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A244858
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).
0
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, 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, 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
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
Cf. A244843.
Sequence in context: A248273 A176396 A198502 * A354782 A064925 A173273
KEYWORD
cons,nonn
AUTHOR
STATUS
approved