A209244 Decimal expansion of a constant arising in slices, slabs, and sections of the unit hypercube.

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

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

Sequence in context: A284865 A221758 A322699 * A300220 A338851 A021850

Adjacent sequences: A209241 A209242 A209243 * A209245 A209246 A209247

Keyword

nonn,easy,cons

Author

Jonathan Vos Post, Jan 13 2013

Status

approved