# Book:T.S. Chihara/An Introduction to Orthogonal Polynomials

## T.S. Chihara: An Introduction to Orthogonal Polynomials

Published $1978$, Gordon and Breach.

### Contents

PREFACE
CHAPTER I. ELEMENTARY THEORY OF ORTHOGONAL POLYNOMIALS
1 Introduction
$(1.1)$
$(1.2)$
$(1.3)$
$(1.4)$
2 The moment functional and orthogonality
3 Existence of OPS
4 The fundamental recurrence formula
5 Zeros
7 Kernel polynomials
8 Symmetric moment functionals
9 Certain related recurrence relations
CHAPTER II. THE REPRESENTATION THEOREM AND DISTRIBUTION FUNCTIONS
1 Introduction
2 Some preliminary theorems
3 The representation theorem
4 Spectral points and zeros of orthogonal polynomials
5 Determinacy of $\mathscr{L}$ in the bounded case
6 The classical moment problems
CHAPTER III. CONTINUED FRACTIONS AND CHAIN SEQUENCES
1 Basic concepts
2 The fundamental recurrence formulas
3 A convergence theorem
4 Jacobi fractions and orthogonal polynomials
5 Chain sequences
6 Additional results on chain sequences
CHAPTER IV. THE RECURRENCE FORMULA AND PROPERTIES OF ORTHOGONAL POLYNOMIALS
1 Introduction
2 Chain sequence and orthogonal polynomials
3 Some spectral analysis
4 OPS whose zeros are dense in intervals
5 Preliminaries to Krein's theorem
6 Krein's theorem
CHAPTER V. SPECIAL FUNCTIONS
1 General remarks
2 The classical orthogonal polynomials
3 The Hahn class of orthogonal polynomials
4 The Meixner class of orthogonal polynomials
5 Other classes of orthogonal polynomials
CHAPTER VI. SOME SPECIFIC SYSTEMS OF ORTHOGONAL POLYNOMIALS
1 The Charlier polynomials
2 The Stieltjes-Wigert polynomials
3 The Meixner polynomials
4 The Bessel polynomials
5 The Pollaczek polynomials
6 Modified Lommel polynomials
7 Tricomi-Carlitz polynomials
8 OPS related to Bernoulli numbers
9 OPS related to Jacobi elliptic functions
10 The $q$-polynomials of Al-Salam and Carlitz
11 Wall polynomials
12 Associated Legendre polynomials
13 Miscellaneous OPS
NOTES
APPENDIX TABLE OF RECURRENCE FORMULAS
LIST OF FREQUENTLY USED SYMBOLS
BIBLIOGRAPHY
INDEX