The root distribution of polynomials with a three-term recurrence
نویسنده
چکیده
For any fixed positive integer n, we study the root distribution of a sequence of polynomials Hm(z) satisfying the rational generating function ∞ ∑ m=0 Hm(z)t m = 1 1 +B(z)t+A(z)tn where A(z) and B(z) are any polynomials in z with complex coefficients. We show that the roots of Hm(z) which satisfy A(z) 6= 0 lie on a specific fixed real algebraic curve for all large m.
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