Application of Incomplete Cylindrical Functions to Problems of Wave Propagation and Diffraction

Abstract

In this and succeeding chapters we shall consider some problems whose solutions are connected with the evaluation of incomplete cylindrical functions. The asymptotic behavior of these functions determined earlier permits us to study analytically those physical situations — often of great interest — in which certain parameters are either very large or very small. Often, however, there arises the need for quantitative analysis in intermediate cases, when asymptotic analysis is inadequate. In such cases, obviously, it is necessary to have tables of incomplete cylindrical functions. In the general case. these functions depend on three parameters w, z, and v, each of which may be complex. It is evident, therefore, that comprehensive tabulation of these functions in their general form is a forbiddingly difficult problem.