Una aproximación a los polinomios casi-ortogonales

Abstract

The purpose of this work is to analyze the article "On quasi-orthogonal polynomials" written by David Dickinson. For this, in the first place some theoretical bases are established that serve as tools to be able to give a good development to the work. Following this the general theory of orthogonal polynomials is stated and it is shown that given a sequence of orthogonal polynomials a relationship of 3 terms is fulfilled, as well as a particular case in which orthogonal polynomials have real coefficients. Finally, a general definition of quasi-orthogonal polynomials is presented, two necessary and sufficient condition theorems that show the strong relationship that exists between orthogonal polynomials and quasi-orthogonal polynomials, a third necessary and sufficient condition theorem about quasi-orthogonal polynomials, and as an example that Sister Celine's polynomials are quasi-orthogonal.