ProofWiki:Books/Andrew Gray/A Treatise on Bessel Functions

Andrew Gray and G.B. Mathews: A Treatise on Bessel Functions and their Applications to Physics

Published 1895, 2nd Edition 1922 with T.M. MacRobert, Dover Publications, Inc..

Subject Matter

• Bessel Functions

Contents

Preface to the First Edition

Preface to the Second Edition

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 IIIL Formulae for Calculation of the Zeros of the Bessel Functions

Explanation of the Tables