A241033 - OEIS

%I #15 Jun 03 2017 15:31:12

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

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

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

%N Decimal expansion of 'c', a constant such that in N steps, the mean longest random walk duration records grow as c*N.

%H Steven Finch, <a href="/A241033/a241033.pdf">Excursion Durations</a>, May 12, 2008. [Cached copy, with permission of the author]

%H Satya N. Majumdar and Robert M. Ziff, <a href="http://arxiv.org/abs/0806.0057">Universal Record Statistics of Random Walks and Lévy Flights</a>, arXiv:0806.0057 [cond-mat.stat-mech], 2008.

%e 0.626507598767175449080634422596159044653245248...

%t 2*NIntegrate[Log[1 + 1/(2*Sqrt[Pi])*Gamma[-1/2, x]], {x, 0, Infinity}, WorkingPrecision -> 105] // RealDigits[#, 10, 100]& // First

%Y Cf. A084945 (the analog constant for i.i.d. random variables).

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Apr 15 2014