*(d^m/da^m(gamma((a+1)/2)/gamma(a/2+1))) at a=0. - _Seiichi Kirikami_ and _Peter J. C. Moses_, Oct 07 2011
%D I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.621.1
%H G. C. Greubel, <a href="/A196878/b196878.txt">Table of n, a(n) for n = 1..5000</a>
%F Equals A019675*(6*A002117 + A002388*A002162 + 4*A002162^3).
%e 6.041882909775093522150424130675995...
%p Pi/8*(6*Zeta(3)+Pi^2*log(2)+4*log(2)^3) ; evalf(%) ; # _R. J. Mathar_, Oct 08 2011
%t RealDigits[N[Pi/8 (6 Zeta[3] + Pi^2 Log[2] + 4 Log[2]^3), 150][[1]]
%t Sqrt[Pi]/2*Derivative[3][Gamma[(#+1)/2]/Gamma[#/2+1]&][0] // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Mar 25 2013 *)
%o (PARI) Pi/8*(6*zeta(3)+Pi^2*log(2)+4*log(2)^3) \\ _G. C. Greubel_, Feb 12 2017
%Y Cf. A173623, A196877.
%K cons,nonn
%O 1,1
%A _Seiichi Kirikami_, Oct 07 2011
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