OFFSET
0,1
COMMENTS
The return probability equals unity minus this constant. The expected number of visits to the origin is the inverse of this constant, A091670.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Shunya Ishioka and Masahiro Koiwa, Random walks on diamond and hexagonal close packed lattices, Phil. Mag. A, 37 (1978), 517-533.
G. L. Montet, Integral methods in the calculation of correlation factors in diffusion, Phys. Rev. B 7 (1973), 650-662.
FORMULA
Pi^2/(4*K(1/sqrt(2))^2), where K is the complete elliptic integral of the first kind.
Equals (4*Pi^3)/Gamma(1/4)^4. - G. C. Greubel, Oct 26 2018
EXAMPLE
0.7177700110461299978211932236657794...
MATHEMATICA
RealDigits[(4*Pi^3)/Gamma[1/4]^4, 10, 100][[1]] (* G. C. Greubel, Oct 26 2018 *)
PROG
(PARI) default(realprecision, 100); (4*Pi^3)/gamma(1/4)^4 \\ G. C. Greubel, Oct 26 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (4*Pi(R)^3)/Gamma(1/4)^4; // G. C. Greubel, Oct 26 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Andrey Zabolotskiy, Oct 03 2017
STATUS
approved