Classical and Quantum Orthogonal Polynomials in One Variable, Volume 13

Couverture
Cambridge University Press, 21 nov. 2005 - 706 pages
Coverage is encyclopedic in the first modern treatment of orthogonal polynomials from the viewpoint of special functions. It includes 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 and multiple orthogonal polynomials are discussed 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.
 

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Table des matières

Preliminaries
1
Orthogonal Polynomials
16
Differential Equations
52
Jacobi Polynomials
80
Some Inverse Problems
133
Discrete Orthogonal Polynomials
174
Zeros and Inequalities
203
Polynomials Orthogonal on the Unit Circle
222
The AskeyWilson Polynomials
377
The AskeyWilson Operators
425
qHermite Polynomials on the Unit Circle
454
Discrete qOrthogonal Polynomials
468
Fractional and qFractional Calculus
490
Polynomial Solutions to Functional Equations
508
Some Indeterminate Moment Problems
529
The RiemannHilbert Problem
577

Linearization Connections and Integral Representations
253
The Sheffer Classification
282
qSeries Preliminaries
293
qSummation Theorems
299
Some qOrthogonal Polynomials
318
Exponential and qBessel Functions
351
Multiple Orthogonal Polynomials
606
Research Problems
647
Bibliography
661
Index
697
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À propos de l'auteur (2005)

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

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