Basic Hypergeometric Series: 96 (Encyclopedia of Mathematics and its Applications, Series Number 96) - Hardcover

Gasper, George; Rahman, Mizan

Hardcover

ISBN 10: 0521833574 ISBN 13: 9780521833578

Publisher: Cambridge University Press, 2004

Synopsis

Significant revision of classic reference in special functions.

About this title

Review

'I love this book! It is great! This really is a book you can learn the subject from. The plentiful exercises vary from elementary to challenging with lots of each. Congratulations and thanks are due the authors.' George Andrews, American Math. Monthly

'The book is remarkable in many ways. It is comprehensive, at least, comprehensive to date. As is typical of most works on the subject, it is clearly and carefully written. While no book can conceivably incorporate all the important results, particularly those obtained in the last decade, many of them are included as exercises. And this is the feature all other books on the subject lack: a set of exercises. Each chapter is topped off by a challenging series of problems which lead the reader to recreate recent discoveries. Anyone who works even a small percentage of them will soon be an expert. A generous series of historical notes concludes each chapter. The book is user friendly in every respect. The book has two excellent Appendices which summarize the identities and summation formulas derived in the text, an exhaustive 25 page list of references, and a nontrivial index. Now anyone working in combinatorics, group representation theory, coding theory, and related fields will want to own it. Many physicists will find it bears directly on matters of interest to them. Computer scientists may find the book increasingly timely. Those who have refrained from entering the field because of the tortuous notation can now have untroubled access to its mysteries. I say, come in, the water's fine.' Jet Wimp, SIAM Review

'This is an excellent and very informative book on the subject. After a gentle introduction to basic series and some special cases (such as the 'q'-binomial theorem) the authors bring the reader up to the latest results on the general theory and its extensions, many such results are due to them. The exercises are utilized to include results that found no room in the detailed treatment. In addition to these exercises, notes at the end of each chapter point the reader to related topics. This alone makes the book an invaluable reference to those who are interested in basic series.' Waleed A. Al-Salam, Math. Reviews

'Thus the present book, devoted to 'q'-hypergeometric series, appears at a very timely moment. The result is excellent. The first chapter presents a clear and elementary introduction to the subject. At the end of the book there are excellent indices and compendia of formulas.' Tom H. Koornwinder, Bulletin of London Mathematical Society

'... a very modern, self-contained, comprehensive and successful monograph, interesting and useful, for physicists as well as for mathematicians from various branches, who wish to learn about the subject.' European Mathematical Society Newsletter

Book Description

This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series. Some sections and exercises have been added and the bibliography has been revised to maintain its comprehensiveness.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2004
• Language: English
• ISBN 10: 0521833574
• ISBN 13: 9780521833578
• Binding: Hardcover
• Edition number: 2
• Number of pages: 456