The Hermite constant is defined for dimension as the value
(1)
(Le Lionnais 1983). In other words, they are given by
(2)
where
is the maximum latticepacking density
for hypersphere packing and is the content of the -hypersphere. The first few
values of
are 1, 4/3, 2, 4, 8, 64/3, 64, 256, ... (OEIS A007361
and A007362; Gruber and Lekkerkerker 1987,
p. 518). Values for larger are not known.
as the value
![gamma_n=(sup_(f)min_(x_i)f(x_1,x_2,...,x_n))/([discriminant(f)]^(1/n))](/images/equations/HermiteConstants/NumberedEquation1.svg)
is the maximum lattice packing density
for hypersphere packing and 
is the content of the 
-hypersphere. The first few
values of 
are 1, 4/3, 2, 4, 8, 64/3, 64, 256, ... (OEIS A007361
and A007362; Gruber and Lekkerkerker 1987,
p. 518). Values for larger 
are not known.
,
