%I
%S 2,9,7,9,5,2,1,9,0,2,8,0,0,4,7,7,6,4,1,6,4,6,5,9,8,7,2,2,8,0,3,1,2,0,
%T 4,6,1,3,8,3,4,6,5,1,4,8,0,9,5,1,7,1,7,5,5,0,2,5,6,8,1,5,1,8,5,9,4,0,
%U 3,0,1,4,8,3,8,6,6,5,5,2
%N Decimal expansion of a constant that appears in flux/diffusion problems with trapping surfaces.
%C The constant appears as a correction in effective radii of flux problems of particles undergoing certain random walks in one or three dimensions.
%C Also related to correction term to the asymptotics of sums of random numbers uniformly distributed on an interval (see Coffman et al., who also present a doublesum formula.)
%D E. G. Coffman, P. Flajolet, L. Flato and M. Hofri, Probab. Engrg. Inform. Sci. 12 (1998), 373
%H S. N. Majumdar, A. Comtet, R. M. Ziff, <a href="http://dx.doi.org/10.1007/s109550059002x">Unified solution of the expected maximum of a discrete time random walk and the discrete flux to a spherical trap</a>, J. Stat. Phys. 122 (2006), 833856
%H R. M. Ziff, <a href="http://dx.doi.org/10.1007/BF01049608">Flux to a trap</a>, J. Stat. Phys. 65 (1991), 12171233
%F 1/Pi * integral_{x=0..infinity} log( (6/x^2)*(1sin(x)/x) ) / x^2 dx
%e 0.29795219028004776416465987228031204613834651480951717550256...
%p evalf(1/Pi * Int(log(6/x^2*(1sin(x)/x))/x^2, x=0..infinity),20); # _Vaclav Kotesovec_, Mar 17 2015
%t For[i = 0; s = 0, i < 100, i++, s = s + (1/Pi)NIntegrate[Log[(1  Sin[x]/ x)/(x^2/6)]/x^2, {x, 2 i Pi, 2 (i + 1) Pi}, WorkingPrecision > 100]; Print[s]]
%t RealDigits[1/Pi * Integrate[Log[(6/x^2) * (1  Sin[x]/x)]/x^2, {x, 0, Infinity}], 10, 100][[1]] (* _Alonso del Arte_, Mar 18 2015 *)
%K cons,nonn
%O 0,1
%A _Robert M. Ziff_, May 13 2009
%E Definition condensed by _R. J. Mathar_, May 30 2009
%E Corrected decimal places 3946 and added more decimals by _Vaclav Kotesovec_, Mar 18 2015
%E More terms from _Vaclav Kotesovec_, Dec 07 2016
