A241026 Decimal expansion of the expected exit time of a planar Brownian motion from a unit square.

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, 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, 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

Offset

0,2

Links

Table of n, a(n) for n=0..99.

Steven Finch, Expected Lifetimes and Inradii, February 23, 2005. [Cached copy, with permission of the author]

Greg Markowsky, On the expected exit time of planar Brownian motion from simply connected domains, arXiv:1108.1188 [math.PR], 2011.

Formula

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

Example

0.147342706563027631127880050332381733621...

Mathematica

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

Crossrefs

Sequence in context: A165663 A254397 A197697 * A198743 A271798 A190357

Adjacent sequences: A241023 A241024 A241025 * A241027 A241028 A241029

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 15 2014

Status

approved