View source for Book:T.S. Chihara/An Introduction to Orthogonal Polynomials

{{Book|An Introduction to Orthogonal Polynomials|1978|Gordon and Breach||T.S. Chihara}}


=== Contents ===
:PREFACE
:CHAPTER I. ELEMENTARY THEORY OF ORTHOGONAL POLYNOMIALS
::1 Introduction
:::[[2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)|$(1.1)$]]
:::[[Orthogonality relation for cosine on (0,pi)|$(1.2)$]]
::2 The moment functional and orthogonality
::3 Existence of OPS
::4 The fundamental recurrence formula
::5 Zeros
::6 Gauss quadrature
::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

[[Category:Book]]