cp's OEIS Frontend

A249456 Decimal expansion of a constant appearing in the expression of the asymptotic expected volume V(d) of the convex hull of uniformly selected n(d) points in the interior of a d-dimensional unit cube.

%I A249456 #7 Jun 02 2017 12:28:11
%S A249456 2,1,3,9,6,9,0,9,4,7,4,1,2,8,5,9,8,6,0,5,0,5,3,0,2,2,6,3,8,5,2,3,5,2,
%T A249456 4,4,4,3,2,3,1,4,6,9,5,6,0,5,5,1,2,9,3,8,5,8,2,4,9,8,0,0,0,7,6,0,1,1,
%U A249456 1,5,5,2,1,8,3,2,5,1,3,3,3,2,3,8,9,6,9,7,2,7,1,2,4,4,0,0,5,2,3,8,4,3,2
%N A249456 Decimal expansion of a constant appearing in the expression of the asymptotic expected volume V(d) of the convex hull of uniformly selected n(d) points in the interior of a d-dimensional unit cube.
%H A249456 Steven R. Finch, <a href="/A249455/a249455.pdf">Convex Lattice Polygons</a>, December 18, 2003. [Cached copy, with permission of the author]
%F A249456 k = exp(log(2*Pi) - gamma - 1/2).
%F A249456 Lim_{d -> infinity} V(d) =
%F A249456   0 if n(d) <= (k - epsilon)^d
%F A249456   1 if n(d) >= (k + epsilon)^d
%e A249456 2.139690947412859860505302263852352444323146956...
%t A249456 k = Exp[Log[2*Pi] - EulerGamma - 1/2]; RealDigits[k, 10, 103] // First
%Y A249456 Cf. A249455.
%K A249456 nonn,cons,easy
%O A249456 1,1
%A A249456 _Jean-François Alcover_, Oct 29 2014