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A244999 Decimal expansion of the moment derivative W_5'(0) associated with the radial probability distribution of a 5-step uniform random walk. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 09 2014

STATUS

approved

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Last modified January 20 03:47 EST 2021. Contains 340301 sequences. (Running on oeis4.)