Classical and Quantum Orthogonal Polynomials in One Variable (Encyclopedia of Mathematics and its Applications, Series Number 98) by Mourad E. H. Ismail (PDF)

Description

Coverage is encyclopedic in the first modern treatment of orthogonal polynomials from the viewpoint of special functions. It includes classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier and Meixner polynomials as well as those (e.g. Askey-Wilson and Al-Salam–Chihara polynomial systems) discovered over the last 50 years and multiple orthogonal polynomials are discussed 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.

User’s Reviews

Editorial Reviews: Review “Simplicity, clarity of exposition, thoughtfully designed exercises are among the book’s strengths. The book will be of interest not only to mathematicians, but also to a wide range of scientists and engineers.” Zentralblatt MATH”It’s delightful to read this book, and one can find many great results and new proofs for insights into known results. Also, most of the chapters have a set of exercises, which vary in difficulty…Ismail’s book is a great book on orthogonal polynomials containing a lot of information on the general theory and on explicit families of orthogonal polynomials. Starting with elementary theory and ending with research problems, this book is well-suited both for classroom use and for researchers.” Erik Koelink, Technische Universiteit Delft, SIAM Review”As one turns the pages, one is truck by how much material is recent, with most of the results being established in the past two decades…. Indeed, it should be on the bookshelf of any mathematician with an interest in either special functions, q-series, or orthogonal polynomials.” Bruce C. Berndt, Mathematical Reviews”… an ambitious and imposing testament to the author’s eminence in and love for the subject. All research workers in orthogonal polynomials will want to own this special work. I feel fortunate to have a copy of it.” The Mathematical Intelligencer Book Description The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback. About the Author Mourad E. H. Ismail is Professor of Mathematics at the University of Central Florida. Read more

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