Abstract
AbstractSuppose \(\{P_n\}_{n=0}^\infty \) is a sequence of polynomials, orthogonal with respect to the weight function w(x) on the interval [a, b]. In this lecture we will show that the zeros of an orthogonal polynomial are simple, that they are located in the interval of orthogonality and that the zeros of polynomials with adjacent degree, separate each other. We will also discuss the main ingredients of the Gauss quadrature formula, where the zeros of orthogonal polynomials are of decisive importance in approximating integrals.KeywordsZerosOrthogonalityInterlacing of zerosGauss quadratureMathematics Subject Classification (2000)33C45
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