Difference between revisions of "Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition"

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:::[[Differential equation for Jacobi P|Theorem 4.2.1]]
 
:::[[Differential equation for Jacobi P|Theorem 4.2.1]]
 
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:::Theorem 4.2.2.
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::4.2. Differential equation
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:::4.21. Hypergeometric functions
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:::4.23. Second solution
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::4.4. Generating function
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::4.5. Recurrence formula
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::4.6. Integral representations in general
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:::4.61. Application; functions of the second kind
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:::4.62. Further properties of the functions of the second kind
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::4.7. Ultraspherical polynomials
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::4.8. Integral representations for Legendre polynomials
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:::4.81. Legendre functions of the second kind
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::4.9. Trigonometric representations
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::4.10. Further properties of Jacobi polynomials
 
:CHAPTER V. LAGUERRE AND HERMITE POLYNOMIALS
 
:CHAPTER V. LAGUERRE AND HERMITE POLYNOMIALS
 
:CHAPTER VI. ZEROS OF ORTHOGONAL POLYNOMIALS
 
:CHAPTER VI. ZEROS OF ORTHOGONAL POLYNOMIALS

Revision as of 03:49, 11 June 2016


Gabor Szegő: Orthogonal Polynomials (fourth edition)

Published $1975$, American Mathematical Society

ISBN 0-8218-1023-5.


Online copies

hosted by The Ohio State University

Contents

PREFACE
PREFACE TO THE REVISED EDITION
PREFACE TO THE THIRD EDITION
PREFACE TO THE FOURTH EDITION
CHAPTER I. PRELIMINARIES
CHAPTER II. DEFINITION OF ORTHOGONAL POLYNOMIALS; PRINCIPAL EXAMPLES
2.1. Orthogonality
2.2. Orthogonal Polynomials
2.3. Further Examples
2.4. The Classical Orthogonal Polynomials
2.5. A formula of Christoffel
2.6. A class of polynomials considered by S. Bernstein and G. Szegő
2.7. Stieltjes-Wigert polynomials
2.8. Distributions of Stieltjes type; an analogue of Legendre polynomials
2.8.1. Poisson-Charlier polynomials
2.8.2. Krawtchouk's polynomials
2.9. Further special cases
CHAPTER III. GENERAL PROPERTIES OF ORTHOGONAL POLYNOMIALS
CHAPTER IV. JACOBI POLYNOMIALS
4.1. Definition; notation; special cases
page 58
Theorem 4.1.
Theorem 4.2.1
Theorem 4.2.2.
4.2. Differential equation
4.21. Hypergeometric functions
4.22. Generalization
4.23. Second solution
4.24. Transformation of the differential equation
4.3. Rodrigues' formula; the orthonormal set
4.4. Generating function
4.5. Recurrence formula
4.6. Integral representations in general
4.61. Application; functions of the second kind
4.62. Further properties of the functions of the second kind
4.7. Ultraspherical polynomials
4.8. Integral representations for Legendre polynomials
4.81. Legendre functions of the second kind
4.82. Generalizations
4.9. Trigonometric representations
4.10. Further properties of Jacobi polynomials
CHAPTER V. LAGUERRE AND HERMITE POLYNOMIALS
CHAPTER VI. ZEROS OF ORTHOGONAL POLYNOMIALS
CHAPTER VII. INEQUALITIES
CHAPTER VIII. ASYMPTOTIC PROPERTIES OF THE CLASSICAL POLYNOMIALS
CHAPTER IX. EXPANSION PROBLEMS ASSOCIATED WITH THE CLASSICAL POLYNOMIALS
CHAPTER X. REPRESENTATION OF POSITIVE FUNCTIONS
CHAPTER XI. POLYNOMIALS ORTHOGONAL ON THE UNIT CIRCLE
CHAPTER XII. ASYMPTOTIC PROPERTIES OF GENERAL ORTHOGONAL POLYNOMIALS
CHAPTER XIII. EXPANSION PROBLEMS ASSOCIATED WITH GENERAL ORTHOGONAL POLYNOMIALS
CHAPTER XIV. INTERPOLATION
CHAPTER XV. MECHANICAL QUADRATURE
CHAPTER XVI. POLYNOMIALS ORTHOGONAL ON AN ARBITRARY CURVE
PROBLEMS AND EXERCISES
FURTHER PROBLEMS AND EXERCISES
APPENDIX
LIST OF REFERENCES
FURTHER REFERENCES
INDEX
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