A Short Note on Interlacing and Monotonicity of Zeros of Orthogonal Polynomials

摘要

We discuss, in this short didactical review, old and recent results on the interlacing and monotonicity of zeros, in the context of orthogonal polynomials, paying special attention to the flexibility and versatility of Sturm's comparison theorem on zeros of Sturm-Liouville functions and the work Stieltjes on monotonicity of zeros.