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arXiv · 1810.01521

Hyperbolic polynomials and linear-type generating functions

Tamás Forgács·Khang Tran
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Abstract

We prove that the polynomials generated by the relation $\displaystyle{\sum_{m=0}^{\infty} H_m(z)t^m=\frac{1}{P(t)+z t^r Q(t)}}$ are hyperbolic for $m \gg 1$ given that the zeros of the real polynomials $P$ and $Q$ are real and sufficiently separated. The paper also contains a result on a certain family of exponential polynomials, which are demonstrated to have infinitely many real zeros.

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Tamás Forgács, Khang Tran. 2018-10-02. Hyperbolic polynomials and linear-type generating functions. https://arxiv.org/abs/1810.01521

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