Polynomials with rational generating functions and real zeros

This paper investigates the location of the zeros of a sequence of polynomials generated by a rational function with a binomial-type denominator. We show that every member of a two-parameter family consisting of such generating functions gives rise to a sequence of polynomials {Pm(z)}m=0∞ that is eventually hyperbolic. Moreover, the real zeros of the polynomials Pm(z)Pm(z) form a dense subset of an interval I⊂R+I⊂R+, whose length depends on the particular values of the parameters in the generating function.