A first study of Zeros of Classical Orthogonal Polynomial

Date: 2018..03..08
Event: Seminario de Matemática Aplicada del CITE III
Venue: Universidad de Almeria, Spain

Abstract

In this short work we consider some basic results connected with the zeros of classical orthogonal polynomials (COP). Given a orthogonal polynomial sequence (OPS), namely \((p_n)_{n\ge 0}\), we set a positive integer \(N\) and we obtain for such value a new set of orthogonality properties for such for \((p_n)_{n\ge 0}\), we obtain closed expressions for \(p_n(x)\) for \(n\le N\) and the Hankel matrix for such polynomials in terms of the zeros of \(p_N(x)\).

With these results we believe we are able to establish some conditions on the parameters of the family. We also prove that the derivative of every COP is the kernel of itself. Explicit expressions are given.

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