A treatise on generating functions

Title page
Preface
Glossary of symbols
Chapter 1 INTRODUCTION AND DEFINITIONS
1.1 Gamma, Beta and Related Functions
1.2 The Gaussian Hypergeometric Function
1.3 The Confluent Hypergeometric Function
1.4 The Generalized Hypergeometric Function
1.5 The E,G,H and Related Functions
1.6 Hypergeometric Functions of Two Variables
1.7 Hypergeometric Functions of Several Variables
1.8 The Classical Orthogonal Polynomials
1.9 Other Polynomial Systems and Generalizations
1.10 Generating Functions
1.11 Examples of Well-Known Generating Functions
Problems
Chapter 2 SERIES REARRANGEMENT TECHNIQUE
2.1 Some Useful Lemmas
2.2 Description of the Series Rearrangement Technique
2.3 Applications to Jacobi Polynomials
2.4 Generating Functions for Gegenbauer (or Ultraspherical) Polynomials
2.5 Generating Functions for Laguerre Polynomials
2.6 Miscellaneous Results
Problems
Chapter 3 DECOMPOSITION TECHNIQUE
3.1 A Hypergeometric Series Identity
3.2 Generating Functions for Jacobi Polynomials
3.3 Generating Functions for Laguerre Polynomials
Problems
Chapter 4 OPERATIONAL TECHNIQUES
4.1 Use of Integral Operators
4.2 Use of Differential Operators
4.3 Some Multiple-Integral Operational Techniques
Problems
Chapter 5 FRACTIONAL DERIVATIVE TECHNIQUE
5.1 Fractional Derivatives and Hypergeometric Functions
5.2 Linear Generating Functions
5.3 Bilinear Generating Functions
5.4 Convergence Conditions
Problems
Chapter 6 LIE ALGEBRAIC TECHNIQUE
6.1 Lie Groups
6.2 Lie Algebras and One-Parameter Subgroups
6.3 Homomorphism
6.4 Linear Differential Operators
6.5 Preliminary Observations
6.6 The Laguerre Function etc.
6.7 The Hypergeometric Function etc.
6.8 The Modified Laguerre Function etc.
6.9 Expansions Involving Two-Variable Hypergeometric Functions
Problems
Chapter 7 GENERATING FUNCTIONS VIA LAGRANGE'S EXPANSION AND GOULD'S IDENTITY
7.1 Some Useful Consequences of Lagrange's Expansion
7.2 A Theorem of Brown
7.3 GeneraHzations by Srivastava and Zeitlin
7.4 Further Results of Srivastava and Buschman
7.5 Carlitz's Theorem on Mixed Generating Functions
7.6 A Multiparameter and Multivariable Extension of Carlitz's Theorem
Problems
Chapter 8 EQUIVALENCE THEOREMS AND BILATERAL GENERATING FUNCTIONS
8.1 An Equivalence Theorem on Generating Functions
8.2 A Theorem on Bilateral Generating Functions
8.3 Generalizations of the Theorem of Singhal and Srivastava
8.4 Further Generalizations and Applications to Special Sequences
8.5 Multivariable Extensions
Problems
Chapter 9 GENERATING FUNCTIONS FOR SYSTEMS IN SEVERAL VARIABLES AND MULTILINEAR EXTENSIONS OF CLASSICAL RESULTS
9.1 A Multivariable Generating Function of Srivastava
9.2 A Generalization of Theorem 1
9.3 Further Generalizations
9.4 Some Multiple Generating Functions of Carlitz and Srivastava
9.5 Multiple-Series Extensions of Some Classical Results
9.6 Generating Functions Involving Laurent Series
Problems
Bibliography
Index