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%I #14 Feb 28 2023 23:48:59
%S 2,0,5,3,1,6,0,7,3,1,4,8,0,5,9,1,6,6,8,9,5,6,5,4,1,2,9,6,0,2,6,5,1,1,
%T 3,6,6,8,5,6,5,5,8,8,4,4,5,7,2,3,9,5,6,9,4,3,8,5,1,8,8,9,2,7,6,5,2,2,
%U 9,2,3,4,2,3,7,9,1,9,1,7,7,1,7,6,7,7,6,9,8,0,7,8,9,0,1,7,4,2,6,7,3,2
%N Decimal expansion of J_4 = Integral_{0..Pi/2} x^4/sin(x) dx.
%H G. C. Greubel, <a href="/A261068/b261068.txt">Table of n, a(n) for n = 1..1000</a>
%H J. M. Borwein, I. J. Zucker and J. Boersma, <a href="http://carma.newcastle.edu.au/MZVs/mzv-week05.pdf">The evaluation of character Euler double sums</a>, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 13.
%F J_4 = Catalan*Pi^3 - 7*i*Pi^5/480 - 24*i*Pi*PolyLog(4, -i) + (93*zeta(5))/2.
%F Also equals Catalan*Pi^3 + (1/64)*(Pi*(PolyGamma(3, 3/4) - PolyGamma(3, 1/4)) + 2976*Zeta(5));
%e 2.05316073148059166895654129602651136685655884457239569438518892765...
%t J4 = Catalan*Pi^3 - 7*I*Pi^5/480 - 24*I*Pi*PolyLog[4, -I] + 93*Zeta[5]/2; RealDigits[J4 // Re, 10, 102] // First
%Y Cf. A006752 (J_1 / 2 = Catalan's constant), A245073 (J_2), A225125 (J_3), A261069 (J_5).
%K cons,nonn
%O 1,1
%A _Jean-François Alcover_, Aug 08 2015
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