Classical and quantum orthogonal polynomials in one variable

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...

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Main Authors: Ismail, Mourad, Assche, Walter van (Author)
Format: eBook
Language:English
Published: Cambridge Cambridge University Press 2005
Series:Encyclopedia of mathematics and its applications
Subjects:
Online Access:
Collection: Cambridge Books Online - Collection details see MPG.ReNa
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100 1 |a Ismail, Mourad 
245 0 0 |a Classical and quantum orthogonal polynomials in one variable  |c Mourad E.H. Ismail ; with two chapters by Walter Van Assche 
246 3 1 |a Classical & Quantum Orthogonal Polynomials in One Variable 
260 |a Cambridge  |b Cambridge University Press  |c 2005 
300 |a xviii, 706 pages  |b digital 
505 0 |a 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 
653 |a Orthogonal polynomials 
700 1 |a Assche, Walter van  |e [author] 
041 0 7 |a eng  |2 ISO 639-2 
989 |b CBO  |a Cambridge Books Online 
490 0 |a Encyclopedia of mathematics and its applications 
856 |u https://doi.org/10.1017/CBO9781107325982  |x Verlag  |3 Volltext 
082 0 |a 515.55 
520 |a 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