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A245672 Decimal expansion of k_3 = 3/(2*Pi*m_3), a constant associated with the asymptotic expansion of the probability that a three-dimensional random walk reaches a given point for the first time, where m_3 is A086231 (Watson's integral). 1
3, 1, 4, 8, 7, 0, 2, 3, 1, 3, 5, 9, 6, 2, 0, 1, 7, 8, 0, 7, 5, 1, 7, 3, 9, 1, 9, 4, 1, 8, 8, 0, 6, 8, 7, 7, 0, 5, 8, 9, 6, 3, 4, 2, 4, 5, 9, 0, 1, 4, 0, 5, 5, 1, 0, 8, 4, 0, 8, 0, 3, 0, 7, 2, 7, 3, 1, 0, 8, 0, 5, 9, 4, 7, 6, 1, 4, 6, 7, 3, 1, 9, 7, 9, 7, 5, 2, 0, 2, 4, 1, 2, 0, 2, 0, 4, 9, 6, 4, 0, 4, 2, 3, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.9 Polya's Random Walk Constants, p. 324.
LINKS
Eric Weisstein's MathWorld, Polya's Random Walk Constants
FORMULA
k_3 = 8*sqrt(6)*Pi^2/(Gamma(5/24)*Gamma(7/24)*Gamma(11/24)), where 'Gamma' is the Euler gamma function.
Asymptotic probability ~ k_3 / ||l||, where the norm ||l|| of the position of the lattice point l tends to infinity.
EXAMPLE
0.314870231359620178075173919418806877058963424590140551084080307273108...
MATHEMATICA
k3 = 8*Sqrt[6]*Pi^2/(Gamma[1/24]*Gamma[5/24]*Gamma[7/24]*Gamma[11/24]); RealDigits[k3, 10, 105] // First
CROSSREFS
Cf. A086231.
Sequence in context: A205878 A329130 A057049 * A303029 A050059 A025121
KEYWORD
nonn,cons,easy,walk
AUTHOR
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)