OFFSET
0,13
COMMENTS
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.
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
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
D. Borwein, J. M. Borwein, and B. A. Mares Jr., Multi-variable sinc integrals and volumes of polyhedra, Ramanujan J. 6 (2002), no. 2, 189-208.
D. Borwein and J. M. Borwein, Some remarkable properties of sinc and related integrals, Ramanujan J. 5 (2001), no. 1, 73-89.
Jean-Luc Marichal and Michael J. Mossinghoff, Slices, slabs, and sections of the unit hypercube, arXiv:math/0607715 [math.MG], 2006-2008.
Jean-Luc Marichal and Michael J. Mossinghoff, Slices, slabs, and sections of the unit hypercube, Online Journal of Analytic Combinatorics, Issue 3 (2008), #1.
FORMULA
Equals 54084649^9 / (181440 * 3234846615^8).
EXAMPLE
1.82013483... * 10^(-12).
MATHEMATICA
Join[Table[0, {11}], RealDigits[54084649^9/(181440*3234846615^8), 10, 120][[1]]] (* Harvey P. Dale, May 24 2013 *)
CROSSREFS
KEYWORD
AUTHOR
Jonathan Vos Post, Jan 13 2013
STATUS
approved