Lectures on Orthogonal Polynomials and Special Functions [Paperback]

Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.This is a collection of graduate-level introductions to five areas of current research interest in orthogonal polynomials and special functions. It derives from the OPSF-S6 Summer School lectures given by international authorities and has been carefully edited into a coherent whole, with examples and exercises.This is a collection of graduate-level introductions to five areas of current research interest in orthogonal polynomials and special functions. It derives from the OPSF-S6 Summer School lectures given by international authorities and has been carefully edited into a coherent whole, with examples and exercises.Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.1. Exceptional Orthogonal Polynomials via Krall Discrete Polynomials Antonio J. Dur?n; 2. A Brief Review of q-series Mourad E. H. Ismail; 3. Applications of Spectral Theory to Special Functions Erik Koelink; 4. Elliptic Hypergeometric Functions Hjalmar Rosengren; 5. Combinatorics of Orthogonal Polynomials and their Moments Jiang Zeng.