A160439 Decimal expansion of a constant that appears in flux/diffusion problems with trapping surfaces.
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
Offset: 0
Examples
0.29795219028004776416465987228031204613834651480951717550256...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.9, p. 327.
Links
- E. G. Coffman, P. Flajolet, L. Flato, and M. Hofri, The maximum of random walk and its application to rectangle packing, Probability in Engineering and Informational Sciences 12:373-386 (1998).
- S. N. Majumdar, A. Comtet, and 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.
- Robert M. Ziff, Flux to a trap, J. Stat. Phys. 65 (1991), 1217-1233.
Programs
-
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 *)
Formula
Equals (-1/Pi) * Integral_{x=0..oo} log( (6/x^2)*(1-sin(x)/x) ) / x^2 dx.
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
Comments