Classical and Quantum Orthogonal Polynomials in One Variable

The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.

Mourad E. H. Ismail (Author)

9780521143479, Cambridge University Press

Paperback, published 23 July 2009

726 pages, 2 b/w illus. 135 exercises
23.4 x 15.7 x 3.7 cm, 1.08 kg

'… a delight to read, since one can find many new results or new approaches to well-known results. Also most of the chapters have a section with exercises, which range from being easy to having to look up research papers in order to be able to solve them. So the book ties in intimately with the current literature, and this is reflected by the 36-page bibliography, giving an excellent starting point to find one's way into the literature.' Erik Koelink, Bulletin of the London Mathematical Society

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.

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.

Subject Areas: Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB], Algebra [PBF]