Ian N Sneddon
Edinburgh and London
This book is intended primarily for the student of applied mathematics, physics, chemistry or engineering who wishes to use the "special" functions associated with the names of Legendre, Bessel, Hermite and Laguerre. It aims at providing in a compact form most of the properties of these functions which arise most frequently in applications, and at establishing these properties in the simplest possible way. For that reason the methods it employs should be intelligible to anyone who has completed a first course in calculus and has a slight acquaintance with the theory of differential equations. Use is made of the theory of functions of a complex variable only very sparingly, and most of the book should be accessible to a reader who has no knowledge of this theory. Throughout the text an attempt is made to show how these functions may be used in the discussion of problems in classical physics and in quantum theory. A brief account is given in an appendix of the main properties of the Dirac delta "function".
I should like to record my debt of gratitude to the late Sir John Lennard-Jones, and to my colleagues Mr B Noble and Dr J G Clunie for their generous help in reading the first draft of the manuscript and making valuable suggestions for its improvement. I am indebted to Miss Janet Burchnall for her assistance in the preparation of the final manuscript, to Mr J S Lowndes for help in correcting proof sheets and to Miss Elizabeth Gildart for preparing the index. I should also like to thank Dr D E Rutherford, general editor of the series, for his advice and criticism throughout the preparation of the book.
My debt of gratitude to Professor T M MacRobert is a much more general one. It was at his lectures that I first acquired a taste for the subject, and it will be obvious to anyone who knows his published writings how much I have been influenced by them.
20 August 1955