A family of self-inversive polynomials with concyclic zeros

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:401

Article

Kim, Eunmi

关键词: Zero distribution;    Self-inversive polynomials;    Jacobi polynomials;   

DOI  :  10.1016/j.jmaa.2012.12.048

来源: Elsevier

【 摘 要 】

We give a one-parameter family of self-inversive polynomials associated with Jacobi polynomials that has all zeros on the unit circle. As the parameter d goes from -1/2 to infinity, the polynomial goes from a constant multiple of (z - 1)(2n) to a constant multiple of (z +1)(2n) with the polynomial Sigma(2n)(k=0) z(k) when d = n. Also, we compute the discriminants and the squared distance sums of their zeros. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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