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arXiv · 2304.12444

Zeros of Taylor polynomials formed by a three-term recurrence

Juhoon Chung·Khang Tran
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Abstract

From a sequence $\left\{ a_{n}\right\} _{n=0}^{\infty}$ of real numbers satisfying a three-term recurrence, we form a sequence of polynomials $\left\{ P_{m}(z)\right\} _{m=0}^{\infty}$ whose coefficients are numbers in this sequence. We showed that under explicit conditions, the zeros of $P_{m}(z)$, $m\gg1$, lie on one side of the circle whose radius is given by modulus of a zero of the denominator of the generating function of $\left\{ a_{n}\right\} _{n=0}^{\infty}$.

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Juhoon Chung, Khang Tran. 2023-04-24. Zeros of Taylor polynomials formed by a three-term recurrence. https://arxiv.org/abs/2304.12444

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