OFFSET
0,1
COMMENTS
Conjectured to be density of densest packing of equal spheres in 8 dimensions (achieved for example by the E_8 lattice).
The above conjecture is true (cf. Viazovska, 2017). - Felix Fröhlich, Jan 08 2018
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.7, p. 507.
LINKS
J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete & Computational Geometry, Vol. 13, No. 3-4 (1995), 383-403.
G. Nebe and N. J. A. Sloane, Home page for E_8 lattice.
N. J. A. Sloane and Andrey Zabolotskiy, Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (some values are only conjectural).
Maryna S. Viazovska, The sphere packing problem in dimension 8, Annals of Mathematics, Vol. 185, No. 3 (2017), 991-1015.
Maryna S. Viazovska, The sphere packing problem in dimension 8, arXiv:1603.04246 [math.NT], 2017.
FORMULA
Equals Sum_{n>=1} Sum_{k>=n} 1/(2*n - 1)^2/(2*k + 1)^2. - Geoffrey Critzer, Nov 03 2013
EXAMPLE
.25366950790104801363656336637683622721283225435595161898819...
MATHEMATICA
RealDigits[Pi^4/ 384, 10, 120][[1]] (* Harvey P. Dale, Aug 11 2015 *)
PROG
(PARI) Pi^4/384 \\ Charles R Greathouse IV, Oct 31 2014
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Feb 10 2013
STATUS
approved