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Softcover ISBN:  9780821810231 
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Product Code:  COLL/23.B 
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Softcover ISBN:  9780821810231 
Product Code:  COLL/23 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470431716 
Product Code:  COLL/23.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
Softcover ISBN:  9780821810231 
eBook ISBN:  9781470431716 
Product Code:  COLL/23.B 
List Price:  $188.00 $143.50 
MAA Member Price:  $169.20 $129.15 
AMS Member Price:  $150.40 $114.80 

Book DetailsColloquium PublicationsVolume: 23; 1939; 432 ppMSC: Primary 33
This first detailed systematic treatment of orthogonal polynomials continues as a bestseller in the Colloquium Series.

Table of Contents

Chapters

Chapter 1. Preliminaries

Chapter 2. Definition of orthogonal polynomials; principal examples

Chapter 3. General properties of orthogonal polynomials

Chapter 4. Jacobi polynomials

Chapter 5. Laguerre and Hermite polynomials

Chapter 6. Zeros of orthogonal polynomials

Chapter 7. Inequalities

Chapter 8. Asymptotic properties of the classical polynomials

Chapter 9. Expansion problems associated with the classical polynomials

Chapter 10. Representation of positive functions

Chapter 11. Polynomials orthogonal on the unit circle

Chapter 12. Asymptotic properties of general orthogonal polynomials

Chapter 13. Expansion problems associated with general orthogonal polynomials

Chapter 14. Interpolation

Chapter 15. Mechanical quadrature

Chapter 16. Polynomials orthogonal on an arbitrary curve

Problems and exercises

Further problems and exercises

Appendix


Reviews

This is the first detailed systematic treatment of ... (a) the asymptotic behaviour of orthogonal polynomials, by various methods, with applications, in particular, to the ‘classical' polynomials of Legendre, Jacobi, Laguerre and Hermite; (b) a detailed study of expansions in series of orthogonal polynomials, regarding convergence and summability; (c) a detailed study of orthogonal polynomials in the complex domain; (d) a study of the zeros of orthogonal polynomials, particularly of the classical ones, based upon an extension of Sturm's theorem for differential equations. The book presents many new results; many results already known are presented in generalized or more precise form, with new simplified proofs.
Mathematical Reviews


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This first detailed systematic treatment of orthogonal polynomials continues as a bestseller in the Colloquium Series.

Chapters

Chapter 1. Preliminaries

Chapter 2. Definition of orthogonal polynomials; principal examples

Chapter 3. General properties of orthogonal polynomials

Chapter 4. Jacobi polynomials

Chapter 5. Laguerre and Hermite polynomials

Chapter 6. Zeros of orthogonal polynomials

Chapter 7. Inequalities

Chapter 8. Asymptotic properties of the classical polynomials

Chapter 9. Expansion problems associated with the classical polynomials

Chapter 10. Representation of positive functions

Chapter 11. Polynomials orthogonal on the unit circle

Chapter 12. Asymptotic properties of general orthogonal polynomials

Chapter 13. Expansion problems associated with general orthogonal polynomials

Chapter 14. Interpolation

Chapter 15. Mechanical quadrature

Chapter 16. Polynomials orthogonal on an arbitrary curve

Problems and exercises

Further problems and exercises

Appendix

This is the first detailed systematic treatment of ... (a) the asymptotic behaviour of orthogonal polynomials, by various methods, with applications, in particular, to the ‘classical' polynomials of Legendre, Jacobi, Laguerre and Hermite; (b) a detailed study of expansions in series of orthogonal polynomials, regarding convergence and summability; (c) a detailed study of orthogonal polynomials in the complex domain; (d) a study of the zeros of orthogonal polynomials, particularly of the classical ones, based upon an extension of Sturm's theorem for differential equations. The book presents many new results; many results already known are presented in generalized or more precise form, with new simplified proofs.
Mathematical Reviews