A242761 Decimal expansion of the escape probability for a random walk on the 3-D cubic lattice (a Polya random walk constant).
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, 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, 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
Offset: 0
Examples
0.6594626704490008571737268155670971...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.9, p. 322.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- Eric Weisstein's MathWorld, Polya's Random Walk Constants
Programs
-
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
-
Mathematica
p = (16*Sqrt[2/3]*Pi^3)/(Gamma[1/24]*Gamma[5/24]*Gamma[7/24]*Gamma[11/24]); RealDigits[p, 10, 100] // First
-
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
Formula
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.