Topics and Methods in q-Series

The book provides a comprehensive introduction to the many aspects of the subject of basic hypergeometric series. The book essentially assumes no prior knowledge but eventually provides a comprehensive introduction to many important topics. After developing a treatment of historically important topics such as the q-binomial theorem, Heine's transformation, the Jacobi triple product identity, Ramanujan's 1-psi-1 summation formula, Bailey's 6-psi-6 summation formula and the Rogers-Fine identity, the book goes on to delve more deeply into important topics such as Bailey- and WP-Bailey pairs and chains, q-continued fractions, and mock theta functions. There are also chapters on other topics such as Lambert series and combinatorial proofs of basic hypergeometric identities.

The book could serve as a textbook for the subject at the graduate level and as a textbook for a topic course at the undergraduate level (earlier chapters). It could also serve as a reference work for researchers in the area.
Contents: ForewordIntroductionBasic NotationThe q-Binomial TheoremHeine's TransformationOther Important Basic Hypergeometric TransformationsThe Jacobi Triple Product IdentityRamanujan's 1ψ1 Summation FormulaBailey's 6ψ6 SummationThe Rogers–Fine IdentityBailey PairsBailey ChainsWP-Bailey Pairs and ChainsFurther Results on Bailey/WP-Bailey Pairs and ChainsGaussian PolynomialsBijective Proofs of Basic Hypergeometric Identitiesq-Continued FractionsLambert SeriesMock Theta FunctionsAppendices:Frequently Used TheoremsWP-Bailey ChainsWP-Bailey PairsBailey ChainsBailey PairsMock Theta FunctionsSelected Summation FormulaeBibliographyAuthor IndexSubject Index
Readership: Undergraduate and graduate students.
Keywords:q-Series;Basic Hypergeometric Series;Bailey Pairs;WP-bailey Pairs;Mock Theta Functions;Rogers-Ramanujan Type Identities;q-Continued FractionsReview:Key Features:The book is essentially self-contained, all the pre-requisites are essentially covered in earlier chapters of the bookThere is a comprehensive selection of guided exercises at the end of each chapter, allowing the reader to go deeper into the subject, and permitting the book to be used both as a graduate text book, and an undergraduate text book for a topics courseNo other book that treats the same or nearby subjects is as accessible to a reader as this one, nor does any such book cover the same selection of topics