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.
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"...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
"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.
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The theory of Bessel functions is intimately connected with the theory of a certain type of differential equation of the first order, known as Riccati's equation. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
The theory of Bessel functions is intimately connected with the theory of a certain type of differential equation of the first order, known as Riccati's equation. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Format:Paperback
In my area of work, Bessel functions play a major role. I have often found texts on applied mathematics much too comprehensible simply because the authors tend to show their vast knowledge about the 'abstractions' and little emphasis on computational details. In my experience authors of applied math. textbooks tend to exhibit some form of muted contempt for the reader who is uninitiated with abstractions.
The main utility of Watson's treatise is in its old-fashioned,
no-nonsense approach. It does not cheat the reader interested
in working out details. Proofs of various theorems & identities can easily be grasped if one knows the relevant aspects of complex analysis. The language is straightforward and lucid. For example, in the section on Airy functions, Watson tells the reader exactly how to convert the Airy function (from its general contour integral form for complex argument) to the form when the argument is real. The details of path deformation and application of Jordan's lemma are spelt out explicitly. This, in my view, raises the level of respect that the reader for the author.
In addition, the contents are simply a goldmine, and time-tested
over 50+ years. It can't be otherwise in the future.
By ralph kelsey
Format: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.
Format: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.
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