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%I #41 Jan 03 2024 05:42:02
%S 0,0,0,0,0,0,0,0,0,0,0,1,8,2,0,1,3,4,8,3,0,6,6,7,7,0,9,9,4,6,1,4,5,7,
%T 1,3,3,1,2,2,5,3,5,0,2,1,7,5,0,0,8,3,1,4,2,3,2,6,4,1,4,2,9,5,7,5,3,9,
%U 4,5,2,8,8,2,4,0,0,8,7,4,7,4,6,5,8,8,2,0,3,5,7,7,2,9,2,4,9,1,5,2,7,1,8,1,9,3,1,7,7,8,6,1,3,8,8,7,1,9,5,9,1,1,5,1,8
%N Decimal expansion of a constant arising in slices, slabs, and sections of the unit hypercube.
%C Marichal, p. 6, gives a surprising formula: Integral_{0..oo} sinc(x) Product_{p prime, 3 <= p <= 29} sinc(x/p) dx = (Pi/2) * (1 - (54084649^9) / (181440 * (3234846615^8))) = (0.49999999999908993...)*Pi.
%C Rational, and thus (eventually) periodic; period 2^4 * 3^10 * 7^8 * 11^7 * 13^7 * 17^7 * 19^7 * 23^7 * 29^7. - _Charles R Greathouse IV_, Jan 14 2013
%H G. C. Greubel, <a href="/A209244/b209244.txt">Table of n, a(n) for n = 0..10000</a>
%H D. Borwein, J. M. Borwein, and B. A. Mares Jr., <a href="https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=882cadb66e972727e80ed66e67f78ea8ebc41aaa">Multi-variable sinc integrals and volumes of polyhedra</a>, Ramanujan J. 6 (2002), no. 2, 189-208.
%H D. Borwein and J. M. Borwein, <a href="http://www.thebigquestions.com/borweinintegrals.pdf">Some remarkable properties of sinc and related integrals</a>, Ramanujan J. 5 (2001), no. 1, 73-89.
%H Jean-Luc Marichal and Michael J. Mossinghoff, <a href="http://arxiv.org/abs/math/0607715">Slices, slabs, and sections of the unit hypercube</a>, arXiv:math/0607715 [math.MG], 2006-2008.
%H Jean-Luc Marichal and Michael J. Mossinghoff, <a href="https://hosted.math.rochester.edu/ojac/vol3/Marichal_2008.pdf">Slices, slabs, and sections of the unit hypercube</a>, Online Journal of Analytic Combinatorics, Issue 3 (2008), #1.
%F Equals 54084649^9 / (181440 * 3234846615^8).
%e 1.82013483... * 10^(-12).
%t Join[Table[0,{11}],RealDigits[54084649^9/(181440*3234846615^8),10,120][[1]]] (* _Harvey P. Dale_, May 24 2013 *)
%K nonn,easy,cons
%O 0,13
%A _Jonathan Vos Post_, Jan 13 2013
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