This book integrates recent developments and related applications in \(q\)-series with a historical development of the field, focusing on major breakthroughs and the author's own research interests. The author develops both the important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory. He concludes with applications to physics and computer algebra and a section on results closely related to Ramanujan's "Lost Notebook."

With its wide range of applications, the book will interest researchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra. It is understandable to even a beginning graduate student in mathematics who has a background in advanced calculus and some mathematical maturity.

Readership

Researchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra.

Table of Contents

• Found opportunities
• Classical special functions and L. J. Rogers
• W. N. Bailey's extension of Roger's work
• Constant terms
• Integrals
• Partitions and \(q\)-series
• Partitions and constant terms
• The hard hexagon model
• Ramanujan
• Computer algebra
• Appendix A. W. Gosper's Proof that \(\lim _{q\rightarrow 1^-}\Gamma _q(x)=\Gamma (x)\)
• Appendix B. Roger's symmetric expansion of \(\psi (\lambda , \mu ,\nu , q, \theta )\)
• Appendix C. Ismail's proof of the \(_1\psi _1\)-summation and Jocobi's triple product identity
• References