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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 (list; constant; graph; refs; listen; history; text; internal format)
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 double-sum formula.)

REFERENCES

E. G. Coffman, P. Flajolet, L. Flato and M. Hofri, Probab. Engrg. Inform. Sci. 12 (1998), 373

LINKS

Table of n, a(n) for n=0..79.

S. N. Majumdar, A. Comtet, R. M. Ziff, Unified solution of the expected maximum of a discrete time random walk and the discrete flux to a spherical trap, J. Stat. Phys. 122 (2006), 833-856

R. M. Ziff, Flux to a trap, J. Stat. Phys. 65 (1991), 1217-1233

FORMULA

-1/Pi * integral_{x=0..infinity} log( (6/x^2)*(1-sin(x)/x) ) / x^2 dx

EXAMPLE

0.29795219028004776416465987228031204613834651480951717550256...

MAPLE

evalf(-1/Pi * Int(log(6/x^2*(1-sin(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

Sequence in context: A241753 A157350 A121837 * A245287 A254595 A137453

Adjacent sequences:  A160436 A160437 A160438 * A160440 A160441 A160442

KEYWORD

cons,nonn

AUTHOR

Robert M. Ziff, May 13 2009

EXTENSIONS

Definition condensed by R. J. Mathar, May 30 2009

Corrected decimal places 39-46 and added more decimals by Vaclav Kotesovec, Mar 18 2015

More terms from Vaclav Kotesovec, Dec 07 2016

STATUS

approved

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Last modified June 25 10:29 EDT 2019. Contains 324351 sequences. (Running on oeis4.)