Zero Distribution of Sequences of Classical Orthogonal Polynomials
نویسنده
چکیده
In this paper, we study the zero distribution of sequences of Jacobi, Laguerre, and Hermite polynomials. Our approach is based on identifying these orthogonal polynomials with certain Fekete polynomials defined below, and using monotonicity properties of the zeros of the polynomials. Let E ⊂ R be a closed set that consists of finitely many intervals. Let w : E→ [0,∞) be a weight function such that w(x) > 0, x ∈ Int(E), and |x|w(x) → 0 as |x| →∞, x ∈ E, if E is unbounded. Consider the function
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