Lectures on Orthogonal Polynomials and Special Functions

Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.

Howard S. Cohl (Edited by), Mourad E. H. Ismail (Edited by)

9781108821599, Cambridge University Press

Paperback / softback, published 15 October 2020

350 pages
22.8 x 15.1 x 2 cm, 0.52 kg

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.

Subject Areas: Combinatorics & graph theory [PBV], Differential calculus & equations [PBKJ], Algebra [PBF]