A Treatise on the Theory of Bessel Functions

by G. N. Watson

Overview

The late Professor G.N. Watson wrote his monumental treatise on the theory of Bessel functions in 1922 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 was compiling a collection of results of value for 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 have resulted in a book that will be indispensable for pure mathematicians, applied mathematicians, and physicists.

Product Details

ISBN-13:	9780521483919
Publisher:	Cambridge University Press
Publication date:	08/25/1995
Series:	Cambridge Mathematical Library
Edition description:	Revised
Pages:	814
Product dimensions:	5.98(w) x 9.02(h) x 1.65(d)

Table of Contents

1. Bessel functions before 1826; 2. The Bessel coefficients; 3. Bessel functions; 4. Differential equations; 5. Miscellaneous properties of Bessel functions; 6. Integral representations of Bessel functions; 7. Asymptotic expansions of Bessel functions; 8. Bessel functions of large order; 9. Polynomials associated with Bessel functions; 10. Functions associated with Bessel functions; 11. Addition theorems; 12. Definite integrals; 13. Infinitive integrals; 14. Multiple integrals; 15. The zeros of Bessel functions; 16. Neumann series and Lommel's functions of two variables; 17. Kapteyn series; 18. Series of Fourier–Bessel and Dini; 19. Schlömlich series; 20. The tabulation of Bessel functions; Tables of Bessel functions; Bibliography; Indices.

Editorial Reviews

"...a monument of erudition....a rigorous mathematical treatment of all types of Bessel functions." L.M. Milne-Thomson, Nature

"A veritable mine of information...indispensable to all those who have occasion to use Bessel functions." S. Chandrasekhar, The Astrophysical Journal

"...now, almost 75 years after the initial publication, it has been reprinted again. The first thing you notice is the scholarship. There are references to Bessel functions which Watson missed, but few of the important ones. Watson was 36 when this book appeared. The next thing you notice is the care with which Watson treats many topics. Sometimes his arguments are more perceptive than he realizes....It is unlikely anyone will write a similar book about other functions, which is a shame. While Watson tried to tell all about Bessel functions, he had enough taste to highlight what he thought was of long-term importance. His judgment was usually right." R.A. Askey, Mathematical Reviews

From the Publisher