Zeros of polynomials with four-term recurrence and linear coefficients

Khang Tran; Andres Zumba

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arXiv · 1808.07133

Zeros of polynomials with four-term recurrence and linear coefficients

Khang Tran·Andres Zumba

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Abstract

This paper investigates the zero distribution of a sequence of polynomials $\left\{ P_{m}(z)\right\} _{m=0}^{\infty}$ generated by the reciprocal of $1+ct+B(z)t^{2}+A(z)t^{3}$ where $c\in\mathbb{R}$ 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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BibTeX RIS

Khang Tran, Andres Zumba. 2018-08-21. Zeros of polynomials with four-term recurrence and linear coefficients. https://arxiv.org/abs/1808.07133

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