A258104 Decimal expansion of W_3(-1), the average reciprocal distance to the origin in a 3-step random walk in the plane.
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, 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, 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
Offset: 0
Examples
0.8964407887767628642327709000349704991387844034162414609834833987...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- Jonathan M. Borwein, Armin Straub, and James Wan, Three-Step and Four-Step Random Walk Integrals.
Crossrefs
Cf. A240946.
Programs
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Mathematica
(3*2^(1/3))/(16*Pi^4)*Gamma[1/3]^6 // RealDigits[#, 10, 107]& // First
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PARI
sqrtn(54,3)/(16*Pi^4)*gamma(1/3)^6 \\ Charles R Greathouse IV, Apr 18 2016
Formula
Equals (3*2^(1/3))/(16*Pi^4)*Gamma(1/3)^6.
Equals (2^(1/3))/(4*Pi^2)*Beta(1/3, 1/3)^2.