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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Marichal, p. 6, gives a surprising formula: Integral_{0..infinity} 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

REFERENCES

Jean-Luc Marichal, Michael J. Mossinghoff, Slices, slabs, and sections of the unit hypercube, Online Journal of Analytic Combinatorics, Issue 3 (2008), #1.

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, Michael J. Mossinghoff, Slices, slabs, and sections of the unit hypercube, arXiv:math/0607715v2 [math.MG], Feb 12, 2008.

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 A021850 A197576

Adjacent sequences:  A209241 A209242 A209243 * A209245 A209246 A209247

KEYWORD

nonn,easy,cons

AUTHOR

Jonathan Vos Post, Jan 13 2013

STATUS

approved

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Last modified April 8 15:38 EDT 2020. Contains 333314 sequences. (Running on oeis4.)