OFFSET
0,1
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.
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
KEYWORD
AUTHOR
Jean-François Alcover, Jul 09 2014
STATUS
approved