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Vitalice Omondi Wamnyolo, Michael Obiero Oyengo, and Isaac Owino Okoth, Properties of pseudo-orthogonal Chebyshev-like polynomials, Eur. J. Math. Appl. 5 (2025), Article ID 7.

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Volume 5 (2025), Article ID 7

https://doi.org/10.28919/ejma.2025.5.7

Published: 10/02/2025

Abstract:

Chebyshev polynomials are one of the classes of rationally generated polynomials that are orthogonal in the interval \([-1,1]\). In this paper, we introduce a new class of Chebyshev-like polynomials denoted by $R_{n}(x)$ and satisfying the recurrence relation \(R_{n}(x)=2xR_{n-1}(x)-R_{n-2}(x),\) with initial conditions $R_{0}(x)=1$ and $R_{1}(x)=3x$. We show that these polynomials are rationally generated and prove connections to the classical Chebyshev polynomials of the first and of the second kind. We then prove that they are pseudo-orthogonal in the interval \([-1,1]\) and have all their zeros in this interval. Lastly, we give identities for resultants involving these polynomials.

How to Cite:

Vitalice Omondi Wamnyolo, Michael Obiero Oyengo, and Isaac Owino Okoth, Properties of pseudo-orthogonal Chebyshev-like polynomials, Eur. J. Math. Appl. 5 (2025), Article ID 7. https://doi.org/10.28919/ejma.2025.5.7