Sea Clutter: Scattering, the K Distribution and Radar Performance

Appendix 2: Some Useful Special Functions

A2.1 Introduction

Much of the material in this book is presented in mathematical terms; these provide us with a compact and precise language in which to discuss engineering problems. Obviously this is not the place to develop a coherent and comprehensive account of engineering mathematics , such as that found in Reference [1], from which we then might pick the few topics we need. Nonetheless, when approaching the literature of sea clutter (or this book) for the first time, the reader can encounter a significant barrier, built from unfamiliar and slightly fantastical objects. Gamma, poly-gamma and hypergeometric functions, Bessel functions, both modified and un-modified, of every order and kind, all conspire to intimidate the beginner. In the days before the widespread availability of computers, the study of these functions formed part of the education of every scientist and engineer; in the final quarter of the 20th century this was supplanted, to a greater or lesser extent, by simulation and other numerical techniques. At the same time, computer based systems, such as Mathematica [2], were developed, that are able to carry out sophisticated mathematical manipulations and evaluate these unfamiliar functions. (The Mathematica web-site also supports an exhaustive on-line compilation of results from classical analysis.) So, paradoxically, this background material has become more useful and accessible at the same time that it has become less generally familiar. In this second appendix we will give a short review of some special functions that are useful in the study of clutter and its...

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