# Book:Andrew Gray/A Treatise on Bessel Functions/Second Edition

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## Andrew Gray, G.B. Mathews and T.M. MacRobert:

## Andrew Gray, G.B. Mathews and T.M. MacRobert: *A Treatise on Bessel Functions and their Applications to Physics (2nd Edition)*

Published $1922$, **Dover Publications, Inc.**.

### Subject Matter

### Contents

- Preface to the First Edition
- Preface to the Second Edition
- Note on the Asymptotic Expansions

- Chapter I: Introductory
- Chapter II: Solution of the Differential Equation
- Chapter III: Other Bessel Functions and Related Functions
- Chapter IV: Functions of Integral Order. Expansions in Series of Bessel Functions
- Chapter V: Definite Integral Expressions for the Bessel Functions. Asymptotic Expansions
- Chapter VI: Definite Integrals Involving Bessel Functions
- Chapter VII: The Zeros of the Bessel Functions
- Chapter VIII: Fourier-Bessel Expansions and Integrals
- Chapter IX: Relations between Bessel Functions and Legendre Functions. Green's Function
- Chapter X: Vibration of Membranes
- Chapter XI: Hydrodynamics
- Chapter XII: Steady Flow of Electricity or of Heat in Uniform Isotropic Media
- Chapter XIII: Propagation of Electromagnetic Waves Along Wires
- Chapter XIV: Diffraction
- Chapter XV: Equilibrium of an Isotropic Rod of Circular Section
- Chapter XVI: Miscellaneous Applications

- Miscellaneous Examples

- Appendix I: Formulae for the Gamma Function and the Hypergeometric Function
- Appendix II: Stokes' Method of obtaining the Asymptotic Expansion of the Bessel Functions
- Appendix III: Formulae for Calculation of the Zeros of the Bessel Functions

- Explanation of the Tables