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).

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

Table of n, a(n) for n=0..104.

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

Adjacent sequences: A244855 A244856 A244857 * A244859 A244860 A244861

Keyword

cons,nonn

Author

Jean-François Alcover, Jul 07 2014

Status

approved