OFFSET
1,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.9 Polya's random walk constants, p. 323.
LINKS
Marc Mezzarobba, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pólya's Random Walk Constants.
FORMULA
m(d) = d/(2*Pi)^d*multipleIntegral(-Pi..Pi) (d-sum_(k=1..d) cos(t_k))^(-1) dt_1 dt_2 ... dt_d, where d is the lattice dimension.
m(d) = Integral_{t>0} exp(-t)*BesselI(0,t/d)^d dt where BesselI(0,x) is the zeroth modified Bessel function.
Equals 1/(1 - A086236). - Amiram Eldar, Aug 28 2020
EXAMPLE
1.0786470120...
MAPLE
m8:= int(exp(-t)*BesselI(0, t/8)^8, t=0..infinity):
s:= convert(evalf(m8, 120), string):
map(parse, subs("."=NULL, [seq(i, i=s)]))[]; # Alois P. Heinz, May 23 2014
MATHEMATICA
d = 8; d/Pi^d*NIntegrate[(d - Sum[Cos[t[k]], {k, 1, d}])^-1, Sequence @@ Table[{t[k], 0, Pi}, {k, 1, d}] // Evaluate] // RealDigits[#, 10, 7]& // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, May 23 2014
EXTENSIONS
More terms from Alois P. Heinz, May 23 2014
STATUS
approved