A245672 - OEIS

%I #10 Aug 01 2014 10:36:12

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

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

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

%N Decimal expansion of k_3 = 3/(2*Pi*m_3), a constant associated with the asymptotic expansion of the probability that a three-dimensional random walk reaches a given point for the first time, where m_3 is A086231 (Watson's integral).

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.9 Polya's Random Walk Constants, p. 324.

%H Vincenzo Librandi, <a href="/A245672/b245672.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/PolyasRandomWalkConstants.html">Polya's Random Walk Constants</a>

%F k_3 = 8*sqrt(6)*Pi^2/(Gamma(5/24)*Gamma(7/24)*Gamma(11/24)), where 'Gamma' is the Euler gamma function.

%F Asymptotic probability ~ k_3 / ||l||, where the norm ||l|| of the position of the lattice point l tends to infinity.

%e 0.314870231359620178075173919418806877058963424590140551084080307273108...

%t k3 = 8*Sqrt[6]*Pi^2/(Gamma[1/24]*Gamma[5/24]*Gamma[7/24]*Gamma[11/24]); RealDigits[k3, 10, 105] // First

%Y Cf. A086231.

%K nonn,cons,easy,walk

%O 0,1

%A _Jean-François Alcover_, Jul 29 2014