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

Author

Jean-François Alcover, May 20 2015

Keywords

• nonn
• cons
• walk

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

Mathematica

(3*2^(1/3))/(16*Pi^4)*Gamma[1/3]^6 // RealDigits[#, 10, 107]& // First

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.