Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications Book 96) 2nd Edition by George Gasper (PDF)

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. Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its strengths. The first five chapters cover basic hypergeometric series and integrals, whilst the next five are devoted to applications in various areas including Askey-Wilson integrals and orthogonal polynomials, partitions in number theory, multiple series, orthogonal polynomials in several variables, and generating functions. Chapters 9-11 are new for the second edition, the final chapter containing a simplified version of the main elements of the theta and elliptic hypergeometric series as a natural extension of the single-base q-series. Some sections and exercises have been added to reflect recent developments, and the Bibliography has been revised to maintain its comprehensiveness.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you are looking for q-hypergeometric series this is THE book. On the publisher’s website they give you a sneak-peek of the first chapter which is already wonderfully useful. But remember that in the book there are also many exercises. If you think there’s a formula relating to the q-binomial theorem, say, then check there. It’s also great that they answer questions about partitions into sums of squares, as well as mentioning applications to statistical mechanics and just partition function identities (like Rogers-Ramanujan). Maybe they could play-up the applications to representations of quantum groups such as Uq(sl2) if there are some. But on the whole this book is wonderful, and wonderfully complete.

⭐A solid reference on the subject. Material on generalized hypergeometric functions (starting with Gauss’ hypergeometric function) is presented followed by the q analogy’s. The material is advanced and is well written with a tight and readable typeface. The introduction to q series will satisfy the beginner. The list of about 500 references covering the entire subject is worth the price alone.Lorenz H. Menke, Jr.

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