A244993 Decimal expansion of phi_3(3) = sqrt(3)/(12*Pi^2), an auxiliary constant in the computation of the radial density of a 4-step uniform random walk.

0, 1, 4, 6, 2, 4, 4, 5, 3, 1, 6, 2, 6, 2, 8, 8, 0, 4, 7, 6, 0, 2, 8, 3, 6, 2, 1, 5, 5, 8, 5, 8, 1, 5, 0, 9, 5, 7, 4, 0, 2, 5, 5, 6, 0, 1, 8, 0, 2, 1, 4, 0, 7, 0, 7, 1, 9, 9, 8, 1, 0, 9, 7, 7, 5, 2, 6, 8, 9, 3, 0, 0, 9, 8, 2, 3, 4, 2, 2, 6, 0, 1, 4, 2, 4, 1, 5, 7, 1, 5, 5, 6, 0, 2, 0, 7, 2, 1, 9, 0, 8, 2, 6, 5, 7

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10001

Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, Densities of Short Uniform Random Walks, p. 969, Canad. J. Math. 64(2012), 961-990.

Index entries for transcendental numbers

Formula

phi_3(x) = (sqrt(3) * 2F1(1/3, 2/3; 1; (x^2*(9-x^2)^2)/(3+x^2)^3))/(Pi^2*(3+x^2)), where 2F1 is the hypergeometric function.

Example

0.0146244531626288047602836215585815095740255601802140707199810977526893...

Maple

Digits:=100: evalf(sqrt(3)/(12*Pi^2)); # Wesley Ivan Hurt, Jul 10 2014

Mathematica

Join[{0}, RealDigits[Sqrt[3]/(12*Pi^2), 10, 104] // First]

Crossrefs

Sequence in context: A059854 A155991 A184083 * A160502 A010669 A225092

Adjacent sequences: A244990 A244991 A244992 * A244994 A244995 A244996

Keyword

nonn,cons,walk

Author

Jean-François Alcover, Jul 09 2014

Status

approved