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A258104 Decimal expansion of W_3(-1), the average reciprocal distance to the origin in a 3-step random walk in the plane. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Jonathan M. Borwein, Armin Straub, and James Wan,Three-Step and Four-Step Random Walk Integrals
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.
EXAMPLE
0.8964407887767628642327709000349704991387844034162414609834833987...
MATHEMATICA
(3*2^(1/3))/(16*Pi^4)*Gamma[1/3]^6 // RealDigits[#, 10, 107]& // First
PROG
(PARI) sqrtn(54, 3)/(16*Pi^4)*gamma(1/3)^6 \\ Charles R Greathouse IV, Apr 18 2016
CROSSREFS
Cf. A240946.
Sequence in context: A195304 A197691 A342948 * A253299 A048271 A203146
KEYWORD
nonn,cons,walk
AUTHOR
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)