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Classical and Quantum Orthogonal Polynomials in One Variable


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: July 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521143479

£ 76.99

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About the Authors
  • 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.

    • 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

    '… 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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    Product details

    • Date Published: July 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: Available
  • Table of Contents

    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
    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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