OFFSET
0,1
COMMENTS
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.
LINKS
D. H. Bailey and J. M. Borwein, Experimental computation as an ontological game changer, 2014. see p. 5.
D. H. Bailey, J. M. Borwein and A. D. Kaiser, Automated Simplification of Large Symbolic Expressions, see p. 13.
FORMULA
Pi^2/16*log(2) - 7/8*zeta(3).
EXAMPLE
-0.6242317612735752156718034442003877374631268152861919268604793703917886...
MATHEMATICA
Pi^2/16*Log[2] - 7/8*Zeta[3] // RealDigits[#, 10, 105]& // First
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jean-François Alcover, Jul 07 2014
STATUS
approved