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).

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.9 Polya's Random Walk Constants, p. 324.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A245669 A245670 A245671 * A245673 A245674 A245675

Keyword

nonn,cons,easy,walk

Author

Jean-François Alcover, Jul 29 2014

Status

approved