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%I #10 Apr 05 2024 11:10:14
%S 6,2,4,2,3,1,7,6,1,2,7,3,5,7,5,2,1,5,6,7,1,8,0,3,4,4,4,2,0,0,3,8,7,7,
%T 3,7,4,6,3,1,2,6,8,1,5,2,8,6,1,9,1,9,2,6,8,6,0,4,7,9,3,7,0,3,9,1,7,8,
%U 8,6,0,2,6,3,0,3,5,0,9,0,8,4,9,4,0,2,7,0,0,7,7,9,0,3,4,3,7,6,4,5,1,9,3,3,3
%N Decimal expansion of the integral of log(x^2+y^2)/((1+x^2)*(1+y^2)) dx dy over the square [0,1]x[0,1] (negated).
%C This integral is mentioned by Bailey & Borwein as the only non-challenging one in the family J(t) = integral of log(t+x^2+y^2)/((1+x^2)*(1+y^2)) dx dy over the square [0,1]x[0,1], with t>=0.
%H D. H. Bailey and J. M. Borwein, <a href="http://moodle.thecarma.net/jon/ontology.pdf">Experimental computation as an ontological game changer</a>, 2014. see p. 5.
%H D. H. Bailey, J. M. Borwein and A. D. Kaiser, <a href="http://carmamaths.org/resources/jon/auto.pdf">Automated Simplification of Large Symbolic Expressions</a>, see p. 13.
%F Pi^2/16*log(2) - 7/8*zeta(3).
%e -0.6242317612735752156718034442003877374631268152861919268604793703917886...
%t Pi^2/16*Log[2] - 7/8*Zeta[3] // RealDigits[#, 10, 105]& // First
%Y Cf. A244843.
%K cons,nonn
%O 0,1
%A _Jean-François Alcover_, Jul 07 2014
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