A Short Course on Orthogonal Polynomials and Special Functions

TL;DR

This paper provides an introductory overview of orthogonal polynomials and special functions, aimed at beginners, including detailed proofs and accessible explanations based on lecture notes from a university course.

Contribution

It offers a beginner-friendly, comprehensive introduction with detailed proofs, filling a gap in accessible educational resources on orthogonal polynomials and special functions.

Findings

Accessible explanations for beginners

Detailed proofs included

Comprehensive coverage of basic concepts

Abstract

These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and 2016-2017 (at University of Coimbra). The notes were written for students who have never contacted with the above topics. Most results presented here can be found in the available bibliography at the end of each text/chapter, although in general more detailed proofs have been included (a few of them different from the ones presented in the source references), hoping this helps the beginner student.