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%I #18 Jan 17 2020 16:22:18
%S 1,1,7,8,7,5,9,9,9,6,5,0,5,0,9,3,2,6,8,4,1,0,1,3,9,5,0,8,3,4,1,3,7,6,
%T 1,8,7,1,5,2,1,7,5,1,3,1,7,5,9,7,5,0,6,3,3,2,2,2,4,5,2,4,1,8,5,4,2,7,
%U 1,1,0,1,2,1,0,1,3,6,4,1,3,2,4,3,7,0,1,7,4,6,4,8,2,7,1,2,5,9,5,1,3,2,4
%N Decimal expansion of the alternating double sum U(3,1) = Sum_{i>=2} (Sum_{j=1..i-1} (-1)^(i+j)/(i^3*j)) (negated).
%H David Broadhurst, <a href="http://arxiv.org/abs/1004.4238">Feynman’s sunshine numbers</a>, arXiv:1004.4238 [physics.pop-ph], 2010, p. 16.
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 6.
%F Pi^4/180 + (Pi^2/12)*log(2)^2 - (1/12)*log(2)^4 - 2*Li_4(1/2).
%e -0.117875999650509326841013950834137618715217513175975...
%t U[3,1] = Pi^4/180 + (Pi^2/12)*Log[2]^2 - (1/12)*Log[2]^4 - 2*PolyLog[4, 1/2]; RealDigits[U[3,1], 10, 103] // First
%o (PARI)
%o Pi^4/180 + (Pi^2/12)*log(2)^2 - (1/12)*log(2)^4 - 2*polylog(4, 1/2) \\ _Gheorghe Coserea_, Sep 30 2018
%Y Cf. A099218.
%K nonn,cons,easy
%O 0,3
%A _Jean-François Alcover_, Mar 02 2015
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