Classical and Quantum Orthogonal Polynomials in One Variable

2005/11/21 by Mourad E. H. Ismail · 29 citations
Mathematics · #Advanced Mathematical Identities #Advanced Mathematical Theories #Advice (programming) #Algebra over a field #Classical orthogonal polynomials #Computer science #Hermite polynomials #Integrable system #Jacobi polynomials #Laguerre polynomials #Library science #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Mathematics Subject Classification #Orthogonal polynomials #Polynomial #Pure mathematics #Special functions #Subject (documents) #Wilson polynomials

paper · doi:10.1017/cbo9781107325982

openalex publication_date 2005/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback. Its encyclopedic coverage includes classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier and Meixner polynomials as well as those discovered over the last 50 years, e.g. Askey–Wilson and Al-Salam–Chihara polynomial systems. Multiple orthogonal polynomials are discussed here for the first time in book form. Many modern applications of the subject are dealt with, including birth and death processes, integrable systems, combinatorics, and physical models. A chapter on open research problems and conjectures is designed to stimulate further research on the subject. Thoroughly updated and corrected since its original printing, this book continues to be valued as an authoritative reference not only by mathematicians, but also a wide range of scientists and engineers. Exercises ranging in difficulty are included to help both the graduate student and the newcomer.

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