This book has been designed with two objects in view. The first is the development of applications of the fundamental processes of the theory of functions of complex variables. For this purpose Bessel functions are admirably adapted; while they offer at the same time a rather wider scope for the application of parts of-the theory of functions of a real variable than is provided by trigonometrical functions in the theory of Fourier series.
The second object is the compilation of a collection of results which would be of value to the increasing number of Mathematicians and Physicists who encounter Bessel functions in the course of their researches. The existence of such a collection seems to be demanded by the greater abstruseness of properties of Bessel functions (especially of functions of large order) which have been required in recent years in various problems of Mathematical Physics.
Author(s): George Neville Watson
Edition: 2
Publisher: Cambridge University Press
Year: 1980
Language: English
Pages: VIII; 804
City: Cambridge
Title Page
Preface
Preface to the Second Edition
Table of Contents
I. BESSEL FUNCTIONS BEFORE 1826
II. THE BESSEL COEFFICIENTS
III. BESSEL FUNCTIONS
IV. DIFFERENTIAL EQUATIONS
V. MISCELLANEOUS PROPERTIES THE BESSEL FUNCTIONS
VI. INTEGRAL REPRESENTATIONS OF BESSEL FUNCTIONS
VII. ASYMPTOTIC EXPANSIONS OF BESSEL FUNCTIONS
VIII. BESSEL FUNCTIONS OF LARGE ORDER
IX. POLYNOMIALS ASSOCIATED WITH BESSEL FUNCTIONS
X. FUNCTIONS ASSOCIATED WITH BESSEL FUNCTIONS
XI. ADDITION THEOREMS
XII. DEFINITE INTEGRALS
XIII. INFINITE INTEGRALS
XIV. MULTIPLE INTEGRALS
XV. THE ZEROS OF BESSEL FUNCTIONS
XVI. NEUMANN SERIES AND LOMMEL'S FUNCTIONS OF TWO VARIABLES
XVII. KAPTEYN SERIES
XVIII. SERIES OF FOURIER-BESSEL AND DINI
XIX. SCHLÖMILCH SERIES
XX. THE TABULATION OF BESSEL FUNCTIONS
TABLES OF BESSEL FUNCTIONS
BIBLIOGRAPHY
INDEX OF SYMBOLS
LIST OF AUTHORS QUOTED
GENERAL INDEX
