A244922 - OEIS

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A244922

Decimal expansion of the integral over the square [0,1]x[0,1] of (x^2 + y^2)^(3/2) dx dy.

6, 2, 7, 1, 8, 0, 7, 8, 4, 8, 8, 3, 5, 1, 4, 7, 2, 0, 8, 6, 5, 4, 8, 2, 4, 5, 2, 2, 2, 0, 3, 6, 3, 1, 7, 3, 8, 5, 3, 6, 0, 9, 2, 0, 5, 6, 2, 1, 1, 7, 7, 1, 3, 7, 2, 2, 4, 8, 3, 2, 2, 4, 9, 5, 9, 4, 7, 6, 2, 9, 4, 5, 0, 9, 5, 0, 4, 1, 3, 7, 6, 7, 7, 2, 6, 9, 1, 6, 7, 0, 8, 0, 1, 2, 1, 2, 9, 5, 6, 8, 8, 5, 7, 6, 5, 8

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..105.

D. H. Bailey, J. M. Borwein, R. E. Crandall, Advances in the theory of box integrals (2010) p. 22.

FORMULA

7/20*sqrt(2) + 3/20*log(1 + sqrt(2)).

Also equals (7*sqrt(2) + 3*arcsinh(1))/20.

EXAMPLE

0.627180784883514720865482452220363173853609205621177137224832249594762945...

MATHEMATICA