Linear combinations of polynomials with three-term recurrence

Khang Tran; Maverick Zhang

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arXiv · 1908.00043

Linear combinations of polynomials with three-term recurrence

Khang Tran·Maverick Zhang

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Abstract

We study the zero distribution of the sum of the first $n$ polynomials satisfying a three-term recurrence whose coefficients are linear polynomials. We also extend this sum to a linear combination, whose coefficients are powers of $az+b$ for $a,b\in\mathbb{R}$, of Chebyshev polynomials. In particular, we find necessary and sufficient conditions on $a$, $b$ such that this linear combination is hyperbolic.

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Khang Tran, Maverick Zhang. 2019-07-31. Linear combinations of polynomials with three-term recurrence. https://arxiv.org/abs/1908.00043

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