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

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

RealDigits[7/20*Sqrt[2] + 3/20*Log[1 + Sqrt[2]], 10, 106] // First

Crossrefs

Cf. A244920, A244921.

Sequence in context: A048595 A302346 A340421 * A153313 A096050 A115731

Adjacent sequences: A244919 A244920 A244921 * A244923 A244924 A244925

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 08 2014

Status

approved