A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library) 2nd Edition by G. N. Watson (PDF)

Description

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.

User’s Reviews

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 This monumental 1995 treatise by the late Professor G. N. Watson wil be indispensable to mathematicians and physicists.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A real classic. Watson is comprehensive and exhaustive. A true pleasure to have a new copy to replace my old version with a completely broken binding. I only regret that I was unable to replace it with a Cambridge hardcover edition, which seems to no longer be available. Beware of the hardcover ‘editions’ from another publisher: they are rather carelessly photo-reduced and, in comparison to the original from Cambridge, are nearly unreadable.

⭐This textbook is exactly what I needed.

⭐This is one of the most thorough treatments of any topic in analysis. It is far from an easy read and there are some very bizarre techniques but little is left as a mystery. This book has saved me in research a multitude of times.

⭐A classic of mathematics. One of the best math books of all time.

⭐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.

⭐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.

⭐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.

⭐No es un libro hecho por Cambridge University Press. Es la misma obra, empero no está editado por ellos. Mejor cómprenlo directamente con ellos. Es un libro de más de 800 páginas y no lo cocieron, razón por la cual se deshojará en la primera lectura. Por un precio de más de 1,800 pesos (80 Dlls approx.) no vale la pena.veru good

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