Lectures on Orthogonal Polynomials and Special Functions

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. Durán; 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.

Howard S. Cohl, mathematician in the Applied and Computational Mathematics Division at the National Institute of Standards and Technology, is Technical Editor for the NIST Digital Library of Mathematical Functions. He has PhD's in mathematics and physics and has published over 60 papers on special functions, orthogonal polynomials, fundamental solutions for linear PDEs on Riemannian manifolds, and mathematical knowledge management.
Mourad E. H. Ismail, Research Professor of Mathematics at the University of Central Florida, is an expert in special functions and approximation theory. He has made substantial contributions to the theory of orthogonal polynomials and q-series. Ismail is an editor of several research journals and author and editor of seven books.