A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library) [Paperback]

G. N. Watson (Author)

Book Description

ISBN-10: 0521483913 | ISBN-13: 978-0521483919 | Publication Date: August 25, 1995 | Edition: 2

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.

Editorial Reviews

Review

"...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

Book Description

Originally published in 1992, this monumental treatise had two major objectives at that time--the development of applications of the fundamental processes of the theory of complex variables and the compiling of a collection of results of value for mathematicians and physicists who encounter Bessel functions.

Product Details

• Paperback: 812 pages
• Publisher: Cambridge University Press; 2 edition (August 25, 1995)
• Language: English
• ISBN-10: 0521483913
• ISBN-13: 978-0521483919
• Product Dimensions: 8.8 x 6 x 1.7 inches
• Shipping Weight: 2.5 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #565,982 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

21 of 22 people found the following review helpful:

5.0 out of 5 stars Classic, January 26, 2000

By 

Jim Curry (MT) - See all my reviews
(VINE VOICE)   

This review is from: A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library) (Paperback)

Watson's classic text was written before the more modern age of "topologically flavored" arguments. Consequently, much of the presentation may appear to be a bit ponderous, relying on explicit calculational detail when that is no longer strictly necessary. By now many points can be deduced "by pure thought". However, the text gives a very complete and deep view of Bessel's functions. Because it "does everything" it is also a fine and practical way to learn complex analysis in the style of the "old school". If you just can't stand older style writing, you should probably look at Olver's book on special functions. If you can tolerate the old style, buy this and have many (many, many) hours of good fun and insight.

16 of 19 people found the following review helpful:

5.0 out of 5 stars The best math book of all time, March 6, 2002

By 

ralph kelsey (Athens, Ohio United States) - See all my reviews
(REAL NAME)   

This review is from: A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library) (Paperback)

'Bessel Functions', by Watson, has often been called the best math book of all time. I have no doubt it is in the top 10. Even though it is 50+ years old, it is well worth studying. It is the best book ever written about any special function.

Watson makes the needed complex analysis, generating functions, etc., simple, even obvious. I own hundreds of advanced math books, and this is one of the few that I can lay on the couch and read for fun.

Here is an old joke: Whittaker was the worst math author of all time (check out 'analytic dynamics'). Watson is so good that 'Modern analysis' by Whittaker and Watson is mediocre.

Another interesting connection: As I recall from the obituary in Physics Today, in the late 1930's Onsager needed a Ph. D. to stay at Harvard and avoid returning home to WW2. He had his notebook in which (as a sophemore chem major in Europe) he had solved all the problems but 4 in Whittaker and Watson. MIT gave him a math Ph. D. on the spot because 8 or 10 had never been solved by anyone, including W&W.

5 of 7 people found the following review helpful:

5.0 out of 5 stars Definitive text, September 28, 2000

By 

Mark Grindell "Mark Grindell" (Shipley,West Yorkshire) - See all my reviews
(VINE VOICE)   

This review is from: A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library) (Paperback)

I found this book a struggle, but there again, I was young and found complex integration a bit strange.

This having been said, I must say that since then I have yearned for this text all the way through my physics degree and beyond. You could almost say that if it ain't here, its ain't nowhere, buddy.... However, that of course isn't quite true these days. The depth of the book is extraordinary. The nicest chapters are in the middle, where the integral representations are described. Quite honestly, by then you are over the rather dry beginning and if you really got over that and the basic material, this where the text flies...

Its a lot of fun, very hard, but my gosh, do you get some heavy duy stuff under your belt.