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

0,1

Links

Table of n, a(n) for n=0..104.

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.

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.

Example

0.42627839881750579092352142659616687305800676962963510754160645802652945...

Mathematica

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

Crossrefs

Cf. A244996.

Sequence in context: A016694 A175038 A035505 * A274516 A202498 A143308

Adjacent sequences: A244994 A244995 A244996 * A244998 A244999 A245000

Keyword

nonn,cons,walk

Author

Jean-François Alcover, Jul 09 2014

Status

approved