Theory, Methods and Applications of the Classical Hypergeometric Orthogonal Polynomial Sequences of Sheffer and Jacobi

Download or read book Theory, Methods and Applications of the Classical Hypergeometric Orthogonal Polynomial Sequences of Sheffer and Jacobi written by Dylan Jacob Langharst and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this Schreyer Honors Thesis is to explore theories, methods and applications oforthogonal polynomial sequences. This thesis is designed to be approachable and understandableby any undergraduate mathematics or physics major at The Pennsylvania State University in orderto serve as a learning resource. This paper is to be comprehensive and self-consistent; that is, wehope to cover all prerequisite information here that is required for the understanding of this paper,hence the thorough introduction. Throughout this paper, several definitions, terminologies andnotations are used, as listed in Chapter 1. The presentation of polynomial sequences here closelyfollow that in [1] and [2]. Limit, series and integral relations involving orthogonal polynomialsare presented in Chapter 2. Chapter 3 covers the inverse method and Schrdinger form for variousorthogonal polynomial sequences. Chapter 4 introduces applications of orthogonal polynomials inphysics and numerical analysis.