  We employ the fact certain divided differences can be written as weighted
means of B-splines and hence are positive. These divided differences include
the complete homogeneous symmetric polynomials of even degree $2p$, the
positivity of which is a classical result by D. B. Hunter. We extend Hunter's
result to complete homogeneous symmetric polynomials of fractional degree,
which are defined via Jacobi's bialternant formula. We show in particular that
these polynomials have positive real part for real degrees $\mu$ with
$|\mu-2p|< 1/2$. We also prove a positivity criterion for linear combinations
of the classical complete homogeneous symmetric polynomials and a sufficient
criterion for the positivity of linear combinations of products of such
polynomials.
