Classical and quantum orthogonal polynomials in one variable


Classical and quantum orthogonal polynomials in one variable

Mourad E.H. Ismail ; with two chapters by Walter Van Assche

(Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 98)

Cambridge University Press, 2005

  • : [pbk.]

大学図書館所蔵 件 / 61



"Transferred to degital printing 2008"--T.p. verso of [pbk.]

Includes bibliographical references (p. [661]-696) and indexes



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.

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  • ISBN
    • 0521782015
    • 9780521143479
  • 出版国コード
  • タイトル言語コード
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  • 出版地
  • ページ数/冊数
    xviii, 706 p.
  • 大きさ
    25 cm
  • 分類
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