A244997 Decimal expansion of the moment derivative W_4'(0) associated with the radial probability distribution of a 4-step uniform random walk.

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

Offset: 0

Author

Jean-François Alcover, Jul 09 2014

Keywords

• nonn
• cons
• walk

Examples

			0.42627839881750579092352142659616687305800676962963510754160645802652945...
		

Links

• Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, Densities of Short Uniform Random Walks p. 978, Canad. J. Math. 64(2012), 961-990.
• Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 142.

Crossrefs

Cf. A244996.

Programs

Mathematica

RealDigits[(7/2)*Zeta[3]/Pi^2, 10, 105] // First

Formula

W_4'(0) = (7/2)*zeta(3)/Pi^2.

W_4'(0) = integral over the square [0,Pi]x[0,Pi] of log(3+2*cos(x)+2*cos(y)+2*cos(x-y)) dx dy.