Classical and Quantum Orthogonal Polynomials in One Variable

Mourad E. H. Ismail - Collection Encyclopedia of Mathematics and its Applications

706 pages, parution le 24/11/2005

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Résumé

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 and for graduate teaching, in which role it has already been successfully class-tested.

A comprehensive coverage of all the orthogonal polynomials discovered in the last fifty years, as well as classical work, and a complete chapter devoted to open problems and conjectures

Contains a chapter on multiple orthogonal polynomials, a first in book form

Contains applications of the subject to such areas as birth- and death-processes, integrable systems, combinatorics, and physical models

L'auteur - Mourad E. H. Ismail

Mourad E.H. Ismail is a professor of mathematics at the University of Central Florida.

Sommaire

Foreword
Preface
Preliminaries
Orthogonal polynomials
Differential equations
Jacobi polynomials
Some inverse problems
Discrete orthogonal polynomials
Zeros and inequalities
Polynomials orthogonal on the unit circle
Linearization, connections and integral representations
The Sheffer classification
q-series preliminaries
q-summation theorems
Some q-orthogonal polynomials
Exponential and q-Bessel functions
The Askey-Wilson polynomials
The Askey-Wilson operators
q-Hermite polynomials on the unit circle
Discrete q-orthogonal polynomials
Fractional and q-fractional calculus
Polynomial solutions to functional equations
Some indeterminate moment problems
The Riemann-Hilbert problem
Multiple orthogonal polynomials
Research problems
Bibliography
Index
Author index

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Mourad E. H. Ismail
Collection	Encyclopedia of Mathematics and its Applications
Parution	24/11/2005
Nb. de pages	706
Format	16 x 24
Couverture	Relié
Poids	1356g
Intérieur	Noir et Blanc
EAN13	9780521782012
ISBN13	978-0-521-78201-2