Mourad E. H. Ismail

Classical and Quantum Orthogonal Polynomials in One Variable (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 23. Juli 2009
• Englisch
• ISBN-13: 9781107109322
• Artikelnr.: 56687313

Autorenporträt

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

Inhaltsangabe

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.