Linear combinations of polynomials with three-term recurrence

2019/07/31 by Tran, Khang, Zhang, Maverick
#26C10 #30C15 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.00043

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∈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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