Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications)

Thorough and up-to-date, this book is an authoritative account of basic hypergeometric series and their applications. The authors provide explicit and detailed information about summation, transformation and expansion formulas and contour integrals. They relate the general results to other important mathematical functions and combinatorial questions.

"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 that 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. One of my favorite features is the page which lists all the elementary identities involving the q-binomial coefficients that one is likely to need in proving q-series identities. No other reference does this so completely." Jet Wimp, SIAM Reviews