Zeros of polynomials with four-term recurrence and linear coefficients

2018/08/21 by Tran, Khang, Zumba, Andres
#11C08 #26C10 #30C15 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.07133

Abstract

This paper investigates the zero distribution of a sequence of polynomials \ P_m(z)\ _m=0^∞ generated by the reciprocal of 1+ct+B(z)t²+A(z)t³ where c∈ℝ and A(z), B(z) are real linear polynomials. We study necessary and sufficient conditions for the reality of the zeros of P_m(z). Under these conditions, we find an explicit interval containing these zeros, whose union forms a dense subset of this interval.

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