Exploring the zeros of real self-reciprocal polynomials by Chebyshev polynomials
arXiv:1709.03037
Originality Synthesis-oriented
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Provides theoretical insights into zero location of self-reciprocal polynomials, relevant for mathematicians studying polynomial theory.
The paper identifies classes of real self-reciprocal polynomials with at most two zeros outside the unit circle, linking them to Chebyshev quasi-orthogonal polynomials, and analyzes the distribution, simplicity, and monotonicity of their zeros.
In this paper we present some classes of real self-reciprocal polynomials with at most two zeros outside the unit circle which are connected with a Chebyshev quasi-orthogonal polynomials of order one. We investigated the distribution, simplicity and monotonicity of their zeros around the unit circle and real line.