What do you think?
Rate this book
A Treatise on the Theory of Bessel Functions
G.N. Watson's "A Treatise on the Theory of Bessel Functions" is a mathematics book originally published in 1922. Author Watson was a well-known mathematician and a Professor of Mathematics at the University of Birmingham. This book, now republished by Forgotten Books, is intended as a resource guide for students and scholars of the theory of functions of complex variables and mathematics in general.
The book opens with a detailed history of Bessel Functions before 1826. This background information serves as the jumping off point for the author's presentation of his treatise on the theory of Bessel functions. From there, the Bessel coefficients are introduced, and Watson's mathematical discussion begins in earnest. The book provides a detailed examination of all aspects of Bessel functions, including asymptotic expansions of Bessel functions, associated polynomials, the zeros of Bessel functions, and the Schlumilch series and its relationships to Bessel functions, among other topics.
"A Treatise on the Theory of Bessel Functions" is clearly and overtly intended for serious students and scholars of mathematics. This is a reference guide for those familiar with advanced principles, and should not be approached by the beginner. This work would not make an appropriate textbook, nor is it suitable for those who have not previously been introduced to the theory of Bessel functions.
As a reference guide, "A Treatise on the Theory of Bessel Functions" is a success. At over 800 pages it is a massive collection, and one that is sure to be beneficial to serious students of mathematics. This book is rich with information for those who have the background knowledge to absorb it, and is thus recommended for those pursuing the study of Bessel functions.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
The book opens with a detailed history of Bessel Functions before 1826. This background information serves as the jumping off point for the author's presentation of his treatise on the theory of Bessel functions. From there, the Bessel coefficients are introduced, and Watson's mathematical discussion begins in earnest. The book provides a detailed examination of all aspects of Bessel functions, including asymptotic expansions of Bessel functions, associated polynomials, the zeros of Bessel functions, and the Schlumilch series and its relationships to Bessel functions, among other topics.
"A Treatise on the Theory of Bessel Functions" is clearly and overtly intended for serious students and scholars of mathematics. This is a reference guide for those familiar with advanced principles, and should not be approached by the beginner. This work would not make an appropriate textbook, nor is it suitable for those who have not previously been introduced to the theory of Bessel functions.
As a reference guide, "A Treatise on the Theory of Bessel Functions" is a success. At over 800 pages it is a massive collection, and one that is sure to be beneficial to serious students of mathematics. This book is rich with information for those who have the background knowledge to absorb it, and is thus recommended for those pursuing the study of Bessel functions.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
814 pages, Paperback
First published January 3, 1944
8 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 of 1 review
August 16, 2016
If anyone should find himself wandering along a dusty stack and from it takes this book in hand, then "Welcome to British mathematics circa 1900"! And a lot of moderns find it off putting, thank your very much! This book is big and makes use of some things that are obsolete today. It slugs things out and has smell of the notorious Cambridge Tripos (Watson was from Cambridge and Senior Wrangler) about it, yet without being pedantic. But work you must and that's probably why youngsters rank it so low. In those days one did one's mathematics sitting bolt upright, pencil and paper in hand--no radio, no TV, no distractions.
How surprising, then, to learn that it was considered to be state of the art; even breaking from the impenetrability that characterized a lot of 19th century British Mathematics. In fact, according to a review (1924) by one R. D. Carmichael (Carmichael's Theorem, anybody?) it was meant not only to meet the standards of the mathematician but also to be a compendium "include[ing] all formulas, whether general or special, which, although without theoretical interest, are likely to be required in practical applications." Imagine that, a mathematician bowing to the practical needs of outsiders and dutifully recording facts! Boring! (speaks the modern mathematician)
Some would say that this kind of yeomanry was once the strength of mathematics. Back then people solved problems as opposed to constructing masterful generalizations. Physics was less speculative and tied to an experimental tradition that had more in common with working in a machinist's shop than in an academic laboratory--as did the great Henry Ford. The scientist was still a tinker making, from scratch, his own equipment; which even affected the Olympian heights of theory for if one goes back a few decades from when Carmichael's review was written he will find it in Maxwell's famous treatise. As I recall, he included details on the construction of actual machines. (As a smart aleck undergrad I thought such shop talk was beneath me--reminded me of my granddad puttering around in the garage.)
Moreover, being partly a repository for formulas, it has meant that very few have actually "read" this work. I certainly haven't but have on many occasions used it as a compendium and occasionally worked out some of the material adjacent to that of my interest. Another beauty of the book is that one can dip into the various sections without having to read the preceding material. The book doesn't require a lot of rabbit hunting for specialized symbols and to ferret out the author's use of jargon of his making.
As Carmichael points out, some of the general theory for the material in this book is to be found in the masterful Course of Modern Analysis, for which, I believe, there is still a following. Rightly so and, as one who is not a mathematician but enjoys math, I have enjoyed my excursions in this latter work.
As I now enter my retirement years I wonder if I'll have occasion to dip into Bessel functions again? They are surprisingly ubiquitous even appearing in probability theory an statistics. You never know!
How surprising, then, to learn that it was considered to be state of the art; even breaking from the impenetrability that characterized a lot of 19th century British Mathematics. In fact, according to a review (1924) by one R. D. Carmichael (Carmichael's Theorem, anybody?) it was meant not only to meet the standards of the mathematician but also to be a compendium "include[ing] all formulas, whether general or special, which, although without theoretical interest, are likely to be required in practical applications." Imagine that, a mathematician bowing to the practical needs of outsiders and dutifully recording facts! Boring! (speaks the modern mathematician)
Some would say that this kind of yeomanry was once the strength of mathematics. Back then people solved problems as opposed to constructing masterful generalizations. Physics was less speculative and tied to an experimental tradition that had more in common with working in a machinist's shop than in an academic laboratory--as did the great Henry Ford. The scientist was still a tinker making, from scratch, his own equipment; which even affected the Olympian heights of theory for if one goes back a few decades from when Carmichael's review was written he will find it in Maxwell's famous treatise. As I recall, he included details on the construction of actual machines. (As a smart aleck undergrad I thought such shop talk was beneath me--reminded me of my granddad puttering around in the garage.)
Moreover, being partly a repository for formulas, it has meant that very few have actually "read" this work. I certainly haven't but have on many occasions used it as a compendium and occasionally worked out some of the material adjacent to that of my interest. Another beauty of the book is that one can dip into the various sections without having to read the preceding material. The book doesn't require a lot of rabbit hunting for specialized symbols and to ferret out the author's use of jargon of his making.
As Carmichael points out, some of the general theory for the material in this book is to be found in the masterful Course of Modern Analysis, for which, I believe, there is still a following. Rightly so and, as one who is not a mathematician but enjoys math, I have enjoyed my excursions in this latter work.
As I now enter my retirement years I wonder if I'll have occasion to dip into Bessel functions again? They are surprisingly ubiquitous even appearing in probability theory an statistics. You never know!
Displaying 1 of 1 review