This updated edition will continue to meet the needs for an authoritative comprehensive analysis of the rapidly growing field of basic hypergeometric series, or q-series. It includes deductive proofs, exercises, and useful appendices. Three new chapters have been added to this edition covering q-series in two and more variables: linear- and bilinear-generating functions for basic orthogonal polynomials; and summation and transformation formulas for elliptic hypergeometric series. In addition, the text and bibliography have been expanded to reflect recent developments. First Edition Hb (1990): 0-521-35049-2
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Book Description
Editorial Reviews
Review
"...the definitive work on the subject. The book is remarkable in many ways....it is clearly and carefully written." SIAM Review
"This is an even better book than the first edition for several reasons: the up-to-date bibliography, the new material, and the opportunity to fix all the known errata...Gasper and Rahman have, once again, done admirably."
MAA Reviews, Warren Johnson, Connecticut College
"The extensive bibliography has been updated to include recent work. At 48 pages, it is almost double the length of the bibliography of the first edition. The authors have succeeded in bringing a vast body of knowledge up to date in this compact, useful an highly readable book."
Shaun Cooper, Mathematical Reviews
"This is an even better book than the first edition for several reasons: the up-to-date bibliography, the new material, and the opportunity to fix all the known errata...Gasper and Rahman have, once again, done admirably."
MAA Reviews, Warren Johnson, Connecticut College
"The extensive bibliography has been updated to include recent work. At 48 pages, it is almost double the length of the bibliography of the first edition. The authors have succeeded in bringing a vast body of knowledge up to date in this compact, useful an highly readable book."
Shaun Cooper, Mathematical Reviews
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. Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its strengths. Chapters 9-11 are new for the second edition. Elsewhere, errata have been corrected, some sections and exercises have been added to reflect recent developments, and the Bibliography has been revised to maintain its comprehensiveness.
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2 of 2 people found the following review helpful:
5.0 out of 5 stars
Solid Reference,
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This review is from: Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications) (Hardcover)
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.
5.0 out of 5 stars
Encyclopedic,
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This review is from: Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications) (Hardcover)
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.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
Our main objective in this chapter is to present the definitions and notations for hypergeometric and basic hypergeometric series, and to derive the elementary formulas that form the basis for most of the summation, transformation and expansion formulas, basic integrals, and applications to orthogonal polynomials and to other fields that follow in the subsequent chapters. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
theta hypergeometric series, elliptic hypergeometric series, biorthogonal rational functions, bilateral basic hypergeometric series, double hypergeometric functions, quadratic transformation formula, bilinear generating functions, hypergeonletric series, nonterminating extension, basic hypergeometric functions, basic hvpergeometric series, bilinear sum, terminating balanced, elliptic analogue, constant term identities, linearization formula, mock theta functions, hypergeometric integrals, quintuple product identity, bilateral series, balancing condition, hard hexagon model, triple product identity, multivariable extension, beta integral New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Our main objective in this chapter is to present the definitions and notations for hypergeometric and basic hypergeometric series, and to derive the elementary formulas that form the basis for most of the summation, transformation and expansion formulas, basic integrals, and applications to orthogonal polynomials and to other fields that follow in the subsequent chapters. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
theta hypergeometric series, elliptic hypergeometric series, biorthogonal rational functions, bilateral basic hypergeometric series, double hypergeometric functions, quadratic transformation formula, bilinear generating functions, hypergeonletric series, nonterminating extension, basic hypergeometric functions, basic hvpergeometric series, bilinear sum, terminating balanced, elliptic analogue, constant term identities, linearization formula, mock theta functions, hypergeometric integrals, quintuple product identity, bilateral series, balancing condition, hard hexagon model, triple product identity, multivariable extension, beta integral New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 59
books:
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88
books
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- Special Functions (Encyclopedia of Mathematics and its Applications) by George E. Andrews on 20 pages
- Graph Theory (Cambridge Mathematical Library) by W. T. Tutte in Back Matter (1), Back Matter (2), and Back Matter (3)
- Number Theory (Dover Books on Mathematics) by George E. Andrews on page 146, Back Matter (1), and Back Matter (2)
- Orthogonal Polynomials of Several Variables (Encyclopedia of Mathematics and its Applications) by Charles F. Dunkl in Front Matter, and Back Matter
- Mathematical Constants (Encyclopedia of Mathematics and its Applications) by Steven R. Finch in Front Matter
See all 59 books this book cites
- Special Functions 2000: Current Perspectives and Future Dire (NATO Science Series II: Mathematics, Physics and Chemistry) by Joaquin Bustoz on 8 pages
- Mathematical Essays in Honor of Gian-Carlo Rota (Progress in Mathematics) by Bruce Sagan on page 111, page 128, and page 395
- Development of the Mathematical Ideas of Mykhailo Kravchuk (Krawtchouk) by N. O. Virchenko on page 212, page 229, and page 241
- Mathematics and Computer Science III: Algorithms, Trees, Combinatorics and Probabilities (Trends in Mathematics) (v. 3) by Michael Drmota on page 24, and page 67
- Advances in Combinatorial Methods and Applications to Probability and Statistics (Statistics for Industry and Technology) by N. Balakrishnan on page 462, and page 470
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