FW: New Book: Classical and Quantum Orthogonal Polynomials in One Variable

["Dan Lozier" <lozier@nist.gov>]

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Subject: New Book: Classical and Quantum Orthogonal Polynomials in One
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Subject: New Book: Classical and Quantum Orthogonal Polynomials in One Variable


Classical and Quantum Orthogonal Polynomials in One Variable
Mourad E. H. Ismail, University of South Florida

This is first modern treatment of orthogonal polynomials from the viewpoint
of special functions. The coverage is encyclopaedic, including 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; multiple orthogonal
polynomials are dicussed 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. Exercises of varying degrees of difficulty
are included to help the graduate student and the newcomer. A comprehensive
bibliography rounds off the work, which will be valued as an authoritative
reference as well as for graduate teaching.

Contents:
1. Preliminaries; 2. Orthogonal polynomials; 3. Differential equations; 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; 23. Multiple orthogonal
polynomials; 24. Research problems; Bibliography; Index.

November 2005 / 0-521-78201-5 / Hardback / $140.00
Series: Encyclopedia of Mathematics and its Applications (No. 98)
688 pages / 1 line diagram / 80 exercises

Please visit www.cambridge.org/0521782015 to order a copy.