Classical and Quantum Orthogonal Polynomials in One Variable
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Classical and Quantum Orthogonal Polynomials in One Variable

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eBook - PDF

Classical and Quantum Orthogonal Polynomials in One Variable

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About This Book

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.

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Yes, you can access Classical and Quantum Orthogonal Polynomials in One Variable by Mourad E. H. Ismail in PDF and/or ePUB format, as well as other popular books in Mathematik & Algebra. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Cambridge University Press
Year
2009
ISBN
9781107109322
Topic
Mathematik
Subtopic
Algebra

Table of contents

  1. Cover
  2. Half Title
  3. Series Page
  4. Title
  5. Copyright
  6. Contents
  7. Foreword
  8. Preface
  9. 1 Preliminaries
  10. 2 Orthogonal Polynomials
  11. 3 Differential Equations Discriminants and Electrostatics
  12. 4 Jacobi Polynomials
  13. 5 Some Inverse Problems
  14. 6 Discrete Orthogonal Polynomials
  15. 7 Zeros and Inequalities
  16. 8 Polynomials Orthogonal on the Unit Circle
  17. 9 Linearization, Connections and Integral Representations
  18. 10 The Sheffer Classification
  19. 11 q-Series Preliminaries
  20. 12 q-Summation Theorems
  21. 13 Some q-Orthogonal Polynomials
  22. 14 Exponential and q-Bessel Functions
  23. 15 The Askey–Wilson Polynomials
  24. 16 The Askey–Wilson Operators
  25. 17 q-Hermite Polynomials on the Unit Circle
  26. 18 Discrete q-Orthogonal Polynomials
  27. 19 Fractional and q-Fractional Calculus
  28. 20 Polynomial Solutions to Functional Equations
  29. 21 Some Indeterminate Moment Problems
  30. 22 The Riemann-Hilbert Problem for Orthogonal Polynomials
  31. 23 Multiple Orthogonal Polynomials
  32. 24 Research Problems
  33. Bibliography
  34. Index
  35. Author index