Hyperbolic polynomials and linear-type generating functions

2018/10/02 by Forgács, Tamás, Tran, Khang · 1 citation
#26C10 #30C15 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.01521

Abstract

We prove that the polynomials generated by the relation ∑_m=0^∞ H_m(z)t^m=(1)/(P(t)+z t^r Q(t)) are hyperbolic for m ≫ 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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