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A209244
Decimal expansion of a constant arising in slices, slabs, and sections of the unit hypercube.
1
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, 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, 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
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
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
Sequence in context: A284865 A221758 A322699 * A300220 A338851 A021850
KEYWORD
nonn,easy,cons
AUTHOR
Jonathan Vos Post, Jan 13 2013
STATUS
approved