cp's OEIS Frontend

A258104 Decimal expansion of W_3(-1), the average reciprocal distance to the origin in a 3-step random walk in the plane.

%I A258104 #15 Apr 06 2024 13:47:35
%S A258104 8,9,6,4,4,0,7,8,8,7,7,6,7,6,2,8,6,4,2,3,2,7,7,0,9,0,0,0,3,4,9,7,0,4,
%T A258104 9,9,1,3,8,7,8,4,4,0,3,4,1,6,2,4,1,4,6,0,9,8,3,4,8,3,3,9,8,7,0,6,5,5,
%U A258104 9,6,7,9,7,8,0,6,1,3,6,0,3,1,4,2,3,3,7,6,9,9,2,2,7,6,0,7,8,1,2,2,3,6,5,5,5,9,5
%N A258104 Decimal expansion of W_3(-1), the average reciprocal distance to the origin in a 3-step random walk in the plane.
%H A258104 G. C. Greubel, <a href="/A258104/b258104.txt">Table of n, a(n) for n = 0..5000</a>
%H A258104 Jonathan M. Borwein, Armin Straub, and James Wan, <a href="https://carmamaths.org/resources/jon/walks2.pdf">Three-Step and Four-Step Random Walk Integrals</a>.
%F A258104 Equals (3*2^(1/3))/(16*Pi^4)*Gamma(1/3)^6.
%F A258104 Equals (2^(1/3))/(4*Pi^2)*Beta(1/3, 1/3)^2.
%e A258104 0.8964407887767628642327709000349704991387844034162414609834833987...
%t A258104 (3*2^(1/3))/(16*Pi^4)*Gamma[1/3]^6 // RealDigits[#, 10, 107]& // First
%o A258104 (PARI) sqrtn(54,3)/(16*Pi^4)*gamma(1/3)^6 \\ _Charles R Greathouse IV_, Apr 18 2016
%Y A258104 Cf. A240946.
%K A258104 nonn,cons,walk
%O A258104 0,1
%A A258104 _Jean-François Alcover_, May 20 2015