Classical and quantum orthogonal polynomials in one variable / Mourad E.H. Ismail ; with two chapters by Walter Van Assche.

Format:

Book

Author/Creator:

Ismail, Mourad, 1944- author.

Assche, Walter van, 1958- author.

Series:

Encyclopedia of mathematics and its applications ; v. 98.

Encyclopedia of mathematics and its applications ; volume 98

Language:

English

Subjects (All):

Orthogonal polynomials.

Physical Description:

1 online resource (xviii, 706 pages) : digital, PDF file(s).

Other Title:

Classical & Quantum Orthogonal Polynomials in One Variable

Place of Publication:

Cambridge : Cambridge University Press, 2005.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. [661]-696) and indexes.

ISBN:

1-139-88281-3

1-107-08945-X

1-107-09575-1

1-107-10382-7

1-107-10133-6

1-107-32598-6