Watson G.N. A Treatise on the Theory of Bessel Functions

Cambridge: Cambridge University Press. – 1922. – 812 p. 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.Bessel functions before 1826.
The Bessel coefficients.
Bessel functions.
Differential equations.
Miscellaneous properties of Bessel functions.
Integral representations of Bessel functions.
Asymptotic expansions of Bessel functions.
Bessel functions of large order.
Polynomials associated with Bessel functions.
Functions associated with Bessel functions.
Addition theorems.
Definite integrals.
Infinite integrals.
Multiple integrals.
The zeros of Bessel functions.
Neumann series and Lommel’s functions of two variables.
Kapteyn series.
Series of Fourier-Bessel and dini.
Schlomilch series.
The tabulation of Bessel functions.
tables of Bessel functions.Index of symbols.
List of authors quoted.
General index.