Monotonicidade dos zeros dos Polinomios ortogonais Classicos: Teoremas de Markov e Stieltjes

Abstract

In this research we study the hypergeometric equations, in particular, the equations with polynomial solutions. We show that such polynomials can be represented explicitly by the Rodrigues's formula. We obtain a characterization of these polynomials that are orthogonal, namely, the Polynomials of Jacobi, Laguerre and Hermite. We use the classical theorems of Markov and of Stieltjes to study the monotonicity of the zeros of classical orthogonal polynomials, in particular the Jacobi, Laguerre, and Gegenbauer polynomials.