Classical And Quantum Orthogonal Polynomials In One Variable

Description:
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.

Review:
'... 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 'The monograph by Mourad Ismail will meet the needs for an authoritative, up-to-date, self-contained and comprehensive account of the theory of orthogonal polynomials treated for the first time from the viewpoint of special functions. The coverage is encyclopedic ... Simplicity, clarity of exposition, thoughtfully designed exercises are among the book's strengths.' Zentralblatt Mathematik '... it should be on the bookshelf of any mathematician with an interest in either special functions, q-series, or orthogonal polynomials.' American Mathematical Society 'This is an impressive and monumental work on classical orthogonal polynomials and their q-analogs from the viewpoint of special functions.' Monatshefte fur Mathematik 'This is the first modern treatment of orthogonal polynomials from the viewpoint of special functions. The coverage is encyclopedic ... [the work] will be valued as an authoritative reference and for graduate teaching, in which role it has already been successfully class-tested.' L'enseignement mathematique

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.

Author Biography:
Mourad E. H. Ismail is Professor of Mathematics at the University of Central Florida.