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Classical and Quantum Orthogonal Polynomials in One Variable

$89.00

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: August 2009
  • availability: In stock
  • format: Paperback
  • isbn: 9780521143479

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About the Authors
  • 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.

    • 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
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    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

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    Product details

    • 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

    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

    Mourad E. H. Ismail, University of South Florida
    Mourad E. H. Ismail is Professor of Mathematics at the University of Central Florida.

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