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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 (list; constant; graph; refs; listen; history; text; internal format)
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 * A064925 A173273 A084945

Adjacent sequences:  A244855 A244856 A244857 * A244859 A244860 A244861

KEYWORD

cons,nonn

AUTHOR

Jean-Fran├žois Alcover, Jul 07 2014

STATUS

approved

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Last modified October 17 11:59 EDT 2019. Contains 328110 sequences. (Running on oeis4.)