Topics And Methods In Q-series

"In addition to presenting such a wonderful sweep of deep and beautiful material, it is very strong pedagogically. It’s very well written, in an accessible and clear style, the material dealt with is effectively motivated and discussed in a sound and rigorous manner, all the proofs are there, and McLaughlin gives the reader a large number of exercises to do along the way, as he travels these paths. Again, the expressions and formulas that pepper the pages of this book are at first sight daunting, but they do yield to persistent pressure. The language of q-series makes for some beautiful poetry." MAA Reviews 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.