具有有理generating functions和实零点的多项式
Polynomials with rational generating functions and real zeros
摘要：
本文研究了由具有二项式型分母的有理函数生成的多项式序列的零点的位置。我们表明，这样的生成函数组成的两个参数的家庭的每一个成员产生一个序列的多项式$\{P_{m}(z)\}_{m=0}^{\infty}$，最终是双曲的。此外，多项式$P_{m}(z)$的实零点形成区间$I\subset\mathbb{R}^{+}$的稠密子集，其长度取决于生成函数中的参数的特定值。
英文摘要：
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 $\{P_{m}(z)\}_{m=0}^{\infty}$ that is eventually hyperbolic. Moreover, the real zeros of the polynomials $P_{m}(z)$ form a dense subset of an interval $I\subset\mathbb{R}^{+}$, whose length depends on the particular values of the parameters in the generating function.
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