Abstract
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 ∞, the polynomial goes from a constant multiple of (z−1)2n to a constant multiple of (z+1)2n with the polynomial ∑k=02nzk when d=n. Also, we compute the discriminants and the squared distance sums of their zeros.
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