A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library)

To incorporate in this work the discoveries of the last twenty years would necessitate the rewriting of at least Chapters XII-XIX; my interest in Bessel functions, however, has waned since 1922, and I am consequently not prepared to undertake such a task to the detriment of tny other activities. In the preparation of this new edition 1 have therefore limited myself to the correction of minor errors and misprints and to the emendation of a few assertions (such as those about the unproven character of Bourget's hypo- hypothesis) which, though they may have been true in 1922, would have been definitely false had they been, made in 1941. My thanks are due to many friends for their kindness in informing me of errors which they had noticed; in.particular, I cannot miss this opportunity of expressing my gratitude to Professor J. R. Wilton for the vigilance which he must have exercised in the compilation of his list of corrigenda. The late Professor G.N. Watson wrote his monumental treatise on the theory of Bessel functions with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables, and the second the compilation of a collection of results of value to mathematicians and physicists who encounter Bessel functions in the course of their researches. The completeness of the theoretical account, combined with the wide scope of the collection of practical examples and the extensive numerical tables, have resulted in a book which is indispensable to pure mathematicians, to applied mathematicians, and to physicists alike. Originally published in 1992, this monumental treatise had two major objectives at that time--the development of applications of the fundamental processes of the theory of complex variables and the compiling of a collection of results of value for mathematicians and physicists who encounter Bessel functions. The theory of Bessel functions is intimately connected with the theory of a certain type of differential equation of the first order, known as Riccati's equation.