A244999 Decimal expansion of the moment derivative W_5'(0) associated with the radial probability distribution of a 5-step uniform random walk.

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

Offset

0,1

Links

Table of n, a(n) for n=0..91.

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.

Formula

W_5'(0) = log(2) - gamma - integral_{x=0..1}((J_0(x)^5-1)/x) - integral_{x>1}(J_0(x)^5/x), where J_0 is the Bessel function of the first kind.

Example

0.54441256175218558519587806274502767666605280202852744228702849390214369...

Mathematica

digits = 92; Log[2] - EulerGamma - NIntegrate[(BesselJ[0, x]^5 - 1)/x, {x, 0, 1}, WorkingPrecision -> digits + 20] - NIntegrate[BesselJ[0, x]^5/x, {x, 1, Infinity}, WorkingPrecision -> digits + 20] // RealDigits[#, 10, digits] & // First

Crossrefs

Cf. A244996, A244997.

Sequence in context: A241183 A137240 A243380 * A201129 A261509 A226578

Adjacent sequences: A244996 A244997 A244998 * A245000 A245001 A245002

Keyword

nonn,cons,walk

Author

Jean-François Alcover, Jul 09 2014

Status

approved