**CBMS Regional Conference Series in Mathematics**

Volume: 66;
1986;
130 pp;
Softcover

MSC: Primary 11;
Secondary 05; 33; 68; 82

**Print ISBN: 978-0-8218-0716-3
Product Code: CBMS/66**

List Price: $26.00

Individual Price: $20.80

**Electronic ISBN: 978-1-4704-2426-8
Product Code: CBMS/66.E**

List Price: $24.00

Individual Price: $19.20

# \(q\)-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra

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*G. Andrews*

A co-publication of the AMS and CBMS

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

# Table of Contents

## $q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents vii8 free
- Preface xi12 free
- Chapter 1. Found Opportunities 114 free
- Chapter 2. Oassical Special Functions and L. J. Rogers 922
- Chapter 3. W. N. Bailey's Extension of Rogers's Work 2134
- Chapter 4. Constant Terms 3346
- Chapter 5. Integrals 4558
- Chapter 6. Partitions and q-Series 5366
- Chapter 7. Partitions and Constant Terms 6376
- Chapter 8. The Hard Hexagon Model 7386
- Chapter 9. Ramanujan 87100
- Chapter 10. Computer Algebra 95108
- Appendix A. W. Gosper's Proof that lim[sub(q→1)]-Γ[sub(q)](x) = Γ(x) 109122
- Appendix B. Rogers's Symmetric Expansion of ψ(λ,μ,υ,q,θ) 111124
- Appendix C. Ismail's Proof of the [sub(1)]ψ[sub(1)]-Summation and Jaeobi's Triple Product Identity 115128
- References 117130
- Back Cover Back Cover1144