A241026 - OEIS

%I #11 Jun 03 2017 13:22:17

%S 1,4,7,3,4,2,7,0,6,5,6,3,0,2,7,6,3,1,1,2,7,8,8,0,0,5,0,3,3,2,3,8,1,7,

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

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

%N Decimal expansion of the expected exit time of a planar Brownian motion from a unit square.

%H Steven Finch, <a href="/A241026/a241026.pdf">Expected Lifetimes and Inradii</a>, February 23, 2005. [Cached copy, with permission of the author]

%H Greg Markowsky, <a href="https://arxiv.org/abs/1108.1188">On the expected exit time of planar Brownian motion from simply connected domains</a>, arXiv:1108.1188 [math.PR], 2011.

%F 4F3(1/4, 1/4, 1/2, 1/2; 5/4, 5/4, 1; 1)*4/Beta(1/4, 1/2)^2.

%e 0.147342706563027631127880050332381733621...

%t 1/4 - 8/Pi^3*NSum[(-1)^k*Sech[1/2*(2*k + 1)*Pi]/(2*k + 1)^3, {k, 0, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> 100] // RealDigits[#, 10, 100]& // First

%K nonn,cons

%O 0,2

%A _Jean-François Alcover_, Apr 15 2014