Whittaker and Watson’s analysis textbook is a true classic. My only complaint about the book is that the typesetting is poor. I said years ago that I wish someone would redo the book in LaTeX and touch it up a bit.
I found out while writing my previous post that in fact someone has done just that. That post explains the image on the cover of a reprint of the 4th edition from 1927. There’s now a fifth edition, published last year (2021).
The foreword of the fifth edition begins with this sentence:
There are few books which remain in print and in constant use for over a century; “Whittaker and Watson” belongs to this select group.
That statement is true of books in general, but it’s especially rare for math books to age so well.
The first edition came out in 1902. The book shows its age, for example, by spelling “show” with an e rather than an o. And yet I routinely run into references to the book. Nobody has written a better reference over the last century.
The new edition corrects some errors and adds references for more up-to-date results. But in some sense the mathematics in Whittaker and Watson is finished. This has a bizarre side effect: much of the material in Whittaker and Watson is no longer common knowledge precisely because the content is settled.
The kind of mathematics presented in Whittaker and Watson is very useful, but it falls between two stools. It’s too difficult for undergraduates, and it’s not a hot enough topic of research for graduate students.
When I finished my PhD, I knew some 20th century math and some 18th century math, but there was a lot of useful mathematics developed in the 19th century that I wouldn’t learn until later, the kind of math you find in Whittaker and Watson.
Someone may reasonably object that the emphasis on special functions in classical analysis is inappropriate now that we can easily compute everything numerically. But how are we able to compute things accurately and efficiently? By using libraries developed by people who know about special functions and other 19th century math! I’ve done some of this work, speeding up calculations a couple orders of magnitude on 21st century computers by exploiting arcane theorems developed in the 19th century.