Abstract
We consider some perturbation of the Chebyshev polynomials of second kind obtained by modifying one of its recurrence coefficients at an arbitrary order. The goal of this work is to point out that perturbed Chebyshev polynomials of fixed degree and different values of parameters of perturbation have some common points that are zeros of two Chebyshev polynomials of second kind of lower degrees. These common points can be simple or double. We identify the cases in which they are common zeros.
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Acknowledgements
The author was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020. The author would like to thank the referee for some comments and bibliographic references.
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da Rocha, Z. Common Points Between Perturbed Chebyshev Polynomials of Second Kind. Math.Comput.Sci. 15, 5–13 (2021). https://doi.org/10.1007/s11786-020-00469-x
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DOI: https://doi.org/10.1007/s11786-020-00469-x