Orthogonal Polynomials: An Introduction

We introduce the idea of a collection of orthogonal polynomials over an interval on the real line. We show that the coefficients of the polynomials can be determined inductively by solving a system of linear equations. The inner product from which orthogonality is defined arises from a non-negative weight function over the interval. We give examples of classical weights and briefly discuss special cases of Jacobi polynomials. #mikethemathematician, #profdabkowski, #mikedabkowski