Book:T.S. Chihara/An Introduction to Orthogonal Polynomials
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T.S. Chihara: An Introduction to Orthogonal Polynomials
Published $1978$, Gordon and Breach.
Contents
- PREFACE
- CHAPTER I. ELEMENTARY THEORY OF ORTHOGONAL POLYNOMIALS
- 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