Classical and Quantum Orthogonal Polynomials in One Variable
Classical and Quantum Orthogonal Polynomials in One Variable
$99.99
USDThe 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.
- Now in paperback, with corrections and thoroughly updated references
- Comprehensive coverage of all the orthogonal polynomials discovered in the last fifty years, as well as classical work, and a complete chapter devoted to open problems and conjectures
- With applications of the subject to such areas as birth- and death-processes, integrable systems, combinatorics, and physical models
Reviews & endorsements
"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
Product details
August 2009Paperback
9780521143479
726 pages
234 × 157 × 37 mm
1.08kg
2 b/w illus. 135 exercises
Available
Table of Contents
- Foreword
- Preface
- 1. Preliminaries
- 2. Orthogonal polynomials
- 3. Differential equations, Discriminants and electrostatics
- 4. Jacobi polynomials
- 5. Some inverse problems
- 6. Discrete orthogonal polynomials
- 7. Zeros and inequalities
- 8. Polynomials orthogonal on the unit circle
- 9. Linearization, connections and integral representations
- 10. The Sheffer classification
- 11. q-series Preliminaries
- 12. q-Summation theorems
- 13. Some q-Orthogonal polynomials
- 14. Exponential and q-bessel functions
- 15. The Askey-Wilson polynomials
- 16. The Askey-Wilson operators
- 17. q-Hermite polynomials on the unit circle
- 18. Discrete q-orthogonal polynomials
- 19. Fractional and q-fractional calculus
- 20. Polynomial solutions to functional equations
- 21. Some indeterminate moment problems
- 22. The Riemann-Hilbert problem for orthogonal polynomials
- 23. Multiple orthogonal polynomials
- 24. Research problems
- Bibliography
- Index
- Author index.
