  In this paper, we introduce a new family of symmetric polynomials which
depends on a parameter r. They are defined by specifying certain of their
zeros. For the parameter values 1/2, 1, and 2 they have an interpretation in
terms of Capelli identities.
  First, we give explicit formulas in some special cases. Then we show that the
polynomials can also be defined in terms of difference equations. As a
corollary we obtain that their top homogeneous part is a Jack polynomial. This
is used to give a new proof of the Pieri formula for Jack polynomials.
