Orthogonal Polynomials from a Complex Perspective

Complex function theory and its close companion — potential theory — provide a wealth of tools for analyzing orthogonal polynomials and orthogonal expansions. This paper is designed to show how the complex perspective leads to insights on the behavior of orthogonal polynomials. In particular, we discuss the location of zeros and the growth of orthogonal polynomials in the complex plane. For some of the basic results we provide proofs that are not typically found in the standard literature on orthogonal polynomials.

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