Book contents
- Frontmatter
- Contents
- Foreword
- Preface to the Fifth Edition
- Preface to the Fourth Edition
- Preface to the Third Edition
- Preface to the Second Edition
- Preface to the First Edition
- Introduction
- Part I The Process of Analysis
- 1 Complex Numbers
- 2 The Theory of Convergence
- 3 Continuous Functions and Uniform Convergence
- 4 The Theory of Riemann Integration
- 5 The Fundamental Properties of Analytic Functions; Taylor’s, Laurent’s and Liouville’s Theorems
- 6 The Theory of Residues; Application to the Evaluation of Definite Integrals
- 7 The Expansion of Functions in Infinite Series
- 8 Asymptotic Expansions and Summable Series
- 9 Fourier Series and Trigonometric Series
- 10 Linear Differential Equations
- 11 Integral Equations
- Part II The Transcendental Functions
- 12 The Gamma-Function
- 13 The Zeta-Function of Riemann
- 14 The Hypergeometric Function
- 15 Legendre Functions
- 16 The Confluent Hypergeometric Function
- 17 Bessel Functions
- 18 The Equations of Mathematical Physics
- 19 Mathieu Functions
- 20 Elliptic Functions. General Theorems and the Weierstrassian Functions
- 21 The Theta-Functions
- 22 The Jacobian Elliptic Functions
- 23 Ellipsoidal Harmonics and Lamé’s Equation
- Appendix The Elementary Transcendental Functions
- References
- Author index
- Subject index
16 - The Confluent Hypergeometric Function
Published online by Cambridge University Press: 07 August 2021
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Book contents
- Frontmatter
- Contents
- Foreword
- Preface to the Fifth Edition
- Preface to the Fourth Edition
- Preface to the Third Edition
- Preface to the Second Edition
- Preface to the First Edition
- Introduction
- Part I The Process of Analysis
- 1 Complex Numbers
- 2 The Theory of Convergence
- 3 Continuous Functions and Uniform Convergence
- 4 The Theory of Riemann Integration
- 5 The Fundamental Properties of Analytic Functions; Taylor’s, Laurent’s and Liouville’s Theorems
- 6 The Theory of Residues; Application to the Evaluation of Definite Integrals
- 7 The Expansion of Functions in Infinite Series
- 8 Asymptotic Expansions and Summable Series
- 9 Fourier Series and Trigonometric Series
- 10 Linear Differential Equations
- 11 Integral Equations
- Part II The Transcendental Functions
- 12 The Gamma-Function
- 13 The Zeta-Function of Riemann
- 14 The Hypergeometric Function
- 15 Legendre Functions
- 16 The Confluent Hypergeometric Function
- 17 Bessel Functions
- 18 The Equations of Mathematical Physics
- 19 Mathieu Functions
- 20 Elliptic Functions. General Theorems and the Weierstrassian Functions
- 21 The Theta-Functions
- 22 The Jacobian Elliptic Functions
- 23 Ellipsoidal Harmonics and Lamé’s Equation
- Appendix The Elementary Transcendental Functions
- References
- Author index
- Subject index
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- A Course of Modern Analysis , pp. 355 - 372Publisher: Cambridge University PressPrint publication year: 2021