Textbook in PDF format

A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials, which distinguishes it from other contributions in the field.
Features
Suitable for a graduate course in orthogonal polynomials
Can be used for a short course on the algebraic theory of orthogonal polynomials and its applicability to the study of the “old” classical orthogonal polynomials
Includes numerous exercises for each topic
Real and complex analyses are the only prerequisites
Dedication
Preface
Authors
Symbol Description
Foundations of the Algebraic Theory
Orthogonal Polynomial Sequences
Zeros and Gauss-Jacobi Mechanical Quadrature
The Spectral Theorem
The Markov Theorem
Orthogonal Polynomials and Dual Basis
Functional Differential Equation
Classical Orthogonal Polynomials: General Properties
Functional Equation on Lattices
Classical Orthogonal Polynomials: The Positive Definite Case
Hypergeometric Series
Locally Convex Spaces
Bibliography
Index