Softcover ISBN:  9780821807163 
Product Code:  CBMS/66 
130 pp 
List Price:  $26.00 
Individual Price:  $20.80 
Electronic ISBN:  9781470424268 
Product Code:  CBMS/66.E 
130 pp 
List Price:  $24.00 
Individual Price:  $19.20 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 66; 1986MSC: Primary 11; Secondary 05; 33; 68; 82;
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.ReadershipResearchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra.

Table of Contents

Chapters

Chapter 1. Found Opportunities

Chapter 2. Classical Special Functions and L. J. Rogers

Chapter 3. W. N. Bailey’s Extension of Rogers’s Work

Chapter 4. Constant Terms

Chapter 5. Integrals

Chapter 6. Partitions and $q$Series

Chapter 7. Partitions and Constant Terms

Chapter 8. The Hard Hexagon Model

Chapter 9. Ramanujan

Chapter 10. Computer Algebra

Appendix A. W. Gosper’s Proof that $\lim _{q \to 1^{}}\Gamma _q(x) = \Gamma (x)$

Appendix B. Rogers’s Symmetric Expansion of $\psi (\lambda , \mu , \nu , q, \theta )$

Appendix C. Ismail’s Proof of the $_1\psi _1$Summation and Jacobi’s Triple Product Identity


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

Chapters

Chapter 1. Found Opportunities

Chapter 2. Classical Special Functions and L. J. Rogers

Chapter 3. W. N. Bailey’s Extension of Rogers’s Work

Chapter 4. Constant Terms

Chapter 5. Integrals

Chapter 6. Partitions and $q$Series

Chapter 7. Partitions and Constant Terms

Chapter 8. The Hard Hexagon Model

Chapter 9. Ramanujan

Chapter 10. Computer Algebra

Appendix A. W. Gosper’s Proof that $\lim _{q \to 1^{}}\Gamma _q(x) = \Gamma (x)$

Appendix B. Rogers’s Symmetric Expansion of $\psi (\lambda , \mu , \nu , q, \theta )$

Appendix C. Ismail’s Proof of the $_1\psi _1$Summation and Jacobi’s Triple Product Identity