|
%I #16 Mar 05 2023 11:29:40
%S 2,8,4,6,6,8,1,3,7,0,4,0,8,3,8,4,6,1,6,8,0,2,2,5,6,7,6,7,6,9,7,1,9,1,
%T 3,0,9,8,6,5,0,2,6,7,0,5,8,5,0,4,5,4,3,1,5,1,6,9,3,1,4,7,0,9,7,7,6,6,
%U 8,9,4,3,9,0,2,5,9,2,4,4,3,7,8,3,9,6,3,7,5,5,9,8,6,0,1,1,0,7,5,0,6,3,7,4,3
%N Decimal expansion of constant K, the unique solution > 1 to 2*Pi*log(k) == Pi*(1 - 1/k).
%C Decimal expansion of the number K > 1 such that the surface area equals the volume of Gabriel's horn from x=1 to x=K, where x is the radial (central) axis and Gabriel's horn is a function y=1/x rotated about the x-axis.
%H L. Bayon, P. Fortuny Ayuso, J. M. Grau, A. M. Oller-Marcen, and M.M. Ruiz, <a href="https://arxiv.org/abs/1706.07185">The Best-or-Worst and the Postdoc problems</a>, arXiv:1706.07185 [math.PR], 2017.
%H L. Bayon, J. Grau, A. M. Oller-Marcen, M. Ruiz, and P. M. Suarez, <a href="http://arxiv.org/abs/1603.03928">A variant of the Secretary Problem: the Best or the Worst</a>, arXiv preprint arXiv:1603.03928 [math.PR], 2016.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GabrielsHorn.html">Gabriel's Horn</a>.
%F -1/(2*ProductLog(-1, -1/(2*sqrt(e))))
%e 0.2846681370408384616802256767697191309865026705850454315169314709776689439...
%t RealDigits[ -1/(2*ProductLog[ -1, -1/(2*Sqrt[E])]), 10, 128][[1]]
%K cons,nonn
%O 0,1
%A Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 23 2004
|
