Edition 
2nd ed. 
Description 
1 online resource (440 pages) 
Series 
Encyclopedia of Mathematics and its Applications ; v. 155


Encyclopedia of mathematics and its applications.

Contents 
Cover; HalfTitle page; Series page; Title page; Copyright page; Dedication page; Contents; Preface to the Second Edition; Preface to the First Edition; 1 Background; 1.1 The Gamma and Beta Functions; 1.2 Hypergeometric Series; 1.2.1 Lauricella series; 1.3 Orthogonal Polynomials of One Variable; 1.3.1 General properties; 1.3.2 Threeterm recurrence; 1.4 Classical Orthogonal Polynomials; 1.4.1 Hermite polynomials; 1.4.2 Laguerre polynomials; 1.4.3 Gegenbauer polynomials; 1.4.4 Jacobi polynomials; 1.5 Modified Classical Polynomials; 1.5.1 Generalized Hermite polynomials. 

1.5.2 Generalized Gegenbauer polynomials1.5.3 A limiting relation; 1.6 Notes; 2 Orthogonal Polynomials in Two Variables; 2.1 Introduction; 2.2 Product Orthogonal Polynomials; 2.3 Orthogonal Polynomials on the Unit Disk; 2.4 Orthogonal Polynomials on the Triangle; 2.5 Orthogonal Polynomials and Differential Equations; 2.6 Generating Orthogonal Polynomials of Two Variables; 2.6.1 A method for generating orthogonal polynomials; 2.6.2 Orthogonal polynomials for a radial weight; 2.6.3 Orthogonal polynomials in complex variables; 2.7 First Family of Koornwinder Polynomials. 

2.8 A Related Family of Orthogonal Polynomials2.9 Second Family of Koornwinder Polynomials; 2.10 Notes; 3 General Properties of Orthogonal Polynomials in Several Variables; 3.1 Notation and Preliminaries; 3.2 Moment Functionals and Orthogonal Polynomials in Several Variables; 3.2.1 Definition of orthogonal polynomials; 3.2.2 Orthogonal polynomials and moment matrices; 3.2.3 The moment problem; 3.3 The ThreeTerm Relation; 3.3.1 Definition and basic properties; 3.3.2 Favard''s theorem; 3.3.3 Centrally symmetric integrals; 3.3.4 Examples; 3.4 Jacobi Matrices and Commuting Operators. 

3.5 Further Properties of the ThreeTerm Relation3.5.1 Recurrence formula; 3.5.2 General solutions of the threeterm relation; 3.6 Reproducing Kernels and Fourier Orthogonal Series; 3.6.1 Reproducing kernels; 3.6.2 Fourier orthogonal series; 3.7 Common Zeros of Orthogonal Polynomials in Several Variables; 3.8 Gaussian Cubature Formulae; 3.9 Notes; 4 Orthogonal Polynomials on the Unit Sphere; 4.1 Spherical Harmonics; 4.2 Orthogonal Structures on S[sup(d)] and on B[sup(d)]; 4.3 Orthogonal Structures on B[sup(d)] and on S[sup(d+m1)]; 4.4 Orthogonal Structures on the Simplex. 

4.5 Van der Corput  Schaake Inequality4.6 Notes; 5 Examples of Orthogonal Polynomials in Several Variables; 5.1 Orthogonal Polynomials for Simple Weight Functions; 5.1.1 Product weight functions; 5.1.2 Rotationinvariant weight functions; 5.1.3 Multiple Hermite polynomials on R[sup(d)]; 5.1.4 Multiple Laguerre polynomials on R[sub(+)sup(d)]; 5.2 Classical Orthogonal Polynomials on the Unit Ball; 5.2.1 Orthonormal bases; 5.2.2 Appell''s monic orthogonal and biorthogonalpolynomials; 5.2.3 Reproducing kernel with respect to W[sup(B) sub[Mu] on B[sup(d)]. 
Bibliography 
Includes bibliographical references and indexes. 
Summary 
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade. 
Local Note 
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection  North America 
Subject 
Orthogonal polynomials.


Functions of several real variables.

Genre/Form 
Electronic books.

Added Author 
Xu, Yuan.

Other Form: 
Print version: Dunkl, Charles F. Orthogonal Polynomials of Several Variables. Cambridge : Cambridge University Press, ©2014 9781107071896 
ISBN 
9781316078457 

1316078450 

9781316073711 (electronic bk.) 

1316073718 (electronic bk.) 

9781107786134 

1107786134 

9781322177083 (MyiLibrary) 

1322177082 (MyiLibrary) 

9781316076088 (ebook) 

1316076083 (ebook) 

9781107071896 

1107071895 
