A242761 - OEIS

%I #13 Feb 16 2025 08:33:22

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

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

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

%N Decimal expansion of the escape probability for a random walk on the 3-D cubic lattice (a Polya random walk constant).

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.9, p. 322.

%H G. C. Greubel, <a href="/A242761/b242761.txt">Table of n, a(n) for n = 0..10000</a>

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

%F Equals (16*sqrt(2/3)*Pi^3)/(Gamma(1/24)*Gamma(5/24)*Gamma(7/24)*Gamma(11/24)), where Gamma is the Euler Gamma function.

%e 0.6594626704490008571737268155670971...

%t p = (16*Sqrt[2/3]*Pi^3)/(Gamma[1/24]*Gamma[5/24]*Gamma[7/24]*Gamma[11/24]); RealDigits[p, 10, 100] // First

%o (PARI) default(realprecision, 100); (16*sqrt(2/3)*Pi^3)/(gamma(1/24)* gamma(5/24)*gamma(7/24)*gamma(11/24)) \\ _G. C. Greubel_, Oct 26 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (16*Sqrt(2/3)*Pi(R)^3)/(Gamma(1/24)*Gamma(5/24)*Gamma(7/24)*Gamma(11/24)); // _G. C. Greubel_, Oct 26 2018

%Y Cf. A086230, A086231, A086232-A086236, A043546, A293237, A293238, A242812-A242816.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, May 22 2014