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
Examples
0.0146244531626288047602836215585815095740255601802140707199810977526893...
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
Programs
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Maple
Digits:=100: evalf(sqrt(3)/(12*Pi^2)); # Wesley Ivan Hurt, Jul 10 2014
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Mathematica
Join[{0}, RealDigits[Sqrt[3]/(12*Pi^2), 10, 104] // First]
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.