

A160439


Decimal expansion of a constant that appears in flux/diffusion problems with trapping surfaces.


0



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, 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, 3, 0, 1, 4, 8, 3, 8, 6, 6, 5, 5, 2
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OFFSET

0,1


COMMENTS

The constant appears as a correction in effective radii of flux problems of particles undergoing certain random walks in one or three dimensions.
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.)


LINKS



FORMULA

Equals (1/Pi) * Integral_{x=0..oo} log( (6/x^2)*(1sin(x)/x) ) / x^2 dx.


EXAMPLE

0.29795219028004776416465987228031204613834651480951717550256...


MAPLE

evalf(1/Pi * Int(log(6/x^2*(1sin(x)/x))/x^2, x=0..infinity), 20); # Vaclav Kotesovec, Mar 17 2015


MATHEMATICA

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]]
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 *)


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS

Corrected decimal places 3946 and added more decimals by Vaclav Kotesovec, Mar 18 2015


STATUS

approved



