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.
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.
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Mourad E. H. Ismail is Professor of Mathematics at the University of Central Florida.
'… 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 für 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
'… 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
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