Chebyshev-like polynomials satisfying fourth-order linear recurrences: Zeros and Hankel determinants
Date
2019-08
Authors
Onyango, Michael
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
We study sequences of polynomials that satisfy certain fourth-order linear recurĀ
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 deterĀ 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.
Description
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya.