# MODERN ANALYSIS

## Preface

Advantage has been taken of the preparation of the third edition of this work to add a chapter on Ellipsoidal Harmonics and Lame’s Equation, and to rearrange the chapter on Trigonometrical Series so that the parts which are used in Applied Mathematics come at the beginning of the chapter. A number of minor errors have been corrected and we have endeavoured to make the references more complete.

Our thanks are due to Miss Wrinch for reading the greater part of the proofs and to the staff of the University Press for much courtesy and consideration during the progress of the printing.

E.T.W.
G.N.W.

July, 1920.

## Editor’s Note

After twenty-five years of failed predictions, the paperless office finally seems to have arrived. The near print quality resolution of the ‘New iPad’ and its competitors will likely further reduce the use of paper. Most mathematicians and physicists have been distributing their work electronically for a long time using files produced by TeX based typesetting software.[1] This software, as excellent as it is, was designed around print, which, I have noted, is quickly vanishing. It might be time to think seriously about publishing mathematics directly on the web or on its cousin the e-book.[2] As an experiment,[3] I am transcribing for the web Whittaker and Watson’s classic work on complex analysis and special functions. Its value as a reference work, extensive use of parenthetical comments, and numerous footnotes and references may combine to make it more pleasant and useful to read on the web than on paper. You may judge for yourself.

[1]TeX, a typesetting system that Donald Knuth originally designed to typeset mathematics, now forms the core for the LaTeX document preparation system widely used to prepare scientific papers for publication.  ↩
[2]There are software tools for converting LaTeX into .html and .css files from which one might build a website, notably LaTeX2HTML and TeX4ht, but the quality of the result is poor, and the .css files produced are muddled and difficult to customize. ↩
[3]I prepare the text for these pages with Fletcher Penny’s MultiMarkdown, which can generate either web pages or a LaTeX document from the text. The excellent MathJax script renders the mathematics. ↩

I am transcribing the third edition from 1920, which is in the public domain. According to the preface for the fourth and final edition of 1927, very little had changed from the third edition. I have retained the old-fashioned spelling and heavy use of semi-colons, but I have altered the typography and layout to fit the web and improve readability. The footnotes have been reformed as margin notes which are initially hidden, but become visible when tapped. I have, when possible, added links to on-line versions of the mentioned references and, occasionally, added editorial comments, which I have clearly marked.

This effort has just begun: I have only the first two chapters finished as of this writing. Given my other commitments and my determination to do all the examples,[4] I expect to complete a chapter every month, roughly. Thus, I should finish sometime late 2013 or early 2014. Feel free to offer comments or corrections.[5] I will update this note as things move along.

[4]Whittaker and Watson, in the British tradition, refer to problems for the reader as examples. Those marked with “Math.Trip.” are from the famous Cambridge Tripos exam and can be difficult. ↩
[5]Contact me at nithardt@uw.edu. ↩

Eric Nitardy

April, 2012.

Imagining that the this effort would be finished by early 2014 was wildly too optimistic. At the moment, I have completed chapters one through six and the appendix, have begun work on chapter seven, and am proceeding at about a chapter every month and a half. Whether that rate continues, we shall see.

I am grateful to Brian Wignall for the use of portions of his standard Latex transcription of Whittaker and Watson.

Eric Nitardy

April, 2014.