Chebyshev-like polynomials satisfying fourth-order linear recurrences: Zeros and Hankel determinants
Abstract
We study sequences of polynomials that satisfy certain fourth-order linear recur
rences with a parameter c. We show that for c real, their zeros lie on two concentric and
inversely related circles. The associated n x n Hankel determinants are deter mined. Here, the 2
x 2 case is the most challenging, and has an intriguing connection with questions concerning sets
of polynomials with all roots on the unit circle. These polynomials arise from Chebyshevian
modifications of finite geometric series.
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- SIMC 2019 [99]