Ortogonální systémy polynomů

Abstract

Orthogonal systems of polynomials have many applications in modern-day scientific and technical fields. The goal of this thesis is to explore some aspects of these kinds of polynomials. That is why, in this thesis, we will firstly review the basics that are essential to understanding the other topics we will later discuss. Then we are going to look at their common properties and introduce a way of producing orthogonal polynomials. Next, we will pick a few of their significant representatives and derive some of their properties. The following chapter will be dedicated to one of their applications, the Gauss quadrature formulas. And the appendix will contain an overview of all the orthogonal systems we have previously discussed.