A family of self-inversive polynomials with concyclic zeros

作者：Kim Eunmi^*

来源：Journal of Mathematical Analysis and Applications, 2013, 401(2): 695-701.

DOI：10.1016/j.jmaa.2012.12.048

• Zero distribution
• Self-inversive polynomials
• Jacobi polynomials

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.

• 出版日期2013-5