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Is Knopp's Theory and Application of Infinite Series out of date? It's looks terrific to me, but the Dover edition I bought new maybe a year ago: seems to be the same as an edition published in 1951 and may go back as far as 1921. 60 or 90 years is a lot of math years. How about it? Does my book leave out some important developments? Is it old-fashioned in some other ways?

I've seen this question: what is the current state of the art in methods of summing "exotic" series? but it doesn't have a full answer yet.


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up vote 1 down vote accepted

Konrad Knopp's books are nice to read and the results still holds. I remember some strange "hunt" for a "convergence border" in that book, which is a bit absurd to me..

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Thanks. I thought that surely there would be developments in this area in the 60 years or more since publication that the modern reader should know about. None? Only a few? Actually, I hope there aren't, because I can see the book becoming one of my favorites. – NotSuper Nov 30 '10 at 16:11

I realize this is an old thread but in case anybody else looks here I will share my thoughts. This book is not out of date, if any math graduate student can find the time to read it, they definitely should. Had it been written 20 years earlier then it would be too old to read today, but happily the notation has been pretty well locked in since the 1920's. He even gives nice histories of the development of the terminology and notation, usually in footnotes.

The real problem I see with this book is the first couple chapters where he lays down the foundations. He talks at extreme length almost philosophically about the construction of the real numbers in an almost Shakespearean style. It could be cut down by 2/3 and be much more readable. Also, he uses "nests" instead of Cauchy sequences to complete $\Bbb Q$. In modern treatments it's almost always Cauchy sequences. But once he gets past this, the rest of the book read just like modern math, the meat and potatoes of it is great and wouldn't need to be modified for a current student of the 21st century.

So recently I undertook the task of rewriting the first couple chapters to modern exposition, and then I plan to just transcribe the rest of the book nearly verbatim. I assume this book is no longer under copyright protection, if it is then my version will just have to wait until it becomes public domain. But I would think 90 years would be enough. In any case this book deserves to be read by future generations for a long time to come.

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