cp's OEIS Frontend

A130590 Decimal expansion of the mean Euclidean distance from a point in the unit 3D cube to a given vertex of the cube.

%I A130590 #18 Feb 16 2025 08:33:06
%S A130590 9,6,0,5,9,1,9,5,6,4,5,5,0,5,2,9,5,9,4,2,5,1,0,7,9,5,1,3,9,3,8,0,6,3,
%T A130590 6,0,2,4,0,9,7,6,9,0,7,5,4,5,7,2,3,9,8,7,6,9,0,8,9,8,5,1,5,3,1,0,3,8,
%U A130590 7,6,6,3,3,4,0,1,6,3,2,8,9,0,3,1,2,2,7,9,3,5,6,9,1,7,7,4,8,2,4,5,3,1,2,1,6
%N A130590 Decimal expansion of the mean Euclidean distance from a point in the unit 3D cube to a given vertex of the cube.
%H A130590 D. H. Bailey, J. M. Borwein and R. E. Crandall, <a href="https://doi.org/10.1016/j.cam.2006.06.010">Box Integrals</a>, J. Comp. Appl. Math., Vol. 206, No. 1 (2007), pp. 196-208.
%H A130590 D. H. Bailey, J. M. Borwein, and R. E. Crandall, <a href="http://dx.doi.org/10.1090/S0025-5718-10-02338-0">Advances in the theory of box integrals</a>, Math. Comp. 79 (271) (2010) 1839-1866, Table 2. [From _R. J. Mathar_, Oct 13 2010]
%H A130590 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BoxIntegral.html">Box Integral</a>.
%F A130590 Equals sqrt(3)/4 + log(2+sqrt(3))/2 - Pi/24 = A010527/2 + A065914/2 - A019691.
%F A130590 Equals 2 * A135691. - _Amiram Eldar_, Jun 04 2023
%e A130590 0.960591956455052959425107951...
%p A130590 evalf( sqrt(3)/4+log(2+sqrt(3))/2-Pi/24);
%t A130590 RealDigits[Sqrt[3]/4 + Log[2+Sqrt[3]]/2 - Pi/24, 10, 120][[1]] (* _Amiram Eldar_, Jun 04 2023 *)
%Y A130590 Cf. A010527, A019691, A065914, A135691.
%Y A130590 Analogous constants: A244921 (square), A254979 (4-cube).
%K A130590 cons,easy,nonn
%O A130590 0,1
%A A130590 _R. J. Mathar_, Aug 10 2007
%E A130590 Name corrected by _Amiram Eldar_, Jun 04 2023