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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.Read more
- 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 MATHSee more reviews
"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
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- Date Published: August 2009
- format: Paperback
- isbn: 9780521143479
- length: 726 pages
- dimensions: 234 x 157 x 37 mm
- weight: 1.08kg
- contains: 2 b/w illus. 135 exercises
- availability: In stock
Table of Contents
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
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